. This operation changes exactly r - l + 1 array elements. \n\n\n\nExpression means applying bitwise xor operation to numbers x and y. The given operation exists in all modern programming languages, for example in language C++ and Java it is marked as \"^\", in Pascal — as \"xor\".\n\nYou've got a list of m operations of the indicated type. Your task is to perform all given operations, for each sum query you should print the result you get.\n\nInput\n\nThe first line contains integer n (1 ≤ n ≤ 105) — the size of the array. The second line contains space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 106) — the original array.\n\nThe third line contains integer m (1 ≤ m ≤ 5·104) — the number of operations with the array. The i-th of the following m lines first contains an integer ti (1 ≤ ti ≤ 2) — the type of the i-th query. If ti = 1, then this is the query of the sum, if ti = 2, then this is the query to change array elements. If the i-th operation is of type 1, then next follow two integers li, ri (1 ≤ li ≤ ri ≤ n). If the i-th operation is of type 2, then next follow three integers li, ri, xi (1 ≤ li ≤ ri ≤ n, 1 ≤ xi ≤ 106). The numbers on the lines are separated by single spaces.\n\nOutput\n\nFor each query of type 1 print in a single line the sum of numbers on the given segment. Print the answers to the queries in the order in which the queries go in the input.\n\nPlease, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams, or the %I64d specifier.\n\nExamples\n\nInput\n\n5\n4 10 3 13 7\n8\n1 2 4\n2 1 3 3\n1 2 4\n1 3 3\n2 2 5 5\n1 1 5\n2 1 2 10\n1 2 3\n\n\nOutput\n\n26\n22\n0\n34\n11\n\n\nInput\n\n6\n4 7 4 0 7 3\n5\n2 2 3 8\n1 1 5\n2 3 5 1\n2 4 5 6\n1 2 3\n\n\nOutput\n\n38\n28"}}},{"rowIdx":60,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2\\n2\\n1 2\\n2 1\\n4\\n2 1 4 1\\n2 4 1 4\",\n \"2\\n2\\n1 2\\n2 1\\n4\\n2 1 4 1\\n2 5 1 4\",\n \"2\\n2\\n2 2\\n2 1\\n4\\n2 1 4 1\\n4 4 1 4\",\n \"2\\n2\\n1 2\\n2 1\\n4\\n1 1 4 1\\n2 5 1 4\",\n \"2\\n2\\n2 2\\n2 1\\n4\\n2 1 4 1\\n2 4 1 4\",\n \"2\\n2\\n2 2\\n2 1\\n4\\n2 1 4 1\\n1 4 1 4\",\n \"2\\n2\\n1 2\\n2 1\\n4\\n1 1 1 1\\n2 5 1 4\",\n \"2\\n2\\n2 2\\n2 1\\n3\\n2 1 4 1\\n1 4 1 4\",\n \"2\\n2\\n2 2\\n2 1\\n4\\n2 1 2 1\\n4 4 1 4\",\n \"2\\n2\\n2 2\\n2 1\\n3\\n0 1 4 1\\n1 4 1 4\",\n \"2\\n2\\n2 2\\n2 2\\n3\\n0 1 4 1\\n1 4 1 4\",\n \"2\\n1\\n2 2\\n2 1\\n4\\n2 1 4 1\\n2 4 1 4\",\n \"2\\n2\\n1 2\\n2 1\\n4\\n1 1 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He likes watching different kinds of movies: from drama movies to comedy movies, from teen movies to horror movies. He is planning to visit cinema this weekend, but he's not sure which movie he should watch.\nThere are n movies to watch during this weekend. Each movie can be characterized by two integers Li and Ri, denoting the length and the rating of the corresponding movie. Egor wants to watch exactly one movie with the maximal value of Li × Ri. If there are several such movies, he would pick a one with the maximal Ri among them. If there is still a tie, he would pick the one with the minimal index among them.\nYour task is to help Egor to pick a movie to watch during this weekend.\n\nInput\nThe first line of the input contains an integer T denoting the number of test cases.\nThe first line of the test case description contains an integer n.\nThe second line of the test case description contains n integers L1, L2, ...,Ln. The following line contains n integers R1, R2, ..., Rn.\n\nOutput\nFor each test case, output a single integer i denoting the index of the movie that Egor should watch during this weekend. Note that we follow 1-based indexing.\n\nConstraints\n\n1 ≤ T ≤ 5\n1 ≤ n ≤ 100\n1 ≤ Li, Ri ≤ 100\n\n\nExample\nInput:\n2\n2\n1 2\n2 1\n4\n2 1 4 1\n2 4 1 4\n\nOutput:\n1\n2\n\nExplanation\nIn the first example case, both films have the same value of L × R, but the first film has a better rating.\nIn the second example case, the second and the fourth movies are equally good, but the second movie has a smaller index."}}},{"rowIdx":61,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"6\\n382253568 723152896 37802240 379425024 404894720 471526144\",\n \"4\\n5 6 8 10\",\n \"3\\n8 12 40\",\n \"6\\n382253568 723152896 37802240 379425024 590201381 471526144\",\n \"3\\n10 12 40\",\n \"3\\n16 36 16\",\n \"4\\n5 6 13 10\",\n \"6\\n382253568 723152896 32183854 379425024 590201381 471526144\",\n \"4\\n5 6 22 10\",\n \"3\\n10 12 27\",\n \"6\\n348324507 723152896 32183854 379425024 590201381 471526144\",\n \"4\\n5 6 24 10\",\n \"3\\n10 12 31\",\n \"6\\n348324507 1154626501 32183854 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integer X on the blackboard by X divided by 2.\n\n\n\nFind the maximum possible number of operations that Snuke can perform.\n\nConstraints\n\n* 1 \\leq N \\leq 200\n* 1 \\leq A_i \\leq 10^9\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nA_1 A_2 ... A_N\n\n\nOutput\n\nPrint the maximum possible number of operations that Snuke can perform.\n\nExamples\n\nInput\n\n3\n8 12 40\n\n\nOutput\n\n2\n\n\nInput\n\n4\n5 6 8 10\n\n\nOutput\n\n0\n\n\nInput\n\n6\n382253568 723152896 37802240 379425024 404894720 471526144\n\n\nOutput\n\n8"}}},{"rowIdx":62,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2\\n4\\nbbcb\\naada\\naada\\n3\\nabc\\nbbb\\nbbb\\n\",\n \"9\\n5\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbbcb\\naada\\naada\\n5\\nabc\\nbbb\\nbbb\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbcbb\\naada\\naada\\n2\\nabc\\nbbb\\nbbb\\n\",\n \"9\\n5\\nbcdbbcc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbbcb\\naaad\\naada\\n5\\nabc\\nbbb\\nbbb\\n\",\n \"2\\n6\\nbbcb\\naada\\naada\\n1\\nabc\\nbbb\\nbbb\\n\",\n \"9\\n13\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n5\\nbcdbbcc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\naaaedde\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\ncbcbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n2\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n5\\nbcdbbcc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\nbcdabcbebbcedcddcadaabaaeacd\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nccbca\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\naaaedde\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\ncbcbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n2\\nb\\na\\na\\n1\\na\\na\\na\\n11\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n6\\nccbbb\\naaabc\\nccbca\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\naaaedde\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n8\\ncbcbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n2\\nb\\na\\na\\n1\\na\\na\\na\\n11\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n6\\nbcdbbcc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\nbcdabcbebbcedcddcadaabaaeacd\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n6\\nbbbcc\\naaabc\\nccbca\\n3\\nccbcccbacbbbbbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n6\\nbcdbbbc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacacccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nccbca\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n3\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\ncccbdcb\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\ncbcbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n7\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n5\\nbcdbbcc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nccbca\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncccbcdc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nccbca\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n6\\nbcdbbcc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\nbcdabcbebbcedcddcadaabaaeacd\\nddbacaaabdaeedaacbabebccebbd\\n9\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncdcbccc\\n3\\nccbcb\\ncbaaa\\nccbaa\\n6\\nbbbcc\\naaabc\\nccbca\\n3\\nccbcccbacbbbbbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n6\\nbcdbbbc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\nbcdabcbebbcedcddcadaabaaeacd\\nddbacaaabdaeedaacbabebccebbd\\n7\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacacccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n6\\nbcdbbbc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naabbc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacacccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbbcb\\naada\\ndaaa\\n5\\nbac\\nbbb\\nbbb\\n\",\n \"9\\n16\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n3\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\ncccbdcb\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n7\\ncbcbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbcbb\\naada\\naada\\n3\\naac\\nbbb\\nbcb\\n\",\n \"2\\n4\\nbbcb\\naada\\naada\\n1\\nabc\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbbcb\\naada\\naada\\n2\\nabc\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbbcb\\naada\\naada\\n1\\n`bc\\nbbb\\nbbb\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\ncbcbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbcbb\\naada\\naada\\n3\\nabc\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbcbb\\naada\\naada\\n2\\nbbc\\nbbb\\nbbb\\n\",\n \"9\\n10\\nbcdbccc\\naaaedde\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\ncbcbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbbcb\\naada\\naada\\n3\\ncba\\nbbb\\nbbb\\n\",\n \"2\\n6\\nbcbb\\naada\\naada\\n1\\nabc\\nbbb\\nbbb\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbcbb\\naada\\naad`\\n2\\nbbc\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbbcb\\naada\\nabda\\n3\\ncba\\nbbb\\nbbb\\n\",\n \"9\\n5\\nbcdbbcc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\nbcdabcbebbcedcddcadaabaaeacd\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbbcb\\naada\\nabda\\n3\\ncba\\nbcb\\nbbb\\n\",\n \"2\\n4\\nbbcb\\naada\\nabda\\n3\\ncba\\nbcb\\nbbc\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n6\\nccbbb\\naaabc\\nccbca\\n3\\nccbcccbacbbbbbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n6\\nbcdbbbc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\nbcdabcbebbcedcddcadaabaaeacd\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbbcb\\nadaa\\nabda\\n3\\ncba\\nbcb\\nbbc\\n\",\n \"9\\n6\\nbcdbbbc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\nbcdabcbebbcedcddcadaabaaeacd\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacacccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n6\\nbcdbbbc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacccc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacacccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbcbb\\naada\\nadaa\\n3\\nabc\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbbcb\\naada\\naada\\n5\\nbac\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbcbb\\naada\\naada\\n2\\nacc\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbcbb\\naada\\naada\\n3\\naac\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbcbb\\naaad\\naada\\n5\\nabc\\nbbb\\nbbb\\n\",\n \"2\\n6\\nbbcb\\naada\\naada\\n1\\nabd\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbbcb\\naada\\naada\\n3\\ncba\\nbba\\nbbb\\n\",\n \"2\\n4\\nacbb\\naada\\naad`\\n2\\nbbc\\nbbb\\nbbb\\n\",\n \"9\\n10\\nbcdbccc\\naaaedde\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\ncbcbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbacbacbcccb\\n2\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbbcb\\naada\\nabda\\n3\\ndba\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbbcb\\naada\\nabda\\n3\\ncba\\nbcc\\nbbc\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n6\\nccbbb\\naaabc\\nccbca\\n3\\nccbcccbacbbbbbcccb\\nbbabcccbacaaccbaac\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"9\\n6\\nbcdbbbc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\nbcdabcbebbcedcddcadaabaaeacd\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccadcc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\ncbbaa\\n4\\nccbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccb`caaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbbbc\\nadaa\\nabda\\n3\\ncba\\nbcb\\nbbc\\n\",\n \"2\\n4\\nbcbb\\naada\\naaad\\n3\\nabc\\nbbb\\nbbb\\n\",\n \"9\\n10\\nbcdbccc\\nad`edae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabacecbe\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\naaabc\\nccbca\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n1\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nbcbb\\naada\\naada\\n2\\ncac\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbcbb\\naaad\\naada\\n3\\nabc\\nbbb\\nbbb\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedbb\\ncccacdc\\ncdcbccc\\n3\\nccacb\\ncbaaa\\nccbaa\\n7\\ncbbbb\\naaabc\\nacbcc\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\",\n \"2\\n4\\nacbb\\naada\\naad`\\n3\\nbbc\\nbbb\\nbbb\\n\",\n \"2\\n4\\nbbcb\\nadaa\\nabda\\n3\\ndba\\nbbb\\nbbb\\n\",\n \"9\\n10\\nbcdbccc\\nadaedae\\neecdaca\\n5\\ndbeedcbcbaccdddbdcbcabbcecae\\ndcaeaabaadacddcdecbbebcbadcb\\nddbacaaabdaeedaacbabebccebbd\\n5\\nbdbedab\\ncccacdc\\ncccbcdc\\n3\\nccacb\\ncbaaa\\nccbaa\\n4\\nccbbb\\nabaac\\nccbca\\n3\\nccbcccbacbbabbcccb\\nbbabcccbacaaccbaab\\nbcccabcbabbacbcccb\\n26\\nb\\na\\na\\n2\\na\\na\\na\\n7\\nfffbaegccd\\naaagebfccd\\naaagebfccd\\n\"\n ],\n \"outputs\": [\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nabcde\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nabcde\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\ncabd\\nNO\\n\",\n \"YES\\nbadcef\\nNO\\n\",\n \"YES\\nabcdefghijklm\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcde\\nYES\\nacedb\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nba\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcde\\nYES\\nabdce\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\nacbd\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nba\\nYES\\na\\nYES\\negcdbafhijk\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\nacbdef\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbadefgh\\nYES\\nacb\\nYES\\nba\\nYES\\na\\nYES\\negcdbafhijk\\n\",\n \"YES\\nabcdef\\nYES\\nabdce\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\nabcdef\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdef\\nYES\\nacedb\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\nacbd\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncba\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nacbdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbadefg\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcde\\nYES\\nacedb\\nYES\\nbceda\\nNO\\nYES\\nacbd\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nNO\\nYES\\nabc\\nYES\\nacbd\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdef\\nYES\\nabdce\\nYES\\nbcedafghi\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nbac\\nYES\\nabcdef\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdef\\nYES\\nabdce\\nYES\\nbcedafg\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdef\\nYES\\nacedb\\nYES\\nbceda\\nNO\\nYES\\nbcad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcd\\nNO\\n\",\n \"YES\\nabcdefghijklmnop\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncba\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nacbdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbadefg\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"NO\\nYES\\nbac\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"NO\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nabcde\\nYES\\nabdce\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\nacbdef\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdef\\nYES\\nabdce\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nabcdef\\nYES\\nabdce\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdef\\nYES\\nacedb\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\ncabd\\nNO\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nbadcef\\nNO\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbad\\nYES\\nacb\\nYES\\nba\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nbadc\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\nacbdef\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"YES\\nabcdef\\nYES\\nabdce\\nYES\\nbceda\\nNO\\nYES\\ncbad\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"NO\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\nacbd\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\na\\nYES\\negcdbaf\\n\",\n \"NO\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nYES\\nbceda\\nYES\\nabc\\nYES\\ncbadefg\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\",\n \"NO\\nNO\\n\",\n \"NO\\nNO\\n\",\n \"YES\\nabcdefghij\\nYES\\nacedb\\nNO\\nYES\\nabc\\nYES\\nacbd\\nYES\\nacb\\nYES\\nbacdefghijklmnopqrstuvwxyz\\nYES\\nab\\nYES\\negcdbaf\\n\"\n ]\n}"},"problem":{"kind":"string","value":"Vasya owns three strings s , a and b, each of them consists only of first k Latin letters.\n\nLet a template be such a string of length k that each of the first k Latin letters appears in it exactly once (thus there are k! distinct templates). Application of template p to the string s is the replacement of each character in string s with p_i, i is the index of this letter in the alphabet. For example, applying template \"bdca\" to a string \"aabccd\" yields string \"bbdcca\".\n\nVasya wants to know if there exists such a template which yields a string lexicographically greater than or equal to string a and lexicographically less than or equal to string b after applying it to s.\n\nIf there exist multiple suitable templates, print any of them.\n\nString a is lexicographically less than string b if there is some i (1 ≤ i ≤ n) that a_i < b_i and for any j (1 ≤ j < i) a_j = b_j.\n\nYou are required to answer t testcases independently.\n\nInput\n\nThe first line contains a single integer t (1 ≤ t ≤ 10^6) — the number of testcases.\n\nIn hacks you can only use t = 1.\n\nEach of the next t lines contains the description of the testcase in the following form:\n\nThe first line of the testcase contains a single integer k (1 ≤ k ≤ 26) — the length of the template.\n\nThe second line of the testcase contains the string s (1 ≤ |s| ≤ 10^6).\n\nThe third line of the testcase contains the string a.\n\nThe fourth line of the testcase contains the string b.\n\nStrings s, a and b have the same length (|s| = |a| = |b|) and consist only of the first k Latin letters, all letters are lowercase.\n\nIt is guaranteed that string a is lexicographically less than or equal to string b.\n\nIt is also guaranteed that the total length of strings over all testcase won't exceed 3 ⋅ 10^6.\n\nOutput\n\nPrint the answers to all testcases in the following form:\n\nIf there exists no suitable template then print \"NO\" in the first line.\n\nOtherwise print \"YES\" in the first line and the template itself in the second line (k lowercase letters, each of the first k Latin letters should appear exactly once).\n\nIf there exist multiple suitable templates, print any of them.\n\nExample\n\nInput\n\n2\n4\nbbcb\naada\naada\n3\nabc\nbbb\nbbb\n\n\nOutput\n\nYES\nbadc\nNO"}}},{"rowIdx":63,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2\\n1\\n2\\n\\nSAMPLE\",\n \"2\\n2\\n2\\n\\nSAMPLE\",\n \"2\\n4\\n2\\n\\nSAMPLE\",\n \"2\\n4\\n1\\n\\nSALPLE\",\n \"2\\n7\\n1\\n\\nSALPLE\",\n \"2\\n6\\n1\\n\\nSALPLE\",\n \"2\\n5\\n1\\n\\nTALPLE\",\n \"2\\n10\\n1\\n\\nTALLPD\",\n \"2\\n3\\n1\\n\\nTALLPD\",\n \"2\\n1\\n2\\n\\nSAMPKE\",\n \"2\\n6\\n2\\n\\nSAMPLE\",\n \"2\\n13\\n1\\n\\nSALPLE\",\n \"2\\n1\\n1\\n\\nTALPLE\",\n \"2\\n10\\n2\\n\\nTALLPD\",\n \"2\\n2\\n3\\n\\nSALPLE\",\n \"2\\n2\\n1\\n\\nTALPLE\",\n \"2\\n3\\n2\\n\\nTALLPD\",\n \"2\\n1\\n4\\n\\nSAMPKD\",\n \"2\\n5\\n2\\n\\nEPMLAT\",\n \"2\\n1\\n6\\n\\nSAMPKD\",\n \"2\\n8\\n2\\n\\nRAMPLE\",\n \"2\\n15\\n2\\n\\nTALLPD\",\n \"2\\n15\\n4\\n\\nTALLPD\",\n \"2\\n15\\n6\\n\\nTALLPD\",\n \"2\\n11\\n2\\n\\nSAMQLD\",\n \"2\\n5\\n4\\n\\nDPLLAT\",\n \"2\\n11\\n3\\n\\nSMAQLD\",\n \"2\\n3\\n3\\n\\nAPSKEL\",\n \"2\\n11\\n1\\n\\nSOAQLD\",\n \"2\\n4\\n3\\n\\nAPLKES\",\n \"2\\n1\\n3\\n\\nSAMPLE\",\n \"2\\n10\\n3\\n\\nTALLPD\",\n \"2\\n20\\n2\\n\\nRAMPLE\",\n \"2\\n2\\n6\\n\\nSAMPKD\",\n \"2\\n29\\n2\\n\\nTALLPD\",\n \"2\\n16\\n2\\n\\nRAMPLD\",\n \"2\\n6\\n4\\n\\nTALLPD\",\n \"2\\n15\\n12\\n\\nTALLPD\",\n \"2\\n8\\n4\\n\\nSAMQLD\",\n \"2\\n15\\n11\\n\\nDPLLAT\",\n \"2\\n16\\n4\\n\\nDPLLAT\",\n \"2\\n11\\n4\\n\\nSMAQLD\",\n \"2\\n11\\n5\\n\\nSNAQLD\",\n \"2\\n1\\n5\\n\\nSAMPLE\",\n \"2\\n6\\n3\\n\\nSALPLE\",\n \"2\\n7\\n2\\n\\nTLALPD\",\n \"2\\n13\\n3\\n\\nTALLPD\",\n \"2\\n49\\n2\\n\\nTALLPD\",\n \"2\\n9\\n2\\n\\nRAMPLD\",\n \"2\\n3\\n4\\n\\nTALLPD\",\n \"2\\n15\\n14\\n\\nTALLPD\",\n \"2\\n15\\n19\\n\\nDPLLAT\",\n \"2\\n10\\n4\\n\\nSMAQLD\",\n \"2\\n5\\n3\\n\\nDPLTAL\",\n \"2\\n20\\n5\\n\\nSNAQLD\",\n \"2\\n2\\n4\\n\\nAPLEKS\",\n \"2\\n13\\n4\\n\\nTALLPD\",\n \"2\\n27\\n2\\n\\nRANPLE\",\n \"2\\n3\\n8\\n\\nTALLPD\",\n \"2\\n25\\n14\\n\\nTALLPD\",\n \"2\\n7\\n19\\n\\nDPLLAT\",\n \"2\\n18\\n2\\n\\nDLQMAS\",\n \"2\\n20\\n8\\n\\nSNAQLD\",\n \"2\\n7\\n3\\n\\nDPLALT\",\n \"2\\n7\\n4\\n\\nEOMLAT\",\n \"2\\n49\\n3\\n\\nSALLPD\",\n \"2\\n50\\n14\\n\\nTALLPD\",\n \"2\\n3\\n6\\n\\nAPLEKS\",\n \"2\\n8\\n1\\n\\nLTAPLE\",\n \"2\\n5\\n7\\n\\nDPLLAS\",\n \"2\\n49\\n1\\n\\nSALLPD\",\n \"2\\n7\\n18\\n\\nTALLPD\",\n \"2\\n20\\n6\\n\\nRNAQLD\",\n \"2\\n5\\n14\\n\\nDPLLAS\",\n \"2\\n19\\n4\\n\\nTALMOD\",\n \"2\\n4\\n6\\n\\nSALPEJ\",\n \"2\\n50\\n10\\n\\nTAKLPD\",\n \"2\\n7\\n16\\n\\nTALLPD\",\n \"2\\n13\\n2\\n\\nDRQAOK\",\n \"2\\n3\\n12\\n\\nSKELPA\",\n \"2\\n10\\n14\\n\\nDPLLAS\",\n \"2\\n7\\n8\\n\\nCOMLAT\",\n \"2\\n2\\n5\\n\\nTELOKA\",\n \"2\\n27\\n10\\n\\nTAKLPD\",\n \"2\\n31\\n2\\n\\nDAQMKS\",\n \"2\\n20\\n7\\n\\nRNAQKD\",\n \"2\\n4\\n9\\n\\nSPLAEJ\",\n \"2\\n4\\n4\\n\\nSMAQLD\",\n \"2\\n20\\n10\\n\\nRNAQKD\",\n \"2\\n24\\n2\\n\\nROASMD\",\n \"2\\n6\\n14\\n\\nDPKLAS\",\n \"2\\n2\\n8\\n\\nTEMOKA\",\n \"2\\n31\\n3\\n\\nD@QMKS\",\n \"2\\n20\\n4\\n\\nRNAQKD\",\n \"2\\n4\\n12\\n\\nTEKLPA\",\n \"2\\n14\\n2\\n\\nDLAMPS\",\n \"2\\n26\\n10\\n\\nCPLKAT\",\n \"2\\n47\\n3\\n\\nD@QMKS\",\n \"2\\n4\\n5\\n\\nBPSLEK\",\n \"2\\n6\\n13\\n\\nDOKLAS\",\n \"2\\n2\\n9\\n\\nTAMOKE\"\n ],\n \"outputs\": [\n \"1.000000\\n4.000000\",\n \"4.000000\\n4.000000\\n\",\n \"10.500000\\n4.000000\\n\",\n \"10.500000\\n1.000000\\n\",\n \"20.428571\\n1.000000\\n\",\n \"17.111111\\n1.000000\\n\",\n \"13.800000\\n1.000000\\n\",\n \"30.400000\\n1.000000\\n\",\n \"7.222222\\n1.000000\\n\",\n \"1.000000\\n4.000000\\n\",\n \"17.111111\\n4.000000\\n\",\n \"40.384615\\n1.000000\\n\",\n \"1.000000\\n1.000000\\n\",\n \"30.400000\\n4.000000\\n\",\n \"4.000000\\n7.222222\\n\",\n \"4.000000\\n1.000000\\n\",\n \"7.222222\\n4.000000\\n\",\n \"1.000000\\n10.500000\\n\",\n \"13.800000\\n4.000000\\n\",\n \"1.000000\\n17.111111\\n\",\n \"23.750000\\n4.000000\\n\",\n \"47.044444\\n4.000000\\n\",\n \"47.044444\\n10.500000\\n\",\n \"47.044444\\n17.111111\\n\",\n \"33.727273\\n4.000000\\n\",\n \"13.800000\\n10.500000\\n\",\n \"33.727273\\n7.222222\\n\",\n \"7.222222\\n7.222222\\n\",\n \"33.727273\\n1.000000\\n\",\n \"10.500000\\n7.222222\\n\",\n \"1.000000\\n7.222222\\n\",\n \"30.400000\\n7.222222\\n\",\n \"63.700000\\n4.000000\\n\",\n \"4.000000\\n17.111111\\n\",\n \"93.689655\\n4.000000\\n\",\n \"50.375000\\n4.000000\\n\",\n \"17.111111\\n10.500000\\n\",\n \"47.044444\\n37.055556\\n\",\n \"23.750000\\n10.500000\\n\",\n \"47.044444\\n33.727273\\n\",\n \"50.375000\\n10.500000\\n\",\n \"33.727273\\n10.500000\\n\",\n \"33.727273\\n13.800000\\n\",\n \"1.000000\\n13.800000\\n\",\n \"17.111111\\n7.222222\\n\",\n \"20.428571\\n4.000000\\n\",\n \"40.384615\\n7.222222\\n\",\n \"160.346939\\n4.000000\\n\",\n \"27.074074\\n4.000000\\n\",\n \"7.222222\\n10.500000\\n\",\n \"47.044444\\n43.714286\\n\",\n \"47.044444\\n60.368421\\n\",\n \"30.400000\\n10.500000\\n\",\n \"13.800000\\n7.222222\\n\",\n \"63.700000\\n13.800000\\n\",\n \"4.000000\\n10.500000\\n\",\n \"40.384615\\n10.500000\\n\",\n \"87.024691\\n4.000000\\n\",\n \"7.222222\\n23.750000\\n\",\n \"80.360000\\n43.714286\\n\",\n \"20.428571\\n60.368421\\n\",\n \"57.037037\\n4.000000\\n\",\n \"63.700000\\n23.750000\\n\",\n \"20.428571\\n7.222222\\n\",\n \"20.428571\\n10.500000\\n\",\n \"160.346939\\n7.222222\\n\",\n \"163.680000\\n43.714286\\n\",\n \"7.222222\\n17.111111\\n\",\n \"23.750000\\n1.000000\\n\",\n \"13.800000\\n20.428571\\n\",\n \"160.346939\\n1.000000\\n\",\n \"20.428571\\n57.037037\\n\",\n \"63.700000\\n17.111111\\n\",\n \"13.800000\\n43.714286\\n\",\n \"60.368421\\n10.500000\\n\",\n \"10.500000\\n17.111111\\n\",\n \"163.680000\\n30.400000\\n\",\n \"20.428571\\n50.375000\\n\",\n \"40.384615\\n4.000000\\n\",\n \"7.222222\\n37.055556\\n\",\n \"30.400000\\n43.714286\\n\",\n \"20.428571\\n23.750000\\n\",\n \"4.000000\\n13.800000\\n\",\n \"87.024691\\n30.400000\\n\",\n \"100.354839\\n4.000000\\n\",\n \"63.700000\\n20.428571\\n\",\n \"10.500000\\n27.074074\\n\",\n \"10.500000\\n10.500000\\n\",\n \"63.700000\\n30.400000\\n\",\n \"77.027778\\n4.000000\\n\",\n \"17.111111\\n43.714286\\n\",\n \"4.000000\\n23.750000\\n\",\n \"100.354839\\n7.222222\\n\",\n \"63.700000\\n10.500000\\n\",\n \"10.500000\\n37.055556\\n\",\n \"43.714286\\n4.000000\\n\",\n \"83.692308\\n30.400000\\n\",\n \"153.680851\\n7.222222\\n\",\n \"10.500000\\n13.800000\\n\",\n \"17.111111\\n40.384615\\n\",\n \"4.000000\\n27.074074\\n\"\n ]\n}"},"problem":{"kind":"string","value":"Daenerys Targaryen has set her eyes on The kingdom of Dorne. Dornishmen, known for their strong sense of national identity, have refused to surrender to the whims of Daenerys. Fearing the imminent attack on their kingdom and knowing their strength as Spearmen, they have devised a battle plan which they think will give them an upperhand. They have divided the battlefield as an N*N chessboard grid and have put one soldier on each of the square in the grid.\n\nOn seeing this master plan Danerys has decided to send in her dragon Drogon first. Drogon is supposed to first kill one soldier on one of the square on the chessboard grid and land on it. Then, using fire, it will kill all soldiers in horizontal, vertical and diagonal squares from end to end relative to the square it is standing on (just like a 'Queen' piece but unlike Queen, it will kill all men in one go in all the squares a Queen can cover if standing on the particular square) and then will return back. Daenerys is very happy with the strategy but she has a small problem. Drogon, being a dragon, can not be tamed and hence will uniformly at random choose any square for its landing. Daenerys, given N, wants to know what is the expected number of soldiers Drogon will kill.\n\nCan you help Daenerys to calculate the expected number if soldiers Drogon will kill.\n\nInput\n\nThe first line contains T, the number of test cases.\n\nEach test case contains only one integer N denoting the dimension of the N*N chessboard grid.\n\nOutput\n\nThe output should contain 1 real number per test case denoting the expected number of soldiers Drogon will kill for the given sized grid.\n\nConstraints\n\n1 ≤ T ≤ 10^6\n\n1 ≤ N ≤ 10^5\n\nNote\n\nOutput value should be within 1e-6 of the correct value(Output should be printed to exactly six places of decimal precision).\n\nPartial marks are awarded if any test case passes.\n\nSAMPLE INPUT\n2\n1\n2\n\nSAMPLE OUTPUT\n1.000000\n4.000000\n\nExplanation\n\nIn first test case, grid is 1*1, and hence Drogon will kill the only soldier present on the single square.\n\nIn second test case, grid is 2*2. Whichever be the square Drogon lands by killing the soldier, it can kill all other soldiers (as they are covered by its 'Queen like' fire attack)."}}},{"rowIdx":64,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"8\\nfced\\nxyz\\nr\\ndabcef\\naz\\naa\\nbad\\nbabc\\n\",\n \"1\\nshh\\n\",\n \"1\\nsoo\\n\",\n \"1\\naaaab\\n\",\n \"1\\nabcdefghijkm\\n\",\n \"1\\nabczz\\n\",\n \"1\\naadde\\n\",\n \"1\\ndaa\\n\",\n \"1\\nefhi\\n\",\n \"2\\nrtsuvwyz\\nzyxwvutsrqponmlkjihgfedcbaaa\\n\",\n \"1\\nabbdf\\n\",\n \"69\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\n\",\n \"1\\nsooo\\n\",\n \"1\\nshhhh\\n\",\n 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\"2\\nzyxwvutsrqponmlkjihgfedcba\\nzyxwvutsrqponmljjihgfedcba\\n\",\n \"1\\nsohhrt\\n\",\n \"1\\nshpi\\n\",\n \"1\\nd\\n\",\n \"8\\ndecf\\nxyz\\nr\\ndabcef\\naz\\naa\\naad\\nbabc\\n\",\n \"1\\ntih\\n\",\n \"1\\nons\\n\",\n \"1\\nebcdaeghijkm\\n\",\n \"1\\nbbzcz\\n\",\n \"1\\naaddf\\n\",\n \"1\\nfhhe\\n\",\n \"2\\nzywwustr\\nzyxvvutsrqponmlkjihgfedcbaaa\\n\",\n \"1\\nfebaa\\n\",\n \"69\\nabc\\nabc\\nabc\\nabc\\nabc\\ncba\\nabc\\nabc\\nabc\\nacb\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nbbc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\nabc\\n\",\n \"1\\noson\\n\",\n \"1\\nhhiis\\n\",\n \"1\\nhkuriosh\\n\",\n \"1\\nohrir\\n\",\n \"1\\nccfd\\n\",\n \"1\\naecfb\\n\",\n \"1\\najfcdsukafds\\n\",\n \"1\\nadce\\n\",\n \"1\\nzcbyxa\\n\",\n 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\"YES\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\nNO\\n\",\n \"NO\\n\",\n \"YES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\nNO\\nNO\\nYES\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nYES\\nYES\\nNO\\nNO\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\nYES\\nYES\\nNO\\nNO\\nNO\\nNO\\nNO\\nNO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"YES\\nYES\\n\",\n \"NO\\n\",\n \"NO\\n\",\n \"YES\\n\",\n \"No\\n\",\n \"No\\nNo\\n\",\n \"Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\n\",\n \"No\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\",\n \"Yes\\nNo\\n\",\n \"Yes\\n\",\n \"Yes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\n\",\n \"No\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\nNo\\n\",\n \"No\\n\",\n \"Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\nNo\\nNo\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nNo\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\nNo\\nNo\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"Yes\\nNo\\n\",\n \"No\\n\",\n \"No\\n\",\n \"Yes\\n\",\n \"Yes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\nNo\\n\",\n \"No\\n\",\n \"Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"Yes\\nNo\\n\",\n \"No\\n\",\n \"No\\n\",\n \"Yes\\n\",\n \"Yes\\nYes\\nYes\\nYes\\nNo\\nNo\\nNo\\nNo\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\nNo\\n\",\n \"No\\n\",\n \"Yes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nNo\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\nYes\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\",\n \"No\\n\"\n ]\n}"},"problem":{"kind":"string","value":"A string is called diverse if it contains consecutive (adjacent) letters of the Latin alphabet and each letter occurs exactly once. For example, the following strings are diverse: \"fced\", \"xyz\", \"r\" and \"dabcef\". The following string are not diverse: \"az\", \"aa\", \"bad\" and \"babc\". Note that the letters 'a' and 'z' are not adjacent.\n\nFormally, consider positions of all letters in the string in the alphabet. These positions should form contiguous segment, i.e. they should come one by one without any gaps. And all letters in the string should be distinct (duplicates are not allowed).\n\nYou are given a sequence of strings. For each string, if it is diverse, print \"Yes\". Otherwise, print \"No\".\n\nInput\n\nThe first line contains integer n (1 ≤ n ≤ 100), denoting the number of strings to process. The following n lines contains strings, one string per line. Each string contains only lowercase Latin letters, its length is between 1 and 100, inclusive.\n\nOutput\n\nPrint n lines, one line per a string in the input. The line should contain \"Yes\" if the corresponding string is diverse and \"No\" if the corresponding string is not diverse. You can print each letter in any case (upper or lower). For example, \"YeS\", \"no\" and \"yES\" are all acceptable.\n\nExample\n\nInput\n\n\n8\nfced\nxyz\nr\ndabcef\naz\naa\nbad\nbabc\n\n\nOutput\n\n\nYes\nYes\nYes\nYes\nNo\nNo\nNo\nNo"}}},{"rowIdx":65,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2 4\\n5000\\n\",\n \"2 2\\n7\\n\",\n \"3 1\\n9\\n\",\n \"3 3\\n9\\n\",\n \"8934829 12\\n5048272609027744689584230909741172415239400471666476392160572093949157832786399486962245730213411626\\n\",\n \"5893919 9\\n2210309498556502639082865806054288036968702568515503990010345752069086486014544763616785766171083029\\n\",\n \"3286427 3\\n32824120217168867503177075773101487258651027053054498182388625841560564426484376370000468826643786\\n\",\n \"8030623 1\\n7391946705\\n\",\n \"4540993 10\\n5694761289449694169154104450970948644405389630203784854430413891269455104899781759279256470945063996\\n\",\n \"6243073 4\\n54400052247879189148039137626578952762968555544521623972286314204888279306920422704563468161626006\\n\",\n \"999999937 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problem.\n\nExamples\n\nInput\n\n2 2\n7\n\n\nOutput\n\n3\n\n\nInput\n\n3 1\n9\n\n\nOutput\n\n17\n\n\nInput\n\n3 3\n9\n\n\nOutput\n\n0\n\n\nInput\n\n2 4\n5000\n\n\nOutput\n\n8576851\n\nNote\n\nIn the first sample three binominal coefficients divisible by 4 are , and ."}}},{"rowIdx":66,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"1 3\\n0 3\",\n \"5 21600\\n2 14\\n3 22\\n1 3\\n1 10\\n1 9\",\n \"3 7\\n2 0\\n3 2\\n0 3\",\n \"7 57\\n0 25\\n3 10\\n2 4\\n5 15\\n3 22\\n2 14\\n1 15\",\n \"1 3\\n0 0\",\n \"5 21600\\n2 14\\n3 22\\n1 3\\n0 10\\n1 9\",\n \"7 57\\n0 25\\n3 10\\n2 4\\n5 15\\n3 22\\n2 14\\n1 9\",\n \"1 0\\n1 -1\",\n \"7 149\\n0 25\\n3 10\\n2 4\\n2 20\\n3 22\\n2 23\\n1 2\",\n \"7 28\\n0 25\\n3 10\\n2 4\\n5 20\\n3 22\\n2 14\\n1 9\",\n \"7 149\\n0 25\\n3 10\\n0 4\\n0 8\\n3 23\\n1 23\\n1 2\",\n \"7 446\\n0 25\\n3 0\\n4 -1\\n5 0\\n0 22\\n0 14\\n1 6\",\n \"3 5\\n2 0\\n3 2\\n0 3\",\n \"1 3\\n0 -1\",\n \"5 21600\\n2 14\\n3 22\\n1 3\\n0 10\\n1 3\",\n \"3 5\\n2 0\\n3 2\\n1 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Takahashi, who is at his house at time 0, is planning to visit some of these stores.\n\nIt takes Takahashi one unit of time to travel from his house to one of the stores, or between any two stores.\n\nIf Takahashi reaches Store i at time t, he can do shopping there after standing in a queue for a_i \\times t + b_i units of time. (We assume that it takes no time other than waiting.)\n\nAll the stores close at time T + 0.5. If Takahashi is standing in a queue for some store then, he cannot do shopping there.\n\nTakahashi does not do shopping more than once in the same store.\n\nFind the maximum number of times he can do shopping before time T + 0.5.\n\nConstraints\n\n* All values in input are integers.\n* 1 \\leq N \\leq 2 \\times 10^5\n* 0 \\leq a_i \\leq 10^9\n* 0 \\leq b_i \\leq 10^9\n* 0 \\leq T \\leq 10^9\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN T\na_1 b_1\na_2 b_2\n\\vdots\na_N b_N\n\n\nOutput\n\nPrint the answer.\n\nExamples\n\nInput\n\n3 7\n2 0\n3 2\n0 3\n\n\nOutput\n\n2\n\n\nInput\n\n1 3\n0 3\n\n\nOutput\n\n0\n\n\nInput\n\n5 21600\n2 14\n3 22\n1 3\n1 10\n1 9\n\n\nOutput\n\n5\n\n\nInput\n\n7 57\n0 25\n3 10\n2 4\n5 15\n3 22\n2 14\n1 15\n\n\nOutput\n\n3"}}},{"rowIdx":67,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"6\\n1 3\\n2 3\\n3 3\\n4 -3\\n5 -1\\n6 -100\\n\",\n \"3\\n-5 9\\n0 1\\n5 -1\\n\",\n \"14\\n-916171372 999999988\\n-892307487 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]\n}"},"problem":{"kind":"string","value":"Recently the construction of Berland collider has been completed. Collider can be represented as a long narrow tunnel that contains n particles. We associate with collider 1-dimensional coordinate system, going from left to right. For each particle we know its coordinate and velocity at the moment of start of the collider. The velocities of the particles don't change after the launch of the collider. Berland scientists think that the big bang will happen at the first collision of particles, whose velocities differs in directions. Help them to determine how much time elapses after the launch of the collider before the big bang happens.\n\nInput\n\nThe first line contains single integer n (1 ≤ n ≤ 5·105) — amount of particles in the collider. Next n lines contain description of particles. Each particle is described by two integers xi, vi ( - 109 ≤ xi, vi ≤ 109, vi ≠ 0) — coordinate and velocity respectively. All the coordinates are distinct. The particles are listed in order of increasing of coordinates. All the coordinates are in meters, and all the velocities — in meters per second. The negative velocity means that after the start of collider the particle will move to the left, and the positive — that the particle will move to the right.\n\nOutput\n\nIf there will be no big bang, output -1. Otherwise output one number — how much time in seconds elapses after the launch of the collider before the big bang happens. Your answer must have a relative or absolute error less than 10 - 9.\n\nExamples\n\nInput\n\n3\n-5 9\n0 1\n5 -1\n\n\nOutput\n\n1.00000000000000000000\n\n\nInput\n\n6\n1 3\n2 3\n3 3\n4 -3\n5 -1\n6 -100\n\n\nOutput\n\n0.02912621359223301065"}}},{"rowIdx":68,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"5 229 8419\\n1795 95\\n4873 720\\n3149 81\\n6101 2325\\n3674 629\\n\\nSAMPLE\",\n \"5 438 8419\\n1795 95\\n4873 720\\n3149 81\\n6101 2325\\n3674 629\\n\\nSAMPLE\",\n \"5 438 8419\\n1795 21\\n4873 720\\n3149 81\\n6101 2325\\n3674 629\\n\\nELPMAS\",\n \"5 438 8419\\n1795 21\\n4873 720\\n3149 81\\n6101 2325\\n3674 795\\n\\nSLPMAE\",\n \"5 438 8419\\n1795 21\\n4873 720\\n868 81\\n6101 2325\\n3674 795\\n\\nSLPMAE\",\n \"5 438 8419\\n1795 21\\n4873 720\\n868 81\\n6101 2325\\n4262 795\\n\\nEAMPLS\",\n \"5 438 8419\\n1795 21\\n4873 720\\n868 81\\n6101 2325\\n2027 795\\n\\nEAMPLS\",\n \"5 438 8419\\n1795 21\\n4873 720\\n868 81\\n6101 2325\\n2027 1259\\n\\nEAMPLS\",\n \"5 438 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However they need some information about the protection status along the length of the border. The border can be viewed as the real x-axis. Along the axis, Indian army has N checkpoints for lookout. \nWe know that each checkpoint is located at an integer location xi. Each checkpoint must have a fleet of armed men which are responsible for guarding the neighboring areas of the checkpoint and provide military assistance of all kinds. The size of the fleet is based on the location of the checkpoint and how active the region is for terrorist activities.\n\nGiven the number of armed men assigned at the i^th checkpoint, as pi, this information is available for all checkpoints. \nWith the skills of the armed men, it is known that if for the i^th checkpoint, the length on the x axis that they can defend is a closed interval [xi-pi, xi+pi].\nNow, your task is to transport some military items from position S to the end position E on the x-axis.\nInput:\nFirst line of the input contains 3 integers N, S and E. N is the number of checkpoints that the Indian Army has on the border.\nThen N lines follow. i^th line contains 2 integers, xi and pi.\n\nOutput:\nPrint the total distance of the x-axisfrom S to E, that is not protected by the armed forces.\n\nConstraints:\n1 ≤ N ≤ 10^5\n1 ≤ xi, pi ≤ 10^18\nxi + pi ≤ 10^18\n1 ≤ S ≤ E ≤ 10^18\n\nSAMPLE INPUT\n5 229 8419\n1795 95\n4873 720\n3149 81\n6101 2325\n3674 629\n\nSAMPLE OUTPUT\n2626"}}},{"rowIdx":69,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"3 6 1 2 1\\n\",\n \"5 10 1 2 5\\n\",\n \"10000 1 999999999 1000000000 1\\n\",\n \"9103 555078149 86703 93382 8235\\n\",\n \"9102 808807765 95894 96529 2021\\n\",\n \"39 407 62 63 2\\n\",\n \"8367 515267305 49370 57124 723\\n\",\n \"59 770 86 94 2\\n\",\n \"39 252 51 98 26\\n\",\n \"10000 1 1 2 1\\n\",\n \"59 96 75 98 9\\n\",\n \"1 1 1 2 1\\n\",\n \"10000 1000000000 999999999 1000000000 3\\n\",\n \"9538 765513348 52584 86675 8268\\n\",\n \"9274 783669740 44989 60995 6973\\n\",\n \"87 422 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They need to overcome the path with the length l meters. Each of the pupils will go with the speed equal to v1. To get to the excursion quickly, it was decided to rent a bus, which has seats for k people (it means that it can't fit more than k people at the same time) and the speed equal to v2. In order to avoid seasick, each of the pupils want to get into the bus no more than once.\n\nDetermine the minimum time required for all n pupils to reach the place of excursion. Consider that the embarkation and disembarkation of passengers, as well as the reversal of the bus, take place immediately and this time can be neglected. \n\nInput\n\nThe first line of the input contains five positive integers n, l, v1, v2 and k (1 ≤ n ≤ 10 000, 1 ≤ l ≤ 109, 1 ≤ v1 < v2 ≤ 109, 1 ≤ k ≤ n) — the number of pupils, the distance from meeting to the place of excursion, the speed of each pupil, the speed of bus and the number of seats in the bus. \n\nOutput\n\nPrint the real number — the minimum time in which all pupils can reach the place of excursion. Your answer will be considered correct if its absolute or relative error won't exceed 10 - 6.\n\nExamples\n\nInput\n\n5 10 1 2 5\n\n\nOutput\n\n5.0000000000\n\n\nInput\n\n3 6 1 2 1\n\n\nOutput\n\n4.7142857143\n\nNote\n\nIn the first sample we should immediately put all five pupils to the bus. The speed of the bus equals 2 and the distance is equal to 10, so the pupils will reach the place of excursion in time 10 / 2 = 5."}}},{"rowIdx":70,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"5\\n1 2 3 4 5\\n\",\n \"10\\n635370 154890 909382 220996 276501 716105 538714 140162 171960 271264\\n\",\n \"1\\n1\\n\",\n \"10\\n371054 506438 397130 1 766759 208409 769264 549213 641270 771837\\n\",\n \"1\\n1000000\\n\",\n \"1\\n2\\n\",\n \"2\\n3 2\\n\",\n \"50\\n110876 835020 859879 999908 712969 788264 287153 921820 330355 499311 209594 484829 296329 940051 174081 931503 1 780512 390075 97866 124255 950067 697612 244256 782385 789882 37608 82153 399889 598867 416717 377988 535636 511221 792568 683271 131077 290194 496712 330720 587436 563481 645817 942562 654093 980561 382937 48293 582608 116156\\n\",\n \"2\\n2 3\\n\",\n \"50\\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 70997 393786 337382 663642 131184 637 273801 799870 295017 392338 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It uses banknotes of several values. But the problem is, the system is not perfect and sometimes it happens that Geraldionians cannot express a certain sum of money with any set of banknotes. Of course, they can use any number of banknotes of each value. Such sum is called unfortunate. Gerald wondered: what is the minimum unfortunate sum?\n\nInput\n\nThe first line contains number n (1 ≤ n ≤ 1000) — the number of values of the banknotes that used in Geraldion. \n\nThe second line contains n distinct space-separated numbers a1, a2, ..., an (1 ≤ ai ≤ 106) — the values of the banknotes.\n\nOutput\n\nPrint a single line — the minimum unfortunate sum. If there are no unfortunate sums, print - 1.\n\nExamples\n\nInput\n\n5\n1 2 3 4 5\n\n\nOutput\n\n-1"}}},{"rowIdx":71,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"1 8\\n2 8 81\\n\",\n \"2 30\\n20 30 80\\n3 9 85\\n\",\n \"4 319\\n63 79 89\\n79 97 91\\n75 87 88\\n75 90 83\\n\",\n \"2 98\\n77 86 82\\n17 21 91\\n\",\n \"50 1872\\n45 85 93\\n37 67 97\\n62 77 83\\n50 71 81\\n59 62 84\\n52 82 96\\n67 73 96\\n59 92 99\\n33 66 96\\n18 43 94\\n4 82 96\\n15 29 93\\n47 87 84\\n33 67 83\\n78 99 88\\n48 93 84\\n19 74 98\\n14 47 99\\n23 87 88\\n5 20 86\\n12 39 94\\n6 52 93\\n14 89 94\\n54 71 85\\n43 52 97\\n24 85 82\\n11 13 95\\n44 77 95\\n63 100 84\\n31 88 80\\n18 96 90\\n1 41 83\\n65 87 91\\n29 65 98\\n23 73 83\\n22 48 96\\n19 62 89\\n23 94 83\\n47 92 97\\n49 99 86\\n16 94 80\\n24 38 85\\n85 88 96\\n18 71 83\\n26 64 95\\n64 76 96\\n48 72 80\\n12 22 97\\n1 68 90\\n40 56 87\\n\",\n \"49 1595\\n35 59 98\\n19 20 89\\n44 73 99\\n9 85 93\\n24 98 97\\n37 73 98\\n46 49 98\\n50 89 99\\n15 25 97\\n37 96 96\\n2 22 98\\n11 83 87\\n23 83 94\\n8 45 99\\n53 98 99\\n4 96 96\\n43 58 92\\n53 74 94\\n27 58 93\\n15 98 96\\n9 10 91\\n35 90 95\\n23 86 99\\n30 99 92\\n71 93 91\\n18 28 99\\n25 43 92\\n33 40 98\\n37 60 99\\n36 62 91\\n20 50 94\\n57 97 94\\n63 75 99\\n73 91 96\\n37 44 98\\n29 63 96\\n12 71 98\\n4 47 97\\n12 32 87\\n2 68 98\\n24 97 99\\n21 74 93\\n49 90 97\\n6 70 96\\n16 40 91\\n35 81 99\\n74 89 89\\n3 28 99\\n19 94 90\\n\",\n \"50 2355\\n48 91 87\\n49 89 98\\n25 74 83\\n30 86 88\\n45 50 84\\n19 39 86\\n58 60 91\\n13 84 89\\n56 61 94\\n1 50 94\\n27 68 85\\n66 75 93\\n37 54 89\\n79 89 94\\n59 65 83\\n2 3 85\\n35 57 91\\n19 80 96\\n17 87 84\\n2 61 90\\n19 68 99\\n32 51 95\\n27 69 94\\n22 58 90\\n48 83 94\\n15 27 97\\n41 94 92\\n37 39 86\\n32 79 80\\n16 37 87\\n37 38 83\\n41 59 87\\n2 92 85\\n23 45 80\\n68 99 88\\n56 67 81\\n57 94 95\\n4 63 99\\n26 39 88\\n66 67 96\\n69 99 84\\n22 92 84\\n24 88 93\\n17 35 84\\n46 77 96\\n34 57 87\\n65 89 96\\n10 31 96\\n22 66 87\\n50 93 85\\n\",\n \"49 1959\\n29 38 99\\n4 88 83\\n3 64 83\\n12 85 84\\n44 84 88\\n40 57 91\\n23 63 95\\n66 92 87\\n10 50 96\\n1 8 85\\n10 86 85\\n64 80 95\\n6 38 85\\n66 88 90\\n19 94 84\\n44 83 87\\n28 63 87\\n59 73 95\\n59 80 86\\n21 100 97\\n58 96 84\\n40 67 99\\n52 73 90\\n1 45 95\\n19 32 96\\n37 73 80\\n3 81 85\\n51 65 83\\n5 88 85\\n36 58 94\\n30 59 84\\n50 75 99\\n24 49 94\\n33 71 89\\n41 46 92\\n35 72 91\\n2 43 85\\n84 88 95\\n15 71 84\\n16 30 86\\n51 66 84\\n55 62 99\\n4 91 95\\n75 86 89\\n7 13 90\\n19 23 95\\n72 88 82\\n61 72 92\\n42 91 93\\n\",\n \"30 1056\\n11 72 80\\n40 89 80\\n8 35 80\\n59 83 80\\n33 48 80\\n34 74 80\\n79 93 80\\n41 82 80\\n34 38 80\\n33 46 80\\n31 83 80\\n5 79 80\\n52 53 80\\n3 53 80\\n40 43 80\\n63 72 80\\n20 72 80\\n13 78 80\\n45 93 80\\n56 77 80\\n29 95 80\\n45 82 80\\n53 86 80\\n22 49 80\\n25 95 80\\n9 58 80\\n4 61 80\\n78 92 80\\n70 86 80\\n21 96 80\\n\",\n \"40 1766\\n4 33 90\\n23 88 91\\n56 79 81\\n3 80 94\\n53 72 87\\n75 79 92\\n44 67 97\\n18 40 99\\n42 76 82\\n51 75 83\\n23 30 98\\n66 86 96\\n56 87 94\\n26 62 82\\n48 100 83\\n37 66 97\\n6 9 89\\n90 100 81\\n1 15 91\\n22 76 98\\n22 56 90\\n26 56 93\\n7 43 84\\n78 79 81\\n26 75 90\\n28 92 99\\n8 78 84\\n3 76 87\\n37 69 93\\n46 83 97\\n15 29 92\\n18 29 93\\n5 83 83\\n78 89 88\\n21 61 92\\n80 83 84\\n21 100 94\\n1 61 87\\n87 93 92\\n67 100 98\\n\",\n \"45 1686\\n66 99 98\\n79 98 92\\n54 92 97\\n65 74 90\\n27 54 87\\n5 43 97\\n1 89 85\\n62 73 89\\n28 69 89\\n34 71 90\\n43 71 90\\n1 65 97\\n56 63 87\\n22 46 86\\n75 84 87\\n16 89 81\\n58 83 81\\n87 97 82\\n12 61 88\\n30 35 83\\n9 93 89\\n63 90 98\\n26 50 85\\n40 98 91\\n21 55 96\\n82 88 83\\n36 81 91\\n36 82 84\\n26 88 86\\n2 39 97\\n21 91 92\\n24 60 97\\n20 73 89\\n9 38 82\\n36 81 95\\n37 86 82\\n63 89 86\\n43 71 85\\n33 38 90\\n34 61 81\\n6 8 94\\n4 40 87\\n7 77 95\\n33 60 91\\n55 97 93\\n\",\n \"5 318\\n82 94 97\\n22 66 82\\n18 34 86\\n31 71 87\\n14 61 95\\n\",\n \"50 3561\\n20 38 90\\n42 46 85\\n28 44 81\\n9 94 97\\n17 37 85\\n25 41 80\\n26 43 96\\n56 61 88\\n42 97 99\\n44 66 93\\n38 88 94\\n59 78 89\\n94 98 96\\n19 87 84\\n44 85 97\\n50 82 80\\n84 94 84\\n49 74 93\\n47 77 90\\n37 45 84\\n68 85 81\\n50 78 96\\n74 88 94\\n57 86 96\\n18 67 83\\n48 91 93\\n64 93 94\\n3 16 85\\n62 76 82\\n51 99 94\\n67 84 91\\n29 77 88\\n22 33 91\\n26 68 89\\n81 84 98\\n38 76 94\\n50 95 84\\n85 96 96\\n27 52 91\\n36 81 97\\n27 40 83\\n34 49 95\\n26 94 80\\n49 83 94\\n59 85 90\\n58 82 89\\n5 23 86\\n44 48 86\\n45 76 89\\n11 81 98\\n\",\n \"48 1568\\n13 90 98\\n51 69 96\\n8 59 89\\n33 37 97\\n51 84 92\\n23 84 96\\n39 96 96\\n20 50 99\\n37 94 99\\n15 81 97\\n77 91 98\\n25 87 95\\n26 38 83\\n29 62 95\\n26 89 94\\n21 61 98\\n66 70 95\\n13 94 99\\n46 56 99\\n4 98 96\\n10 73 99\\n13 81 98\\n14 36 96\\n10 58 99\\n69 77 97\\n10 16 97\\n20 45 97\\n35 56 93\\n64 88 94\\n4 45 97\\n15 99 97\\n33 39 98\\n51 100 97\\n58 87 96\\n70 98 96\\n84 86 97\\n47 68 97\\n31 64 98\\n29 88 95\\n10 72 94\\n32 86 95\\n4 76 92\\n52 65 92\\n12 91 91\\n22 42 95\\n94 100 95\\n18 96 99\\n1 58 97\\n\",\n \"48 2407\\n31 77 98\\n29 32 95\\n20 52 81\\n65 95 85\\n57 94 82\\n16 78 99\\n49 92 83\\n16 61 80\\n39 89 88\\n3 7 81\\n49 79 99\\n40 83 85\\n21 84 89\\n21 65 84\\n48 82 90\\n46 74 84\\n78 84 94\\n31 50 91\\n71 74 95\\n8 90 91\\n17 60 97\\n92 94 99\\n15 90 82\\n9 10 94\\n19 86 81\\n26 86 94\\n10 77 95\\n46 64 93\\n58 73 95\\n31 87 95\\n52 66 87\\n4 60 93\\n39 51 99\\n47 97 95\\n49 81 89\\n6 68 89\\n9 93 85\\n20 25 98\\n40 54 97\\n19 85 80\\n32 60 83\\n29 65 83\\n16 68 91\\n31 37 95\\n73 82 92\\n51 53 98\\n83 99 98\\n17 98 89\\n\",\n \"29 903\\n8 86 80\\n28 72 80\\n33 90 80\\n7 72 80\\n9 77 80\\n16 26 80\\n5 41 80\\n46 90 80\\n22 68 80\\n16 81 80\\n60 63 80\\n30 79 80\\n9 98 80\\n13 16 80\\n5 12 80\\n16 82 80\\n32 41 80\\n46 83 80\\n39 46 80\\n38 69 80\\n66 99 80\\n64 81 80\\n19 38 80\\n34 37 80\\n44 90 80\\n55 68 80\\n40 53 80\\n78 86 80\\n25 27 80\\n\",\n \"50 1705\\n48 64 85\\n7 10 82\\n21 59 83\\n14 91 83\\n28 81 81\\n24 95 80\\n42 97 80\\n8 28 80\\n36 58 81\\n59 65 87\\n25 58 88\\n1 94 89\\n8 86 83\\n55 97 81\\n28 77 84\\n15 30 91\\n49 87 80\\n73 94 82\\n62 83 91\\n3 65 82\\n57 74 83\\n59 75 91\\n6 51 82\\n21 85 87\\n20 45 80\\n76 100 86\\n3 59 80\\n59 98 80\\n21 48 83\\n89 93 81\\n7 22 83\\n10 27 81\\n71 76 80\\n45 75 82\\n82 86 80\\n4 30 90\\n74 95 80\\n26 45 82\\n5 56 85\\n1 33 81\\n39 44 87\\n12 23 89\\n54 85 80\\n11 86 86\\n7 78 81\\n14 79 81\\n9 17 81\\n42 96 84\\n26 70 80\\n25 87 93\\n\",\n \"50 50\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n1 2 99\\n\",\n \"50 1686\\n39 92 87\\n8 21 88\\n39 80 92\\n28 62 88\\n19 68 87\\n43 53 99\\n35 45 94\\n13 80 85\\n25 69 98\\n56 98 93\\n64 84 96\\n5 69 86\\n29 88 96\\n12 92 96\\n20 80 83\\n80 100 83\\n45 100 91\\n15 66 94\\n19 73 80\\n34 74 85\\n72 76 87\\n21 35 94\\n34 52 83\\n10 69 87\\n11 20 80\\n6 44 95\\n34 99 89\\n30 74 92\\n15 100 82\\n71 90 84\\n62 77 84\\n6 66 87\\n22 80 99\\n63 95 80\\n55 73 99\\n24 34 83\\n27 50 91\\n7 44 85\\n45 80 93\\n72 97 91\\n27 55 80\\n20 61 87\\n45 95 99\\n27 71 99\\n74 84 85\\n15 93 91\\n30 59 92\\n55 57 80\\n45 51 90\\n33 43 97\\n\",\n \"49 2491\\n23 66 96\\n73 78 94\\n27 57 94\\n85 94 83\\n11 55 81\\n5 10 84\\n19 97 90\\n28 68 90\\n10 31 89\\n8 48 93\\n57 84 97\\n18 56 88\\n21 43 95\\n42 51 81\\n36 89 90\\n5 17 87\\n23 97 95\\n13 33 82\\n38 81 86\\n8 42 91\\n22 26 85\\n34 45 83\\n70 100 96\\n50 97 81\\n1 70 98\\n12 48 84\\n56 89 88\\n6 54 92\\n36 52 94\\n1 26 97\\n39 85 92\\n74 86 95\\n10 20 90\\n21 41 98\\n35 58 83\\n36 83 88\\n34 62 99\\n21 72 81\\n6 23 89\\n19 65 82\\n16 50 88\\n11 82 98\\n33 55 88\\n55 96 99\\n89 91 91\\n71 86 83\\n40 44 88\\n8 63 97\\n75 91 94\\n\",\n \"1 88\\n77 88 96\\n\",\n \"46 2431\\n4 48 83\\n51 57 99\\n18 46 97\\n50 87 90\\n50 81 92\\n38 100 84\\n49 77 81\\n37 63 85\\n25 26 93\\n13 25 97\\n47 80 85\\n62 73 80\\n39 90 90\\n6 93 90\\n87 96 96\\n19 57 98\\n8 43 96\\n45 61 91\\n23 84 96\\n44 63 83\\n62 87 80\\n63 94 99\\n6 7 81\\n3 47 91\\n6 71 80\\n8 81 89\\n9 19 97\\n26 69 91\\n23 35 85\\n32 51 85\\n1 30 87\\n1 24 86\\n30 55 87\\n13 27 98\\n19 24 84\\n2 57 93\\n48 82 92\\n20 100 98\\n57 100 96\\n51 53 90\\n74 93 90\\n52 77 96\\n9 31 94\\n17 28 87\\n38 95 98\\n17 44 86\\n\",\n \"49 3344\\n29 57 96\\n12 66 89\\n25 40 99\\n48 98 94\\n1 31 82\\n51 93 87\\n34 56 88\\n25 65 97\\n38 40 99\\n24 25 83\\n4 30 83\\n84 96 83\\n74 88 81\\n13 58 85\\n55 99 91\\n40 99 88\\n67 91 80\\n6 74 96\\n32 79 94\\n37 84 99\\n14 48 95\\n44 57 99\\n9 87 94\\n33 56 96\\n32 86 97\\n4 7 84\\n56 67 91\\n61 77 94\\n17 44 95\\n48 62 97\\n10 84 84\\n4 91 83\\n63 100 82\\n20 94 95\\n9 34 84\\n54 69 80\\n27 72 94\\n39 43 80\\n39 89 88\\n15 83 80\\n4 90 81\\n18 90 96\\n33 64 92\\n53 67 98\\n37 65 97\\n24 54 92\\n26 64 98\\n30 71 97\\n12 60 87\\n\",\n \"49 1726\\n16 52 84\\n52 80 84\\n27 63 82\\n43 72 82\\n39 62 86\\n32 94 81\\n45 95 88\\n6 70 98\\n1 92 97\\n8 55 96\\n74 96 89\\n31 88 96\\n45 62 97\\n55 92 90\\n46 71 93\\n14 52 81\\n22 97 84\\n75 80 97\\n23 96 99\\n53 87 90\\n48 63 85\\n36 96 82\\n42 97 83\\n17 51 89\\n58 95 86\\n48 65 94\\n10 68 88\\n62 94 97\\n52 75 83\\n42 59 95\\n62 85 91\\n10 76 99\\n71 87 90\\n12 96 83\\n38 63 82\\n19 48 84\\n14 30 94\\n4 93 83\\n66 89 80\\n14 90 94\\n28 30 82\\n35 90 81\\n30 44 87\\n37 39 94\\n36 88 92\\n15 94 89\\n49 63 92\\n11 66 92\\n53 56 99\\n\",\n \"49 1952\\n53 82 82\\n50 53 86\\n15 24 83\\n34 63 81\\n39 81 81\\n3 37 83\\n11 95 80\\n37 41 83\\n60 78 81\\n88 92 81\\n3 47 80\\n15 45 85\\n6 84 83\\n63 71 84\\n30 98 85\\n1 20 81\\n38 53 81\\n53 70 83\\n33 55 85\\n1 41 82\\n51 79 83\\n28 99 82\\n31 38 81\\n60 62 86\\n37 60 81\\n29 60 80\\n30 59 80\\n24 69 81\\n8 35 82\\n44 89 82\\n49 94 85\\n22 47 81\\n40 84 80\\n86 90 81\\n45 73 90\\n24 27 81\\n24 59 86\\n68 98 87\\n60 80 90\\n6 54 91\\n78 89 81\\n4 24 85\\n42 57 85\\n13 98 86\\n76 82 83\\n20 57 86\\n50 61 86\\n30 85 86\\n12 13 82\\n\",\n \"20 838\\n8 17 94\\n46 77 84\\n16 93 82\\n20 44 97\\n23 72 91\\n40 57 83\\n18 79 87\\n45 60 99\\n59 84 84\\n52 97 88\\n71 80 81\\n23 90 87\\n38 47 94\\n1 34 91\\n42 59 98\\n28 48 97\\n81 86 89\\n5 66 96\\n44 73 81\\n47 98 90\\n\",\n \"50 1630\\n61 79 93\\n4 21 96\\n44 70 98\\n9 60 95\\n8 85 94\\n94 98 96\\n3 45 90\\n17 36 94\\n16 71 95\\n41 68 90\\n11 84 96\\n5 28 99\\n25 99 88\\n40 54 99\\n3 64 98\\n33 64 98\\n78 87 95\\n28 30 99\\n17 46 98\\n25 77 98\\n37 68 99\\n10 67 98\\n11 65 98\\n28 92 99\\n34 72 96\\n44 89 97\\n40 58 98\\n73 93 94\\n16 45 97\\n32 45 98\\n10 97 91\\n26 30 94\\n31 78 91\\n24 74 98\\n4 41 99\\n51 66 97\\n28 56 92\\n4 58 97\\n24 42 98\\n44 55 92\\n41 97 91\\n52 55 92\\n30 95 99\\n73 98 95\\n42 96 89\\n51 60 99\\n29 58 92\\n29 77 93\\n73 81 99\\n77 89 99\\n\",\n \"10 371\\n71 80 81\\n26 90 97\\n54 55 86\\n7 17 96\\n47 55 93\\n27 61 80\\n22 30 97\\n20 41 82\\n18 26 98\\n54 100 84\\n\",\n \"48 1976\\n30 97 84\\n80 81 84\\n41 70 86\\n23 57 80\\n17 60 85\\n36 48 81\\n51 87 81\\n38 85 81\\n31 67 80\\n11 40 96\\n63 100 83\\n4 67 82\\n16 67 90\\n45 97 80\\n60 75 82\\n5 95 84\\n43 85 83\\n4 14 81\\n21 85 81\\n32 39 80\\n25 32 80\\n34 79 83\\n67 100 81\\n28 46 80\\n16 19 89\\n32 94 80\\n45 49 81\\n3 37 82\\n60 96 81\\n32 68 88\\n21 36 84\\n76 95 81\\n87 91 84\\n58 60 82\\n71 97 81\\n9 15 81\\n13 24 81\\n32 87 83\\n24 94 85\\n33 56 81\\n55 100 88\\n11 40 82\\n51 60 81\\n52 78 84\\n33 65 82\\n84 99 81\\n32 71 81\\n67 72 87\\n\",\n \"35 1344\\n13 45 80\\n45 56 88\\n41 69 83\\n52 71 89\\n95 96 88\\n55 91 96\\n52 81 94\\n13 90 95\\n26 98 84\\n48 59 99\\n39 86 97\\n66 87 86\\n33 81 96\\n64 94 92\\n57 68 81\\n17 50 91\\n54 57 89\\n40 66 87\\n27 61 90\\n21 33 86\\n45 90 95\\n28 68 90\\n19 83 85\\n32 62 90\\n20 58 94\\n59 80 80\\n14 93 84\\n38 78 84\\n40 84 85\\n3 61 81\\n33 62 85\\n12 44 98\\n26 85 91\\n14 22 84\\n15 76 89\\n\",\n \"20 649\\n39 78 88\\n92 96 84\\n3 53 97\\n13 83 86\\n46 71 86\\n20 59 92\\n86 87 92\\n13 82 83\\n22 32 97\\n38 40 85\\n19 98 89\\n30 73 83\\n17 29 92\\n39 87 86\\n30 89 96\\n49 67 99\\n15 66 80\\n7 96 92\\n17 32 99\\n54 83 95\\n\",\n \"47 1676\\n34 58 88\\n8 96 98\\n6 69 97\\n89 98 97\\n31 80 91\\n49 62 82\\n10 85 93\\n39 90 88\\n22 37 89\\n50 52 91\\n42 44 99\\n30 89 92\\n18 67 86\\n4 47 83\\n27 64 86\\n4 22 95\\n41 77 81\\n65 96 89\\n8 51 82\\n53 66 83\\n81 86 94\\n38 50 95\\n14 40 82\\n26 56 99\\n42 92 96\\n32 84 96\\n74 85 96\\n44 63 95\\n43 81 99\\n26 60 80\\n96 99 94\\n24 93 98\\n18 85 98\\n14 36 88\\n6 64 91\\n8 92 94\\n35 99 85\\n39 85 88\\n41 79 95\\n17 68 99\\n17 98 92\\n40 81 80\\n58 64 99\\n1 36 90\\n18 42 96\\n41 77 95\\n7 23 93\\n\",\n \"30 1591\\n63 80 92\\n47 90 96\\n23 47 90\\n34 40 83\\n64 94 91\\n48 87 99\\n30 78 99\\n29 68 88\\n2 58 83\\n86 96 82\\n64 80 95\\n68 97 80\\n11 75 99\\n52 70 87\\n32 63 84\\n55 76 86\\n44 65 83\\n71 81 98\\n39 89 82\\n34 86 99\\n56 69 83\\n2 17 89\\n24 36 80\\n22 23 88\\n22 28 92\\n71 92 85\\n74 84 82\\n1 44 97\\n7 58 95\\n18 26 93\\n\",\n \"50 50\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n1 100 80\\n\",\n \"50 1670\\n44 45 80\\n76 100 80\\n10 61 80\\n24 79 80\\n9 20 80\\n62 76 80\\n52 85 80\\n13 39 80\\n17 78 80\\n31 61 80\\n58 63 80\\n25 27 80\\n23 72 80\\n31 39 80\\n43 46 80\\n44 83 80\\n2 4 80\\n49 84 80\\n24 84 80\\n43 67 80\\n6 80 80\\n29 86 80\\n59 69 80\\n22 60 80\\n2 57 80\\n5 79 80\\n39 46 80\\n10 94 80\\n60 80 80\\n70 95 80\\n9 76 80\\n29 65 80\\n36 81 80\\n42 67 80\\n10 80 80\\n32 75 80\\n61 71 80\\n81 82 80\\n41 79 80\\n37 89 80\\n4 34 80\\n1 29 80\\n68 78 80\\n62 94 80\\n57 69 80\\n14 77 80\\n48 79 80\\n4 67 80\\n21 79 80\\n31 49 80\\n\",\n \"49 1570\\n5 98 80\\n88 89 80\\n4 28 80\\n2 70 80\\n9 27 80\\n29 80 80\\n39 42 80\\n24 36 80\\n27 81 80\\n22 91 80\\n33 79 80\\n38 43 80\\n10 15 80\\n50 80 80\\n57 58 80\\n6 37 80\\n64 72 80\\n13 48 80\\n11 52 80\\n58 78 80\\n34 83 80\\n35 43 80\\n35 90 80\\n4 81 80\\n81 94 80\\n55 65 80\\n19 88 80\\n10 32 80\\n43 69 80\\n42 64 80\\n4 19 80\\n42 97 80\\n57 83 80\\n17 75 80\\n17 69 80\\n56 80 80\\n3 34 80\\n6 35 80\\n58 67 80\\n61 94 80\\n69 73 80\\n7 37 80\\n1 44 80\\n19 66 80\\n19 100 80\\n38 74 80\\n27 65 80\\n65 78 80\\n57 88 80\\n\",\n \"2 98\\n77 86 49\\n17 21 91\\n\",\n \"50 1872\\n45 85 93\\n37 67 97\\n62 154 83\\n50 71 81\\n59 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The game consists of N levels, which must be completed sequentially in order to beat the game. You usually complete each level as fast as possible, but sometimes finish a level slower. Specifically, you will complete the i-th level in either Fi seconds or Si seconds, where Fi < Si, and there's a Pi percent chance of completing it in Fi seconds. After completing a level, you may decide to either continue the game and play the next level, or reset the game and start again from the first level. Both the decision and the action are instant.\n\nYour goal is to complete all the levels sequentially in at most R total seconds. You want to minimize the expected amount of time playing before achieving that goal. If you continue and reset optimally, how much total time can you expect to spend playing?\n\nInput\n\nThe first line of input contains integers N and R , the number of levels and number of seconds you want to complete the game in, respectively. N lines follow. The ith such line contains integers Fi, Si, Pi (1 ≤ Fi < Si ≤ 100, 80 ≤ Pi ≤ 99), the fast time for level i, the slow time for level i, and the probability (as a percentage) of completing level i with the fast time.\n\nOutput\n\nPrint the total expected time. Your answer must be correct within an absolute or relative error of 10 - 9.\n\nFormally, let your answer be a, and the jury's answer be b. Your answer will be considered correct, if .\n\nExamples\n\nInput\n\n1 8\n2 8 81\n\n\nOutput\n\n3.14\n\n\nInput\n\n2 30\n20 30 80\n3 9 85\n\n\nOutput\n\n31.4\n\n\nInput\n\n4 319\n63 79 89\n79 97 91\n75 87 88\n75 90 83\n\n\nOutput\n\n314.159265358\n\nNote\n\nIn the first example, you never need to reset. There's an 81% chance of completing the level in 2 seconds and a 19% chance of needing 8 seconds, both of which are within the goal time. The expected time is 0.81·2 + 0.19·8 = 3.14.\n\nIn the second example, you should reset after the first level if you complete it slowly. On average it will take 0.25 slow attempts before your first fast attempt. Then it doesn't matter whether you complete the second level fast or slow. The expected time is 0.25·30 + 20 + 0.85·3 + 0.15·9 = 31.4."}}},{"rowIdx":72,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"1\\n0 10 0 10\\n\",\n \"2\\n12 3 4 7\\n1 15 9 1\\n\",\n \"2\\n5 4 8 8\\n4 12 14 0\\n\",\n \"10\\n31181 6 72281 7\\n65255 10 17867 2\\n96212 8 32852 10\\n69668 6 37236 1\\n6031 7 61541 0\\n12286 4 40227 2\\n30573 9 36317 3\\n97429 6 35399 9\\n20907 5 19251 8\\n86446 8 56301 10\\n\",\n \"10\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n1000000000 0 1000000000 0\\n\",\n \"10\\n3 86311 1 17635\\n6 34036 8 37167\\n4 53806 6 25588\\n3 91425 4 86666\\n6 50210 10 7332\\n4 59721 10 697\\n0 15949 2 66047\\n0 68146 10 70354\\n2 1075 0 23359\\n5 48622 9 70531\\n\",\n \"2\\n252323306 923185060 41887968 12082849\\n956989832 311441362 23412620 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]\n}"},"problem":{"kind":"string","value":"Alice and Bonnie are sisters, but they don't like each other very much. So when some old family photos were found in the attic, they started to argue about who should receive which photos. In the end, they decided that they would take turns picking photos. Alice goes first.\n\nThere are n stacks of photos. Each stack contains exactly two photos. In each turn, a player may take only a photo from the top of one of the stacks.\n\nEach photo is described by two non-negative integers a and b, indicating that it is worth a units of happiness to Alice and b units of happiness to Bonnie. Values of a and b might differ for different photos.\n\nIt's allowed to pass instead of taking a photo. The game ends when all photos are taken or both players pass consecutively.\n\nThe players don't act to maximize their own happiness. Instead, each player acts to maximize the amount by which her happiness exceeds her sister's. Assuming both players play optimal, find the difference between Alice's and Bonnie's happiness. That is, if there's a perfectly-played game such that Alice has x happiness and Bonnie has y happiness at the end, you should print x - y.\n\nInput\n\nThe first line of input contains a single integer n (1 ≤ n ≤ 100 000) — the number of two-photo stacks. Then follow n lines, each describing one of the stacks. A stack is described by four space-separated non-negative integers a1, b1, a2 and b2, each not exceeding 109. a1 and b1 describe the top photo in the stack, while a2 and b2 describe the bottom photo in the stack.\n\nOutput\n\nOutput a single integer: the difference between Alice's and Bonnie's happiness if both play optimally.\n\nExamples\n\nInput\n\n2\n12 3 4 7\n1 15 9 1\n\n\nOutput\n\n1\n\n\nInput\n\n2\n5 4 8 8\n4 12 14 0\n\n\nOutput\n\n4\n\n\nInput\n\n1\n0 10 0 10\n\n\nOutput\n\n-10"}}},{"rowIdx":73,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2\\n4 1\\n1 2 5\\n3 1 2\\n3 4 3\\n7 2\\n1 2 5\\n1 3 4\\n1 4 2\\n2 5 1\\n2 6 2\\n4 7 3\\n\",\n \"10\\n9 3\\n7 4 10\\n6 8 1\\n1 3 6\\n2 4 10\\n2 9 1\\n5 4 9\\n3 6 5\\n1 2 5\\n2 6\\n1 2 2\\n2 4\\n1 2 8\\n7 7\\n4 3 2\\n6 5 1\\n3 2 3\\n3 5 7\\n7 1 10\\n1 2 9\\n3 9\\n3 2 6\\n2 1 8\\n7 10\\n1 5 9\\n3 4 2\\n1 3 6\\n7 3 9\\n3 6 3\\n1 2 3\\n6 3\\n2 1 4\\n4 2 10\\n3 5 2\\n3 1 5\\n2 6 5\\n1 2\\n9 8\\n4 7 7\\n4 6 2\\n2 9 9\\n2 3 5\\n5 3 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3 4\\n1 4 2\\n2 5 1\\n2 10 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 2\\n3 1 2\\n3 4 5\\n1 2\\n1 2 7\\n1 3 4\\n1 4 2\\n2 5 1\\n2 6 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 2\\n3 1 2\\n3 4 5\\n1 2\\n1 2 5\\n1 3 4\\n1 0 0\\n2 5 1\\n2 6 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 2\\n3 1 2\\n3 4 3\\n5 2\\n1 2 5\\n1 3 7\\n1 4 2\\n2 5 1\\n2 6 0\\n4 7 2\\n\",\n \"2\\n4 1\\n1 2 2\\n3 1 2\\n3 4 5\\n1 2\\n1 2 7\\n1 3 4\\n1 1 2\\n2 5 1\\n2 6 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 2\\n3 1 2\\n3 4 5\\n1 2\\n0 2 5\\n1 3 4\\n1 0 0\\n2 5 1\\n2 6 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 0\\n3 1 2\\n1 4 5\\n1 2\\n1 2 5\\n1 3 4\\n1 2 0\\n2 5 1\\n2 6 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 2\\n3 1 2\\n3 4 5\\n1 2\\n1 2 3\\n1 3 4\\n1 1 2\\n2 5 1\\n2 6 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 2\\n3 1 2\\n3 4 5\\n1 2\\n0 2 5\\n1 2 4\\n1 0 0\\n2 5 1\\n2 6 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 0\\n3 1 2\\n1 4 5\\n1 2\\n1 2 3\\n1 3 4\\n1 2 0\\n2 5 1\\n2 6 0\\n4 1 3\\n\",\n \"2\\n4 1\\n1 2 2\\n3 1 2\\n3 4 3\\n5 2\\n1 2 5\\n1 3 12\\n1 4 3\\n2 5 1\\n2 6 0\\n4 7 2\\n\"\n ],\n \"outputs\": [\n \"8\\n14\\n\",\n \"47\\n2\\n8\\n32\\n14\\n32\\n26\\n0\\n33\\n29\\n\",\n \"47\\n2\\n8\\n32\\n21\\n32\\n26\\n0\\n33\\n29\\n\",\n \"47\\n2\\n8\\n32\\n14\\n32\\n27\\n0\\n33\\n29\\n\",\n \"8\\n14\\n\",\n \"8\\n18\\n\",\n \"47\\n2\\n8\\n31\\n14\\n32\\n26\\n0\\n33\\n29\\n\",\n \"5\\n14\\n\",\n \"5\\n13\\n\",\n \"5\\n10\\n\",\n \"7\\n10\\n\",\n \"7\\n0\\n\",\n \"47\\n2\\n8\\n32\\n14\\n32\\n26\\n0\\n34\\n29\\n\",\n \"47\\n2\\n8\\n32\\n21\\n32\\n26\\n0\\n33\\n27\\n\",\n \"47\\n2\\n8\\n32\\n14\\n32\\n27\\n0\\n33\\n28\\n\",\n \"8\\n19\\n\",\n \"55\\n2\\n8\\n31\\n14\\n32\\n26\\n0\\n33\\n29\\n\",\n \"5\\n0\\n\",\n \"47\\n2\\n8\\n32\\n14\\n32\\n27\\n0\\n34\\n29\\n\",\n \"43\\n2\\n8\\n31\\n14\\n32\\n26\\n0\\n33\\n29\\n\",\n \"5\\n16\\n\",\n \"5\\n19\\n\",\n \"43\\n0\\n8\\n31\\n14\\n32\\n26\\n0\\n33\\n29\\n\",\n \"5\\n20\\n\",\n \"5\\n18\\n\",\n \"5\\n23\\n\",\n \"6\\n0\\n\",\n \"47\\n2\\n8\\n32\\n14\\n32\\n27\\n0\\n33\\n29\\n\",\n \"8\\n18\\n\",\n \"8\\n18\\n\",\n \"5\\n10\\n\",\n \"7\\n0\\n\",\n \"7\\n0\\n\",\n \"5\\n13\\n\",\n \"8\\n19\\n\",\n \"5\\n13\\n\",\n \"5\\n10\\n\",\n \"7\\n0\\n\",\n \"7\\n0\\n\",\n \"5\\n13\\n\",\n \"7\\n0\\n\",\n \"7\\n0\\n\",\n \"5\\n0\\n\",\n \"7\\n0\\n\",\n \"7\\n0\\n\",\n \"5\\n0\\n\",\n \"5\\n18\\n\"\n ]\n}"},"problem":{"kind":"string","value":"You are given a weighted tree consisting of n vertices. Recall that a tree is a connected graph without cycles. Vertices u_i and v_i are connected by an edge with weight w_i.\n\nLet's define the k-coloring of the tree as an assignment of exactly k colors to each vertex, so that each color is used no more than two times. You can assume that you have infinitely many colors available. We say that an edge is saturated in the given k-coloring if its endpoints share at least one color (i.e. there exists a color that is assigned to both endpoints).\n\nLet's also define the value of a k-coloring as the sum of weights of saturated edges.\n\nPlease calculate the maximum possible value of a k-coloring of the given tree.\n\nYou have to answer q independent queries.\n\nInput\n\nThe first line contains one integer q (1 ≤ q ≤ 5 ⋅ 10^5) – the number of queries.\n\nThe first line of each query contains two integers n and k (1 ≤ n, k ≤ 5 ⋅ 10^5) — the number of vertices in the tree and the number of colors to assign to each vertex, respectively.\n\nEach of the next n - 1 lines describes an edge of the tree. Edge i is denoted by three integers u_i, v_i and w_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i, 1 ≤ w_i ≤ 10^5) — the labels of vertices it connects and the weight of the edge. It is guaranteed that the given edges form a tree.\n\nIt is guaranteed that sum of all n over all queries does not exceed 5 ⋅ 10^5.\n\nOutput\n\nFor each query print one integer — the maximum value of a k-coloring of the given tree.\n\nExample\n\nInput\n\n\n2\n4 1\n1 2 5\n3 1 2\n3 4 3\n7 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 2\n4 7 3\n\n\nOutput\n\n\n8\n14\n\nNote\n\nThe tree corresponding to the first query in the example:\n\n\n\nOne of the possible k-colorings in the first example: (1), (1), (2), (2), then the 1-st and the 3-rd edges are saturated and the sum of their weights is 8.\n\nThe tree corresponding to the second query in the example:\n\n\n\nOne of the possible k-colorings in the second example: (1, 2), (1, 3), (2, 4), (5, 6), (7, 8), (3, 4), (5, 6), then the 1-st, 2-nd, 5-th and 6-th edges are saturated and the sum of their weights is 14."}}},{"rowIdx":74,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"3 4\\n2 2 1 3\\n2 2 3 1\\n\\nSAMPLE\",\n \"100000 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15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 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3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 2860 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 19828 4065 86003 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20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732\",\n \"100000 344\\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 28771 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 71327 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 33181 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \\n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 2860 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 19828 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 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Chandu is up for playing his very first game. His first game is played on a N X N board with some initial stones placed on each cell. He can move each stone in all four direction i.e up,down, left or right. His target of the game is to move all stones to any one of the four corners in minimum moves (different stones can be moved to different corners). \n\nChandu seeks you again for his help. Your task is to write a program that tell the minimum number of moves given a particular state of board.\n\nNOTE: One cell may contain more than one stones.\n\nInput:\n\nFirst line of input contains two integers N and K. Where, N X N is the size of the board and k is the no of stones present on the board. Then, two lines(x[] and y[]) follow each containing K integers where i\\;th integer of first line and i\\;th integer of second line represent the x-coordinate and y-coordinate of i\\;th stone respectively. in short, (x[i], y[i]) is where i\\;th stone is placed at.\n\nOutput:\n\nPrint the minimum number of moves required to move all stone to the corners.\n\nConstraints:\n\n1 ≤ N ≤ 10^6 \n\n1 ≤ k ≤ 10^5 \n\nSAMPLE INPUT\n3 4\r\n2 2 1 3\r\n2 2 3 1\r\n\nSAMPLE OUTPUT\n4\n\nExplanation\n\nFor the two stones lying on the 2,2 cell you can place any of them on any of the two unfilled corner in 2 moves each."}}},{"rowIdx":75,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"3\\n0 0 1\\n0 0 1\\n1 1 0\\n\",\n \"4\\n0 1 1 1\\n1 0 1 1\\n1 1 0 1\\n1 1 1 0\\n\",\n \"3\\n0 0 0\\n0 0 1\\n0 1 0\\n\",\n \"4\\n0 0 1 0\\n0 0 0 1\\n1 0 0 0\\n0 1 0 0\\n\",\n \"4\\n0 0 0 1\\n0 0 0 0\\n0 0 0 1\\n1 0 1 0\\n\",\n \"10\\n0 0 0 0 0 0 1 0 0 0\\n0 0 0 0 0 0 0 0 0 0\\n0 0 0 1 0 0 0 0 0 0\\n0 0 1 0 0 0 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The points are situated in such a way that they form a regular polygon (marked points are its vertices, and they are numbered in counter-clockwise order). You can draw n - 1 segments, each connecting any two marked points, in such a way that all points have to be connected with each other (directly or indirectly).\n\nBut there are some restrictions. Firstly, some pairs of points cannot be connected directly and have to be connected undirectly. Secondly, the segments you draw must not intersect in any point apart from the marked points (that is, if any two segments intersect and their intersection is not a marked point, then the picture you have drawn is invalid).\n\nHow many ways are there to connect all vertices with n - 1 segments? Two ways are considered different iff there exist some pair of points such that a segment is drawn between them in the first way of connection, but it is not drawn between these points in the second one. Since the answer might be large, output it modulo 109 + 7.\n\nInput\n\nThe first line contains one number n (3 ≤ n ≤ 500) — the number of marked points.\n\nThen n lines follow, each containing n elements. ai, j (j-th element of line i) is equal to 1 iff you can connect points i and j directly (otherwise ai, j = 0). It is guaranteed that for any pair of points ai, j = aj, i, and for any point ai, i = 0.\n\nOutput\n\nPrint the number of ways to connect points modulo 109 + 7.\n\nExamples\n\nInput\n\n3\n0 0 1\n0 0 1\n1 1 0\n\n\nOutput\n\n1\n\n\nInput\n\n4\n0 1 1 1\n1 0 1 1\n1 1 0 1\n1 1 1 0\n\n\nOutput\n\n12\n\n\nInput\n\n3\n0 0 0\n0 0 1\n0 1 0\n\n\nOutput\n\n0"}}},{"rowIdx":76,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"8 3\\n2 0\\n7 0\\n8 3\\n\",\n \"8 2\\n2 0\\n7 0\\n\",\n \"99999999 20\\n3 100000000\\n14 100000000\\n22 100000000\\n24 100000000\\n31 100000000\\n41 100000000\\n46 100000000\\n84 100000000\\n94 100000000\\n98 100000000\\n99999912 100000000\\n99999915 100000000\\n99999916 100000000\\n99999923 100000000\\n99999935 100000000\\n99999937 100000000\\n99999954 100000000\\n99999955 100000000\\n99999979 100000000\\n99999982 100000000\\n\",\n \"1 1\\n1 2\\n\",\n \"10 10\\n1 0\\n2 0\\n3 0\\n4 0\\n5 1\\n6 2\\n7 3\\n8 2\\n9 3\\n10 4\\n\",\n \"3 2\\n1 0\\n3 0\\n\",\n 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100000000\\n24 100000000\\n31 100000000\\n41 100100000\\n46 000000000\\n84 100000000\\n94 100000000\\n98 100000000\\n99999912 100000000\\n99999915 100000000\\n99999916 100000000\\n99999923 100000000\\n12733231 100000000\\n99999937 100000000\\n99999954 100000000\\n99999955 100000000\\n99999979 100000000\\n99999982 100000000\\n\",\n \"35 10\\n5 17\\n7 15\\n10 4\\n22 11\\n18 13\\n14 15\\n39 5\\n34 13\\n40 15\\n49 16\\n\",\n \"100000100 2\\n50000000 100000100\\n54463944 100000000\\n\",\n \"10001 2\\n7513 1571461\\n8270 1605287\\n\",\n \"100 50\\n1 53\\n3 51\\n4 50\\n6 48\\n9 45\\n12 48\\n14 46\\n16 48\\n17 47\\n19 49\\n20 48\\n22 46\\n23 45\\n24 44\\n26 46\\n27 47\\n29 49\\n32 59\\n33 53\\n35 55\\n37 53\\n40 50\\n41 51\\n43 53\\n47 57\\n50 60\\n51 40\\n78 60\\n57 65\\n59 63\\n60 62\\n61 61\\n62 60\\n64 62\\n57 66\\n70 64\\n71 63\\n73 65\\n77 69\\n79 67\\n81 65\\n83 63\\n86 66\\n88 68\\n89 69\\n91 67\\n94 64\\n95 63\\n98 60\\n100 58\\n\",\n \"10011 2\\n1812 897970\\n8270 484536\\n\",\n \"190877881 20\\n3 100000000\\n14 100000000\\n22 100000000\\n24 100000000\\n31 100000000\\n41 100100000\\n46 000000000\\n84 100000000\\n94 100000000\\n98 100000000\\n99999912 100000000\\n99999915 100000000\\n99999916 100000000\\n99999923 100000000\\n23060190 100000000\\n99999937 100000000\\n99999954 100000000\\n99999955 100000000\\n99999979 100000000\\n99999982 100000000\\n\",\n \"35 10\\n5 17\\n7 15\\n10 4\\n22 11\\n17 13\\n14 15\\n39 5\\n34 13\\n40 15\\n49 16\\n\",\n \"100000100 2\\n50000000 100000100\\n54463944 101000000\\n\"\n ],\n \"outputs\": [\n \"IMPOSSIBLE\",\n \"2\",\n \"149999907\",\n \"2\",\n \"4\",\n \"1\",\n \"190216165\",\n \"IMPOSSIBLE\",\n \"6\",\n \"IMPOSSIBLE\",\n \"10\",\n \"99999999\",\n \"100\",\n \"10\",\n \"9999999\",\n \"IMPOSSIBLE\",\n \"199999999\",\n \"42\",\n \"5\",\n \"149999999\",\n \"13\",\n \"69\",\n \"149999999\",\n \"199999999\",\n \"16160178\",\n \"901239\",\n \"190877899\\n\",\n \"194685802\\n\",\n \"2\\n\",\n \"IMPOSSIBLE\\n\",\n \"109999999\\n\",\n \"0\\n\",\n \"6\\n\",\n \"10000000\\n\",\n \"199999999\\n\",\n \"150499999\\n\",\n \"150000099\\n\",\n \"209999999\\n\",\n \"29243772\\n\",\n \"901239\\n\",\n \"110000000\\n\",\n \"151000099\\n\",\n \"29243776\\n\",\n \"110000001\\n\",\n \"149999999\\n\",\n \"1\\n\",\n \"190216175\\n\",\n \"14\\n\",\n \"7\\n\",\n \"150004999\\n\",\n \"150000000\\n\",\n \"200999999\\n\",\n \"7454610\\n\",\n \"195685802\\n\",\n \"29243771\\n\",\n \"902314\\n\",\n \"110000100\\n\",\n \"190226175\\n\",\n \"18\\n\",\n \"201000099\\n\",\n \"286966\\n\",\n \"195686802\\n\",\n \"903688\\n\",\n \"153809895\\n\",\n \"3\\n\",\n \"190226275\\n\",\n \"286965\\n\",\n \"186287855\\n\",\n \"200000999\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"110000000\\n\",\n \"IMPOSSIBLE\\n\",\n \"0\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"6\\n\",\n \"199999999\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"1\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"149999999\\n\",\n \"149999999\\n\",\n \"1\\n\",\n \"1\\n\",\n \"199999999\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"150000099\\n\",\n \"29243771\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"199999999\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"150000099\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"IMPOSSIBLE\\n\",\n \"150000099\\n\"\n ]\n}"},"problem":{"kind":"string","value":"A tourist hiked along the mountain range. The hike lasted for n days, during each day the tourist noted height above the sea level. On the i-th day height was equal to some integer hi. The tourist pick smooth enough route for his hike, meaning that the between any two consecutive days height changes by at most 1, i.e. for all i's from 1 to n - 1 the inequality |hi - hi + 1| ≤ 1 holds.\n\nAt the end of the route the tourist rafted down a mountain river and some notes in the journal were washed away. Moreover, the numbers in the notes could have been distorted. Now the tourist wonders what could be the maximum height during his hike. Help him restore the maximum possible value of the maximum height throughout the hike or determine that the notes were so much distorted that they do not represent any possible height values that meet limits |hi - hi + 1| ≤ 1.\n\nInput\n\nThe first line contains two space-separated numbers, n and m (1 ≤ n ≤ 108, 1 ≤ m ≤ 105) — the number of days of the hike and the number of notes left in the journal.\n\nNext m lines contain two space-separated integers di and hdi (1 ≤ di ≤ n, 0 ≤ hdi ≤ 108) — the number of the day when the i-th note was made and height on the di-th day. It is guaranteed that the notes are given in the chronological order, i.e. for all i from 1 to m - 1 the following condition holds: di < di + 1.\n\nOutput\n\nIf the notes aren't contradictory, print a single integer — the maximum possible height value throughout the whole route.\n\nIf the notes do not correspond to any set of heights, print a single word 'IMPOSSIBLE' (without the quotes).\n\nExamples\n\nInput\n\n8 2\n2 0\n7 0\n\n\nOutput\n\n2\n\n\nInput\n\n8 3\n2 0\n7 0\n8 3\n\n\nOutput\n\nIMPOSSIBLE\n\nNote\n\nFor the first sample, an example of a correct height sequence with a maximum of 2: (0, 0, 1, 2, 1, 1, 0, 1).\n\nIn the second sample the inequality between h7 and h8 does not hold, thus the information is inconsistent."}}},{"rowIdx":77,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"4\\n0 0 100 60\\n0 60 50 90\\n50 60 100 90\\n0 90 100 120\\n6\\n0 0 100 40\\n0 40 50 70\\n50 40 100 60\\n50 60 100 80\\n0 70 50 120\\n50 80 100 120\\n0\",\n \"4\\n0 0 100 60\\n0 60 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\"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n2\\n1\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n2\\n1\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n2\\n1\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n2\\n1\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n2\\n1\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\",\n \"1\\n2\\n3\\n4\\n\\n1\\n2\\n4\\n5\\n3\\n6\\n\"\n ]\n}"},"problem":{"kind":"string","value":"Yanagi is a high school student, and she is called \"Hime\" by her boyfriend who is a ninja fanboy. She likes picture books very much, so she often writes picture books by herself. She always asks you to make her picture book as an assistant. Today, you got asked to help her with making a comic.\n\nShe sometimes reads her picture books for children in kindergartens. Since Yanagi wants to let the children read, she wants to insert numbers to frames in order. Of course, such a task should be done by the assistant, you.\n\nYou want to do the task easily and fast, so you decide to write a program to output the order of reading frames based on the positions of the frames.\n\nWrite a program to print the number of order for each frame.\n\nThe comics in this problem satisfy the following rules.\n\nThe each comic is drawn on a sheet of rectangle paper. You can assume that the top side of the paper is on the x-axis. And you can assume that the right-hand side of the paper is on the y-axis. The positive direction of the x-axis is leftward. The positive direction of the y-axis is down direction. The paper is large enough to include all frames of the comic. In other words, no area in a frame is out of the paper.\n\nThe area of each frame is at least one. All sides of each frame are parallel to the x-axis or the y-axis. The frames can't overlap one another. However the frames may share the line of side.\n\nYou must decide the order to read K , where K is a set of frames, with the following steps.\n\n\nStep 1:You must choose an unread frame at the right-most position in K.\nIf you find such frames multiple, you must choose the frame at the top position among them.\nIf you can't find any unread frames, you stop reading K.\nThe frame you chose is \"Starting Frame\".\nIn step 1, you assume that the position of a frame is the top-right point of the frame.\n\n\n\nStep 2:You should draw a line from the right-bottom point of \"Starting Frame\" to leftward horizontally.\nIf the line touch the right-hand side of other frame, you should stop drawing.\nIf the line is on the side of other frame, you should not stop drawing.\nIf the line touch the edge of paper, you should stop drawing.\n\n\n\nStep 3:The set of the unread frames which are above the line ( they may be the bottom-side on the line ) drawn at Step 2 is L.\nAnd you should read L.\n\n\n\nStep 4: Go back to Step 1.\n\n\nConstraints\n\n0 < n < 10\n(x0i != x1i) and (y0i != y1i)\n0 ≤ x0i , y0i , x1i , y1i ≤ 500\n\nInput\n\nThe input consists of multiple datasets. The last dataset is followed by a line containing one zero. You don't have to process this data.\n\nEach datasets is in the following format.\n\n\nn\nx01 y01 x11 y11\nx02 y02 x12 y12\n....\nx0n y0n x1n y1n\n\n\n\nAll numbers of the datasets are integer. They are separated by a space. The first line of a dataset contains one integer. n is the number of frames of the comic. x0i , y0i , x1i , y1i are two non-neighboring points of i th frame in the line.\n\nOutput\n\nPrint n lines for each dataset. Print the number of order for ith frame in the ith line. And you should print blank line between the datasets.\nOutput format:\n\n\nnum1\nnum2\n...\nnumi\n...\nnumn\n\n\nExample\n\nInput\n\n4\n0 0 100 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 40 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0\n\n\nOutput\n\n1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6"}}},{"rowIdx":78,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"10 3 5 2\\n5 50\\n7 60\\n8 100\\n2 2 5\\n3\\n1 3\\n3\\n3\\n\",\n \"484 30 46 67\\n51 74\\n105 26\\n242 24\\n22 81\\n48 46\\n21 11\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 18\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 99\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"1444 13 49 42\\n22 1\\n306 25\\n75 9\\n132 3\\n651 83\\n25 43\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 11 59\\n1 12\\n2 5 21\\n2 13 20\\n1 66\\n1 253\\n1 60\\n3\\n3\\n3\\n1 1190\\n1 32\\n1 570\\n1 494\\n2 11 25\\n2 2 11\\n3\\n1 456\\n3\\n1 840\\n2 3 2\\n3\\n1 108\\n2 13 4\\n1 986\\n3\\n1 36\\n1 299\\n3\\n1 780\\n1 588\\n2 2 8\\n1 680\\n1 135\\n3\\n1 56\\n3\\n1 108\\n2 4 0\\n2 13 0\\n3\\n3\\n3\\n2 10 3\\n3\\n2 1 0\\n2 1 0\\n2 10 4\\n3\\n\",\n \"1444 18 45 31\\n476 56\\n176 31\\n75 47\\n810 56\\n324 13\\n220 17\\n93 36\\n84 58\\n76 58\\n1036 79\\n828 13\\n138 20\\n750 78\\n90 3\\n333 28\\n442 97\\n348 16\\n130 36\\n3\\n1 144\\n1 72\\n1 210\\n2 8 43\\n1 95\\n1 468\\n1 580\\n1 24\\n2 16 93\\n2 16 0\\n2 14 1\\n3\\n1 260\\n2 1 51\\n2 5 5\\n3\\n1 48\\n1 220\\n1 504\\n2 8 10\\n1 925\\n3\\n3\\n1 180\\n1 156\\n2 14 0\\n2 11 5\\n1 143\\n3\\n1 120\\n1 256\\n2 5 1\\n2 1 2\\n2 8 0\\n3\\n1 627\\n2 9 9\\n1 256\\n1 360\\n3\\n2 9 48\\n3\\n2 7 6\\n2 12 16\\n\",\n \"484 30 46 67\\n51 74\\n105 26\\n242 24\\n22 81\\n48 46\\n21 11\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 18\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"1444 13 37 42\\n22 1\\n306 25\\n75 9\\n132 3\\n651 83\\n25 43\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 11 59\\n1 12\\n2 5 21\\n2 13 20\\n1 66\\n1 253\\n1 60\\n3\\n3\\n3\\n1 1190\\n1 32\\n1 570\\n1 494\\n2 11 25\\n2 2 11\\n3\\n1 456\\n3\\n1 840\\n2 3 2\\n3\\n1 108\\n2 13 4\\n1 986\\n3\\n1 36\\n1 299\\n3\\n1 780\\n1 588\\n2 2 8\\n1 680\\n1 135\\n3\\n1 56\\n3\\n1 108\\n2 4 0\\n2 13 0\\n3\\n3\\n3\\n2 10 3\\n3\\n2 1 0\\n2 1 0\\n2 10 4\\n3\\n\",\n \"484 30 46 67\\n51 74\\n105 26\\n242 24\\n22 81\\n48 46\\n21 11\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 19\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"484 30 46 67\\n51 74\\n105 26\\n242 24\\n22 81\\n78 46\\n21 11\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 19\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"484 30 46 77\\n51 74\\n105 26\\n242 24\\n22 81\\n78 46\\n21 20\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 19\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"1444 13 49 42\\n22 1\\n306 25\\n75 8\\n132 3\\n651 83\\n25 43\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 11 59\\n1 12\\n2 5 21\\n2 13 20\\n1 66\\n1 253\\n1 60\\n3\\n3\\n3\\n1 1190\\n1 32\\n1 570\\n1 494\\n2 11 25\\n2 2 11\\n3\\n1 456\\n3\\n1 840\\n2 3 2\\n3\\n1 108\\n2 13 4\\n1 986\\n3\\n1 36\\n1 299\\n3\\n1 780\\n1 588\\n2 2 8\\n1 680\\n1 135\\n3\\n1 56\\n3\\n1 108\\n2 4 0\\n2 13 0\\n3\\n3\\n3\\n2 10 3\\n3\\n2 1 0\\n2 1 0\\n2 10 4\\n3\\n\",\n \"1444 18 45 31\\n476 56\\n176 31\\n75 47\\n810 56\\n324 13\\n220 17\\n93 36\\n84 47\\n76 58\\n1036 79\\n828 13\\n138 20\\n750 78\\n90 3\\n333 28\\n442 97\\n348 16\\n130 36\\n3\\n1 144\\n1 72\\n1 210\\n2 8 43\\n1 95\\n1 468\\n1 580\\n1 24\\n2 16 93\\n2 16 0\\n2 14 1\\n3\\n1 260\\n2 1 51\\n2 5 5\\n3\\n1 48\\n1 220\\n1 504\\n2 8 10\\n1 925\\n3\\n3\\n1 180\\n1 156\\n2 14 0\\n2 11 5\\n1 143\\n3\\n1 120\\n1 256\\n2 5 1\\n2 1 2\\n2 8 0\\n3\\n1 627\\n2 9 9\\n1 256\\n1 360\\n3\\n2 9 48\\n3\\n2 7 6\\n2 12 16\\n\",\n \"1444 13 37 42\\n22 1\\n306 25\\n75 9\\n132 3\\n651 83\\n25 85\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 11 59\\n1 12\\n2 5 21\\n2 13 20\\n1 66\\n1 253\\n1 60\\n3\\n3\\n3\\n1 1190\\n1 32\\n1 570\\n1 494\\n2 11 25\\n2 2 11\\n3\\n1 456\\n3\\n1 840\\n2 3 2\\n3\\n1 108\\n2 13 4\\n1 986\\n3\\n1 36\\n1 299\\n3\\n1 780\\n1 588\\n2 2 8\\n1 680\\n1 135\\n3\\n1 56\\n3\\n1 108\\n2 4 0\\n2 13 0\\n3\\n3\\n3\\n2 10 3\\n3\\n2 1 0\\n2 1 0\\n2 10 4\\n3\\n\",\n \"1444 13 37 42\\n22 1\\n306 25\\n75 9\\n132 3\\n651 83\\n25 43\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 11 59\\n1 12\\n2 5 21\\n2 13 20\\n1 66\\n1 253\\n1 60\\n3\\n3\\n3\\n1 1190\\n1 32\\n1 570\\n1 494\\n2 11 25\\n2 2 11\\n3\\n1 456\\n3\\n1 840\\n2 3 0\\n3\\n1 108\\n2 13 4\\n1 986\\n3\\n1 36\\n1 299\\n3\\n1 780\\n1 588\\n2 2 8\\n1 1308\\n1 135\\n3\\n1 56\\n3\\n1 108\\n2 4 0\\n2 13 0\\n3\\n3\\n3\\n2 10 3\\n3\\n2 1 0\\n2 1 0\\n2 10 4\\n3\\n\",\n \"484 30 46 67\\n51 74\\n105 26\\n242 24\\n22 81\\n78 46\\n21 20\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 16\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"1444 13 37 42\\n22 1\\n306 25\\n75 9\\n132 3\\n651 83\\n25 43\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 11 59\\n1 12\\n2 5 21\\n2 13 20\\n1 66\\n1 253\\n1 60\\n3\\n3\\n3\\n1 1190\\n1 32\\n1 570\\n1 494\\n2 11 25\\n2 2 10\\n3\\n1 456\\n3\\n1 840\\n2 3 0\\n3\\n1 108\\n2 13 4\\n1 986\\n3\\n1 36\\n1 299\\n3\\n1 780\\n1 588\\n2 2 8\\n1 1308\\n1 135\\n3\\n1 56\\n3\\n1 108\\n2 4 0\\n2 13 0\\n3\\n3\\n3\\n2 10 3\\n3\\n2 1 0\\n2 1 0\\n2 10 4\\n3\\n\",\n \"484 30 46 77\\n18 74\\n105 26\\n242 24\\n22 81\\n78 46\\n21 20\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 172\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 19\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 8\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"484 30 46 67\\n51 74\\n105 26\\n242 24\\n22 81\\n78 46\\n21 20\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 12\\n380 14\\n449 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 61\\n1 144\\n1 266\\n3\\n2 16 16\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"1444 13 49 42\\n22 1\\n306 25\\n75 9\\n132 3\\n651 83\\n25 43\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 11 59\\n1 12\\n2 5 39\\n2 13 20\\n1 66\\n1 253\\n1 60\\n3\\n3\\n3\\n1 1190\\n1 32\\n1 570\\n1 494\\n2 11 25\\n2 2 11\\n3\\n1 456\\n3\\n1 840\\n2 3 2\\n3\\n1 108\\n2 13 4\\n1 986\\n3\\n1 36\\n1 299\\n3\\n1 780\\n1 588\\n2 2 8\\n1 680\\n1 135\\n3\\n1 56\\n3\\n1 108\\n2 4 0\\n2 13 0\\n3\\n3\\n3\\n2 10 3\\n3\\n2 1 0\\n2 1 0\\n2 10 4\\n3\\n\",\n \"1444 18 45 31\\n476 56\\n176 31\\n75 47\\n810 56\\n324 13\\n220 17\\n93 36\\n84 58\\n76 58\\n1036 79\\n828 13\\n138 20\\n750 78\\n90 3\\n333 28\\n442 97\\n348 16\\n130 36\\n3\\n1 144\\n1 72\\n1 210\\n2 8 43\\n1 95\\n1 468\\n1 580\\n1 24\\n2 16 93\\n2 16 0\\n2 14 1\\n3\\n1 260\\n2 1 51\\n2 5 5\\n3\\n1 48\\n1 220\\n1 504\\n2 8 10\\n1 925\\n3\\n3\\n1 180\\n1 156\\n2 14 0\\n2 11 5\\n1 143\\n3\\n1 120\\n1 256\\n2 5 1\\n2 1 2\\n2 8 0\\n3\\n1 627\\n2 9 9\\n1 256\\n1 360\\n3\\n2 9 48\\n3\\n2 7 6\\n3 12 16\\n\",\n \"484 30 46 67\\n51 74\\n105 26\\n242 24\\n22 81\\n48 46\\n21 11\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 41\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 18\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"1444 13 37 42\\n22 1\\n306 25\\n75 9\\n132 3\\n89 83\\n25 85\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 11 59\\n1 12\\n2 5 21\\n2 13 20\\n1 66\\n1 253\\n1 60\\n3\\n3\\n3\\n1 1190\\n1 32\\n1 570\\n1 494\\n2 11 25\\n2 2 11\\n3\\n1 456\\n3\\n1 840\\n2 3 2\\n3\\n1 108\\n2 13 4\\n1 986\\n3\\n1 36\\n1 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32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 18\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 127\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 47\\n3\\n3\\n3\\n2 23 15\\n\",\n \"1444 18 45 31\\n476 56\\n176 31\\n75 47\\n810 56\\n324 13\\n220 17\\n93 39\\n84 47\\n76 58\\n1036 79\\n828 13\\n138 20\\n750 78\\n90 3\\n333 28\\n442 97\\n348 16\\n130 36\\n3\\n1 144\\n1 72\\n1 210\\n2 8 43\\n1 95\\n1 468\\n1 580\\n1 24\\n2 16 93\\n2 16 0\\n2 14 1\\n3\\n1 260\\n2 1 51\\n2 5 5\\n3\\n1 48\\n1 220\\n1 504\\n2 8 10\\n1 925\\n3\\n3\\n1 180\\n1 156\\n2 14 0\\n2 11 5\\n1 143\\n3\\n1 120\\n1 256\\n2 5 1\\n2 1 2\\n2 8 0\\n3\\n1 627\\n2 9 9\\n1 256\\n1 360\\n3\\n2 9 48\\n3\\n2 7 6\\n2 12 16\\n\",\n \"1444 13 37 42\\n22 1\\n306 25\\n75 9\\n132 3\\n651 83\\n25 43\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 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41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 19\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 63\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"484 30 46 77\\n18 74\\n105 26\\n242 24\\n22 81\\n78 46\\n21 20\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 19\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 233\\n1 198\\n2 25 18\\n1 108\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"484 30 46 67\\n51 74\\n105 26\\n242 24\\n22 81\\n78 46\\n21 20\\n60 74\\n161 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n449 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 6\\n245 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 16\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"484 30 46 77\\n18 74\\n105 26\\n242 24\\n22 81\\n78 46\\n21 20\\n60 74\\n160 46\\n91 3\\n39 87\\n100 55\\n294 58\\n64 22\\n380 14\\n300 33\\n143 79\\n15 24\\n2 40\\n90 54\\n323 21\\n240 8\\n147 99\\n187 16\\n25 30\\n88 32\\n130 28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 19\\n1 121\\n1 248\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 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28\\n49 98\\n45 25\\n14 41\\n260 74\\n1 144\\n1 266\\n3\\n2 16 19\\n1 121\\n1 270\\n1 28\\n1 3\\n2 24 17\\n3\\n2 17 14\\n2 12 56\\n3\\n1 80\\n1 126\\n1 6\\n2 19 0\\n1 160\\n3\\n1 128\\n1 340\\n1 130\\n1 198\\n2 25 18\\n1 80\\n3\\n1 45\\n1 126\\n1 30\\n1 63\\n3\\n3\\n1 52\\n3\\n3\\n3\\n3\\n2 18 37\\n2 13 4\\n3\\n2 25 7\\n2 10 38\\n3\\n3\\n3\\n2 23 15\\n\",\n \"1444 18 45 31\\n476 56\\n176 31\\n75 47\\n810 56\\n324 13\\n220 17\\n93 39\\n84 47\\n76 58\\n978 79\\n828 13\\n138 20\\n750 78\\n90 3\\n333 28\\n442 97\\n348 16\\n130 36\\n3\\n1 144\\n1 72\\n1 210\\n2 8 43\\n1 95\\n1 468\\n1 580\\n1 24\\n2 16 93\\n2 16 0\\n2 14 1\\n3\\n1 260\\n2 1 51\\n2 5 5\\n3\\n1 48\\n1 220\\n1 504\\n2 8 10\\n1 925\\n3\\n3\\n1 180\\n1 156\\n2 14 0\\n2 11 5\\n1 143\\n3\\n1 120\\n1 256\\n2 5 1\\n2 1 2\\n2 8 0\\n3\\n1 627\\n2 9 9\\n1 256\\n1 360\\n3\\n2 8 48\\n3\\n2 7 6\\n2 12 16\\n\",\n \"1444 13 37 42\\n22 1\\n306 25\\n75 9\\n132 1\\n89 83\\n25 85\\n352 71\\n646 37\\n740 92\\n88 19\\n408 92\\n208 93\\n136 25\\n2 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There are n cells with treasure. We call each of these n cells \"Treasure Cell\". The i-th \"Treasure Cell\" is the ai-th cell and the value of treasure in it is ci dollars.\n\nThen, Freda went in the first cell. For now, she can go just k cells forward, or return to the first cell. That means Freda was able to reach the 1st, (k + 1)-th, (2·k + 1)-th, (3·k + 1)-th cells and so on.\n\nThen Rainbow gave Freda m operations. Each operation is one of the following three types:\n\n 1. Add another method x: she can also go just x cells forward at any moment. For example, initially she has only one method k. If at some moment she has methods a1, a2, ..., ar then she can reach all the cells with number in form , where vi — some non-negative integer. \n 2. Reduce the value of the treasure in the x-th \"Treasure Cell\" by y dollars. In other words, to apply assignment cx = cx - y. \n 3. Ask the value of the most valuable treasure among the cells Freda can reach. If Freda cannot reach any cell with the treasure then consider the value of the most valuable treasure equal to 0, and do nothing. Otherwise take the most valuable treasure away. If several \"Treasure Cells\" have the most valuable treasure, take the \"Treasure Cell\" with the minimum number (not necessarily with the minimum number of cell). After that the total number of cells with a treasure is decreased by one. \n\n\n\nAs a programmer, you are asked by Freda to write a program to answer each query.\n\nInput\n\nThe first line of the input contains four integers: h (1 ≤ h ≤ 1018), n, m (1 ≤ n, m ≤ 105) and k (1 ≤ k ≤ 104).\n\nEach of the next n lines contains two integers: ai (1 ≤ ai ≤ h), ci (1 ≤ ci ≤ 109). That means the i-th \"Treasure Cell\" is the ai-th cell and cost of the treasure in that cell is ci dollars. All the ai are distinct.\n\nEach of the next m lines is in one of the three following formats:\n\n * \"1 x\" — an operation of type 1, 1 ≤ x ≤ h; \n * \"2 x y\" — an operation of type 2, 1 ≤ x ≤ n, 0 ≤ y < cx; \n * \"3\" — an operation of type 3. \n\n\n\nThere are at most 20 operations of type 1. It's guaranteed that at any moment treasure in each cell has positive value. It's guaranteed that all operations is correct (no operation can decrease the value of the taken tresure).\n\nPlease, do not use the %lld specifier to read 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.\n\nOutput\n\nFor each operation of type 3, output an integer indicates the value (in dollars) of the most valuable treasure among the \"Treasure Cells\" Freda can reach. If there is no such treasure, output 0.\n\nExamples\n\nInput\n\n10 3 5 2\n5 50\n7 60\n8 100\n2 2 5\n3\n1 3\n3\n3\n\n\nOutput\n\n55\n100\n50\n\nNote\n\nIn the sample, there are 10 cells and 3 \"Treasure Cells\". The first \"Treasure Cell\" is cell 5, having 50 dollars tresure in it. The second \"Treasure Cell\" is cell 7, having 60 dollars tresure in it. The third \"Treasure Cell\" is cell 8, having 100 dollars tresure in it.\n\nAt first, Freda can only reach cell 1, 3, 5, 7 and 9. In the first operation, we reduce the value in the second \"Treasure Cell\" from 60 to 55. Then the most valuable treasure among the \"Treasure Cells\" she can reach is max(50, 55) = 55. After the third operation, she can also go 3 cells forward each step, being able to reach cell 1, 3, 4, 5, 6, 7, 8, 9, 10. So the most valuable tresure is 100.\n\nNoticed that she took the 55 dollars and 100 dollars treasure away, so the last answer is 50."}}},{"rowIdx":79,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2 10\\n1 2\\n1 9\\n8 7\",\n \"2 10\\n1 2\\n1 9\\n6 7\",\n \"2 10\\n2 2\\n1 9\\n10 7\",\n \"1 10\\n1 2\\n1 9\\n8 7\",\n \"2 10\\n1 2\\n1 9\\n10 7\",\n \"2 20\\n2 2\\n1 9\\n10 7\",\n \"2 10\\n3 2\\n1 9\\n10 7\",\n \"1 10\\n1 2\\n0 9\\n8 7\",\n \"2 11\\n2 2\\n1 9\\n10 7\",\n \"2 13\\n3 2\\n1 9\\n10 7\",\n \"1 10\\n1 0\\n0 9\\n8 7\",\n \"2 14\\n2 2\\n1 9\\n10 7\",\n \"2 13\\n3 2\\n1 18\\n10 7\",\n \"1 13\\n1 0\\n0 9\\n8 7\",\n \"1 14\\n2 2\\n1 9\\n10 7\",\n \"2 13\\n3 2\\n1 18\\n17 7\",\n \"1 11\\n2 2\\n1 9\\n10 7\",\n \"1 11\\n2 2\\n1 9\\n0 7\",\n \"1 17\\n2 2\\n1 9\\n0 7\",\n \"1 17\\n2 2\\n1 15\\n0 7\",\n \"1 17\\n2 2\\n1 15\\n-1 7\",\n \"1 17\\n4 2\\n1 15\\n-1 7\",\n \"1 17\\n4 2\\n0 15\\n-1 7\",\n \"1 17\\n4 2\\n-1 15\\n-1 7\",\n \"1 24\\n4 2\\n-1 15\\n-1 7\",\n \"1 24\\n4 4\\n-1 15\\n-1 7\",\n \"1 24\\n4 8\\n-1 15\\n-1 7\",\n \"2 24\\n4 8\\n-1 15\\n-1 7\",\n \"2 24\\n4 8\\n-1 3\\n-1 7\",\n \"2 24\\n4 9\\n-1 3\\n-1 7\",\n \"2 24\\n4 9\\n-1 3\\n-2 7\",\n \"2 45\\n4 9\\n-1 3\\n-2 7\",\n \"2 45\\n4 9\\n-1 4\\n-2 7\",\n \"2 45\\n4 15\\n-1 4\\n-2 7\",\n \"2 45\\n4 10\\n-1 4\\n-2 7\",\n \"2 10\\n1 2\\n1 8\\n8 7\",\n \"2 10\\n2 2\\n1 9\\n3 7\",\n \"1 10\\n1 2\\n2 9\\n8 7\",\n \"2 20\\n3 2\\n1 9\\n10 7\",\n \"1 10\\n2 2\\n0 9\\n8 7\",\n \"2 11\\n2 2\\n2 9\\n10 7\",\n \"1 10\\n1 0\\n0 11\\n8 7\",\n \"2 14\\n2 2\\n2 9\\n10 7\",\n \"2 13\\n4 2\\n1 18\\n10 7\",\n \"1 8\\n1 0\\n0 9\\n8 7\",\n \"2 13\\n3 2\\n1 1\\n17 7\",\n \"1 11\\n2 2\\n1 9\\n13 7\",\n \"1 9\\n2 2\\n1 9\\n0 7\",\n \"1 17\\n2 1\\n1 9\\n0 7\",\n \"1 17\\n1 2\\n1 15\\n0 7\",\n \"1 17\\n2 3\\n1 15\\n-1 7\",\n \"2 17\\n4 2\\n1 15\\n-1 7\",\n \"1 17\\n4 2\\n0 15\\n-1 13\",\n \"1 17\\n4 4\\n-1 15\\n-1 7\",\n \"1 24\\n4 2\\n0 15\\n-1 7\",\n \"1 24\\n4 4\\n-1 15\\n-2 7\",\n \"1 24\\n4 8\\n-1 15\\n-1 5\",\n \"2 24\\n4 8\\n-1 6\\n-1 7\",\n \"2 24\\n4 13\\n-1 3\\n-1 7\",\n \"2 24\\n4 2\\n-1 3\\n-1 7\",\n \"2 24\\n4 9\\n-1 3\\n-4 7\",\n \"2 88\\n4 9\\n-1 4\\n-2 7\",\n \"2 45\\n4 26\\n-1 4\\n-2 7\",\n \"2 45\\n4 10\\n-1 4\\n-2 9\",\n \"2 10\\n1 2\\n0 8\\n8 7\",\n \"2 10\\n3 2\\n1 9\\n3 7\",\n \"1 10\\n0 2\\n0 9\\n8 7\",\n \"2 20\\n3 2\\n1 15\\n10 7\",\n \"2 11\\n2 2\\n2 14\\n10 7\",\n \"1 10\\n1 0\\n0 11\\n6 7\",\n \"2 13\\n8 2\\n1 18\\n10 7\",\n \"2 13\\n3 2\\n1 1\\n17 0\",\n \"1 11\\n2 2\\n1 9\\n13 9\",\n \"1 9\\n2 0\\n1 9\\n0 7\",\n \"1 17\\n2 1\\n1 9\\n1 7\",\n \"1 17\\n1 2\\n1 15\\n-1 7\",\n \"1 17\\n2 3\\n0 15\\n-1 7\",\n \"2 17\\n4 2\\n0 15\\n-1 7\",\n \"1 17\\n8 2\\n0 15\\n-1 7\",\n \"1 17\\n4 4\\n0 15\\n-1 7\",\n \"1 43\\n4 2\\n0 15\\n-1 7\",\n \"1 24\\n4 4\\n0 15\\n-2 7\",\n \"1 38\\n4 8\\n-1 15\\n-1 5\",\n \"2 24\\n4 8\\n-1 6\\n-1 0\",\n \"2 24\\n3 13\\n-1 3\\n-1 7\",\n \"2 48\\n4 2\\n-1 3\\n-1 7\",\n \"2 24\\n4 9\\n-1 3\\n-4 2\",\n \"2 175\\n4 9\\n-1 4\\n-2 7\",\n \"2 45\\n4 26\\n-1 4\\n-2 9\",\n \"2 10\\n1 2\\n0 8\\n5 7\",\n \"2 10\\n3 2\\n1 9\\n3 4\",\n \"2 20\\n3 3\\n1 15\\n10 7\",\n \"2 11\\n3 2\\n2 14\\n10 7\",\n \"2 13\\n8 4\\n1 18\\n10 7\",\n \"2 13\\n6 2\\n1 1\\n17 0\",\n \"1 11\\n2 2\\n1 9\\n9 9\",\n \"1 17\\n2 1\\n1 9\\n1 0\",\n \"1 17\\n1 2\\n1 29\\n-1 7\",\n \"2 17\\n4 2\\n0 13\\n-1 7\",\n \"1 17\\n8 2\\n0 15\\n-1 8\",\n \"1 17\\n1 4\\n0 15\\n-1 7\"\n ],\n \"outputs\": [\n \"2\\n1\",\n \"2\\n1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"2\\n1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"2\\n1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"2\\n1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"2\\n1\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n\",\n \"1\\n0\\n\",\n \"1\\n\",\n \"1\\n\"\n ]\n}"},"problem":{"kind":"string","value":"H: Colorful Tree\n\nStory\n\nYamiuchi (assassination) is a traditional event that is held annually in JAG summer camp. Every team displays a decorated tree in the dark and all teams' trees are compared from the point of view of their colorfulness. In this competition, it is allowed to cut the other teams’ tree to reduce its colorfulness. Despite a team would get a penalty if it were discovered that the team cuts the tree of another team, many teams do this obstruction.\n\nYou decided to compete in Yamiuchi and write a program that maximizes the colorfulness of your team’s tree. The program has to calculate maximum scores for all subtrees in case the other teams cut your tree.\n\nProblem Statement\n\nYou are given a rooted tree G with N vertices indexed with 1 through N. The root is vertex 1. There are K kinds of colors indexed with 1 through K. You can paint vertex i with either color c_i or d_i. Note that c_i = d_i may hold, and if so you have to paint vertex i with c_i (=d_i).\n\nLet the colorfulness of tree T be the number of different colors in T. Your task is to write a program that calculates maximum colorfulness for all rooted subtrees. Note that coloring for each rooted subtree is done independently, so previous coloring does not affect to other coloring.\n\nInput\n\n\nN K\nu_1 v_1\n:\nu_{N-1} v_{N-1}\nc_1 d_1\n:\nc_N d_N\n\n\nThe first line contains two integers N and K in this order.\n\nThe following N-1 lines provide information about the edges of G. The i-th line of them contains two integers u_i and v_i, meaning these two vertices are connected with an edge.\n\nThe following N lines provide information about color constraints. The i-th line of them contains two integers c_i and d_i explained above.\n\nConstraints\n\n* 1 \\leq N \\leq 10^5\n* 1 \\leq K \\leq 2\\times 10^5\n* 1 \\leq u_i , v_i \\leq N\n* 1 \\leq c_i , d_i \\leq K\n* The input graph is a tree.\n* All inputs are integers.\n\n\n\nOutput\n\nOutput N lines.\n\nThe i-th line of them contains the maximum colorfulness of the rooted subtree of G whose root is i.\n\nSample Input 1\n\n\n2 10\n1 2\n1 9\n8 7\n\n\nOutput for Sample Input 1\n\n\n2\n1\n\n\nSample Input 2\n\n\n3 2\n1 2\n1 3\n1 2\n1 1\n1 2\n\n\nOutput for Sample Input 2\n\n\n2\n1\n1\n\n\nNote that two color options of a vertex can be the same.\n\nSample Input 3\n\n\n5 100000\n4 3\n3 5\n1 3\n2 1\n3 2\n1 3\n2 1\n4 2\n1 4\n\n\nOutput for Sample Input 3\n\n\n4\n1\n3\n1\n1\n\n\n\n\n\n\nExample\n\nInput\n\n2 10\n1 2\n1 9\n8 7\n\n\nOutput\n\n2\n1"}}},{"rowIdx":80,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"A?\\n?\\n3\\n\",\n \"A\\nB\\n10\\n\",\n \"AAAAAAAAAAAAAAAAAAAAA\\n?\\n300000\\n\",\n \"?\\n?\\n300000\\n\",\n \"ABB\\nAB\\n129133\\n\",\n \"A\\n?\\n10\\n\",\n \"A\\nA\\n300000\\n\",\n \"??\\n??\\n1\\n\",\n \"AAAAA\\nAAAAA\\n13\\n\",\n \"?????\\n?????\\n5\\n\",\n \"A\\nB\\n300000\\n\",\n \"AB????\\nAB\\n300000\\n\",\n \"??B?\\n?A?\\n5\\n\",\n \"ABB\\nAB\\n17767\\n\",\n \"A\\n?\\n5\\n\",\n \"A\\nA\\n129338\\n\",\n \"B\\nB\\n300000\\n\",\n \"??B?\\n?B?\\n5\\n\",\n \"B\\nA\\n300000\\n\",\n \"??\\n??\\n2\\n\",\n \"BAAAA\\nAAAAA\\n13\\n\",\n \"??B?\\n?A?\\n3\\n\",\n \"A?\\n?\\n2\\n\",\n \"A\\nB\\n11\\n\",\n \"BBB\\nAB\\n17767\\n\",\n \"A\\nA\\n50011\\n\",\n \"B\\nB\\n284315\\n\",\n \"??B?\\n?A?\\n4\\n\",\n \"A\\nB\\n50011\\n\",\n \"BBA\\nAA\\n14403\\n\",\n \"BBB\\nBA\\n17860\\n\",\n \"BBB\\nBA\\n32655\\n\",\n \"BBB\\nBA\\n40596\\n\",\n \"BBB\\nBA\\n71722\\n\",\n \"A\\nA\\n91043\\n\",\n \"AAAAA\\nAAAAA\\n2\\n\",\n \"?????\\n?????\\n9\\n\",\n \"A\\nB\\n7\\n\",\n \"A\\nA\\n127479\\n\",\n \"??B?\\n?B?\\n2\\n\",\n \"AB????\\nBB\\n232077\\n\",\n \"??B?\\n?A?\\n2\\n\",\n \"A\\nA\\n73515\\n\",\n \"B\\nB\\n95746\\n\",\n \"BBB\\nBA\\n10899\\n\",\n \"A\\nB\\n36831\\n\",\n \"AB@???\\nAB\\n300000\\n\",\n \"ABB\\nBA\\n17767\\n\",\n \"AB@@??\\nAB\\n300000\\n\",\n \"??B?\\n??B\\n5\\n\",\n \"BBA\\nAB\\n17767\\n\",\n \"BBA\\nBA\\n17767\\n\",\n \"AAAAAAAAAAAAAAAAAAABA\\n?\\n300000\\n\",\n \"ABA\\nAB\\n129133\\n\",\n \"AB????\\nAB\\n232077\\n\",\n \"BBA\\nAB\\n14403\\n\",\n \"BBA\\nBA\\n10899\\n\",\n \"AAAAAAAAAAAAAAAAAAABB\\n?\\n300000\\n\",\n \"AAAAB\\nAAAAA\\n13\\n\",\n \"????BA\\nAB\\n232077\\n\",\n \"BBB\\nBA\\n17767\\n\",\n \"BBA\\nAB\\n10899\\n\",\n \"AAAAAAAAAAAAAAAAAAABB\\n@\\n300000\\n\",\n \"BBA\\nAB\\n11749\\n\",\n \"BAB\\nAB\\n11749\\n\",\n \"BAB\\nAB\\n10435\\n\",\n \"ABB\\nAB\\n10435\\n\",\n \"ABB\\nBA\\n10435\\n\",\n \"ABB\\nBA\\n9755\\n\",\n \"BBA\\nBA\\n9755\\n\",\n \"BAA\\nBA\\n9755\\n\",\n \"BAA\\nBA\\n1604\\n\",\n \"AAAAAAAAAAABAAAAAAAAA\\n?\\n300000\\n\",\n \"BBA\\nAB\\n129133\\n\",\n \"AB????\\nBA\\n300000\\n\",\n \"AB@???\\nBA\\n300000\\n\",\n \"BBA\\nAB\\n35150\\n\",\n \"AB@@?>\\nAB\\n300000\\n\",\n \"?B??\\n??B\\n5\\n\",\n \"BBA\\nBA\\n29015\\n\",\n \"AAAAAAAAAAAAAAAAAAABA\\n@\\n300000\\n\",\n \"ABA\\nBA\\n129133\\n\",\n \"BABAA\\nAAAAA\\n13\\n\",\n \"ABB\\nAA\\n14403\\n\",\n \"AAAAAAAAAAAAAAAAAAABB\\n>\\n300000\\n\",\n \"??B?\\n?A?\\n1\\n\"\n ],\n \"outputs\": [\n \"2\\n\",\n \"2046\\n\",\n \"690646514\\n\",\n \"273052679\\n\",\n \"0\\n\",\n \"4188162\\n\",\n \"276200851\\n\",\n \"40\\n\",\n \"268369924\\n\",\n \"194192\\n\",\n \"360325492\\n\",\n \"0\\n\",\n \"78\\n\",\n \"0\\n\",\n \"3906\\n\",\n \"651187684\\n\",\n \"276200851\\n\",\n \"64\\n\",\n \"360325492\\n\",\n \"224\\n\",\n \"16382\\n\",\n \"32\\n\",\n \"2\\n\",\n \"4094\\n\",\n \"345650929\\n\",\n \"69201863\\n\",\n \"716784524\\n\",\n \"78\\n\",\n \"405686776\\n\",\n \"683312777\\n\",\n \"477257680\\n\",\n \"695973257\\n\",\n \"885189464\\n\",\n \"345642627\\n\",\n \"318152748\\n\",\n \"36\\n\",\n \"34487472\\n\",\n \"254\\n\",\n \"1840485\\n\",\n \"20\\n\",\n \"451637407\\n\",\n \"22\\n\",\n \"71746714\\n\",\n \"863864606\\n\",\n \"674534832\\n\",\n \"860757795\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"64\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"16382\\n\",\n \"0\\n\",\n \"345650929\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"64\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"16382\\n\",\n \"683312777\\n\",\n \"0\\n\",\n \"0\\n\"\n ]\n}"},"problem":{"kind":"string","value":"Igor the analyst is at work. He learned about a feature in his text editor called \"Replace All\". Igor is too bored at work and thus he came up with the following problem:\n\nGiven two strings x and y which consist of the English letters 'A' and 'B' only, a pair of strings (s, t) is called good if:\n\n * s and t consist of the characters '0' and '1' only.\n * 1 ≤ |s|, |t| ≤ n, where |z| denotes the length of string z, and n is a fixed positive integer.\n * If we replace all occurrences of 'A' in x and y with the string s, and replace all occurrences of 'B' in x and y with the string t, then the two obtained from x and y strings are equal. \n\n\n\nFor example, if x = AAB, y = BB and n = 4, then (01, 0101) is one of good pairs of strings, because both obtained after replacing strings are \"01010101\".\n\nThe flexibility of a pair of strings x and y is the number of pairs of good strings (s, t). The pairs are ordered, for example the pairs (0, 1) and (1, 0) are different.\n\nYou're given two strings c and d. They consist of characters 'A', 'B' and '?' only. Find the sum of flexibilities of all possible pairs of strings (c', d') such that c' and d' can be obtained from c and d respectively by replacing the question marks with either 'A' or 'B', modulo 109 + 7.\n\nInput\n\nThe first line contains the string c (1 ≤ |c| ≤ 3·105).\n\nThe second line contains the string d (1 ≤ |d| ≤ 3·105).\n\nThe last line contains a single integer n (1 ≤ n ≤ 3·105).\n\nOutput\n\nOutput a single integer: the answer to the problem, modulo 109 + 7.\n\nExamples\n\nInput\n\nA?\n?\n3\n\n\nOutput\n\n2\n\n\nInput\n\nA\nB\n10\n\n\nOutput\n\n2046\n\nNote\n\nFor the first sample, there are four possible pairs of (c', d').\n\nIf (c', d') = (AA, A), then the flexibility is 0.\n\nIf (c', d') = (AB, A), then the flexibility is 0.\n\nIf (c', d') = (AA, B), then the flexibility is 2, as the pairs of binary strings (1, 11), (0, 00) are the only good pairs.\n\nIf (c', d') = (AB, B), then the flexibility is 0.\n\nThus, the total flexibility is 2.\n\nFor the second sample, there are 21 + 22 + ... + 210 = 2046 possible binary strings of length not greater 10, and the set of pairs of good strings is precisely the set of pairs (s, s), where s is a binary string of length not greater than 10."}}},{"rowIdx":81,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"5 1\\n2 1 3 2\\n2 1 2 2\\n0 0\",\n \"5 1\\n2 1 3 2\\n2 1 2 2\\n0 1\",\n \"5 1\\n2 1 5 2\\n2 1 2 2\\n0 1\",\n \"5 1\\n1 1 5 2\\n2 1 2 2\\n0 1\",\n \"5 1\\n1 1 0 2\\n2 1 2 2\\n0 1\",\n \"5 1\\n2 1 3 2\\n2 1 4 2\\n0 1\",\n \"5 1\\n2 1 1 2\\n2 1 2 2\\n0 1\",\n \"5 1\\n1 1 5 1\\n2 1 2 0\\n0 1\",\n \"5 1\\n1 1 1 2\\n4 1 2 2\\n0 1\",\n \"5 1\\n1 1 10 1\\n2 -1 2 0\\n0 2\",\n \"5 1\\n2 1 5 3\\n2 1 2 2\\n0 1\",\n \"5 1\\n3 1 3 2\\n2 1 4 2\\n0 1\",\n \"5 1\\n2 1 2 2\\n3 1 2 2\\n0 1\",\n \"5 1\\n3 2 3 2\\n2 1 2 2\\n0 0\",\n \"5 1\\n5 1 3 2\\n2 1 4 2\\n0 1\",\n \"4 1\\n1 1 1 2\\n6 1 2 2\\n0 1\",\n \"8 1\\n1 2 5 1\\n2 0 2 0\\n0 1\",\n \"8 1\\n1 2 7 1\\n2 0 2 0\\n0 1\",\n \"5 1\\n8 1 3 2\\n2 0 4 2\\n0 1\",\n \"4 1\\n8 1 3 2\\n2 0 4 2\\n0 1\",\n \"5 1\\n3 2 1 2\\n2 0 3 2\\n0 1\",\n \"5 1\\n3 3 1 2\\n2 0 3 2\\n0 1\",\n \"5 1\\n2 1 5 2\\n4 1 2 2\\n0 1\",\n \"5 1\\n2 1 5 1\\n2 0 2 0\\n0 1\",\n \"5 1\\n1 2 10 1\\n2 -1 2 0\\n0 2\",\n \"9 1\\n1 2 7 1\\n2 0 2 0\\n0 1\",\n \"5 1\\n1 1 17 1\\n2 0 2 2\\n0 1\",\n \"5 1\\n3 5 1 2\\n2 1 3 7\\n0 1\",\n \"3 1\\n2 1 5 2\\n4 1 2 2\\n0 1\",\n \"5 1\\n1 1 5 4\\n2 1 2 3\\n0 1\",\n \"5 1\\n4 1 5 3\\n2 1 2 2\\n0 2\",\n \"9 1\\n1 3 7 1\\n2 0 2 0\\n0 1\",\n \"5 1\\n1 2 17 1\\n2 0 2 2\\n0 1\",\n \"5 1\\n1 1 10 4\\n2 1 2 3\\n0 1\",\n \"5 1\\n6 1 3 2\\n4 0 4 2\\n0 0\",\n \"5 1\\n8 2 3 2\\n3 1 2 2\\n0 1\",\n \"5 1\\n1 1 11 4\\n2 1 2 3\\n0 1\",\n \"8 1\\n2 1 9 1\\n2 1 2 0\\n0 1\",\n \"5 1\\n2 1 7 2\\n2 1 2 2\\n0 1\",\n \"5 1\\n1 1 5 2\\n2 1 2 0\\n0 1\",\n \"5 1\\n1 1 0 2\\n4 1 2 2\\n0 1\",\n \"5 1\\n2 1 1 2\\n3 1 2 2\\n0 1\",\n \"5 1\\n1 1 5 1\\n2 0 2 0\\n0 1\",\n \"5 1\\n1 1 0 2\\n4 0 2 2\\n0 1\",\n \"5 1\\n1 1 5 1\\n2 0 2 0\\n0 2\",\n \"5 1\\n1 1 1 2\\n4 0 2 2\\n0 1\",\n \"5 1\\n1 1 5 1\\n2 -1 2 0\\n0 2\",\n \"5 1\\n1 1 10 1\\n2 0 2 0\\n0 2\",\n \"5 1\\n1 1 10 1\\n3 0 2 0\\n0 2\",\n \"5 1\\n1 1 10 1\\n3 0 2 0\\n0 1\",\n \"5 1\\n2 2 3 2\\n2 1 2 2\\n0 0\",\n \"5 1\\n2 1 3 2\\n2 1 2 0\\n0 1\",\n \"5 1\\n1 1 5 2\\n2 1 2 1\\n0 1\",\n \"5 1\\n1 1 0 2\\n4 1 2 2\\n0 2\",\n \"5 1\\n1 1 1 2\\n6 1 2 2\\n0 1\",\n \"5 1\\n1 2 5 1\\n2 0 2 0\\n0 1\",\n \"5 1\\n1 1 0 2\\n4 0 1 2\\n0 1\",\n \"5 1\\n1 1 0 1\\n2 0 2 0\\n0 2\",\n \"5 1\\n1 1 1 2\\n7 0 2 2\\n0 1\",\n \"5 1\\n1 1 10 1\\n3 0 2 1\\n0 1\",\n \"5 1\\n1 1 5 2\\n2 1 2 1\\n0 0\",\n \"5 1\\n0 1 0 2\\n4 1 2 2\\n0 2\",\n \"5 1\\n1 1 0 2\\n4 0 1 2\\n0 2\",\n \"5 1\\n1 1 10 1\\n2 0 2 1\\n0 1\",\n \"5 1\\n3 2 3 2\\n2 0 2 2\\n0 0\",\n \"5 1\\n5 1 3 2\\n2 0 4 2\\n0 1\",\n \"5 1\\n1 2 5 2\\n2 1 2 1\\n0 0\",\n \"5 1\\n0 1 0 2\\n4 1 2 3\\n0 2\",\n \"5 1\\n1 1 0 2\\n4 0 1 2\\n0 4\",\n \"5 1\\n1 1 10 1\\n2 0 2 2\\n0 1\",\n \"5 1\\n3 2 3 2\\n2 0 3 2\\n0 0\",\n \"5 1\\n1 2 5 2\\n2 2 2 1\\n0 0\",\n \"5 1\\n0 1 0 2\\n2 1 2 3\\n0 2\",\n \"5 1\\n1 1 0 1\\n4 0 1 2\\n0 4\",\n \"5 1\\n1 1 10 1\\n2 0 1 2\\n0 1\",\n \"5 1\\n3 2 3 2\\n2 0 3 2\\n0 1\",\n \"5 1\\n0 2 0 2\\n2 1 2 3\\n0 2\",\n \"5 1\\n1 1 0 1\\n4 0 2 2\\n0 4\",\n \"5 1\\n1 1 10 1\\n2 1 1 2\\n0 1\",\n \"5 1\\n0 3 0 2\\n2 1 2 3\\n0 2\",\n \"5 1\\n0 1 0 1\\n4 0 2 2\\n0 4\",\n \"5 1\\n0 3 0 3\\n2 1 2 3\\n0 2\",\n \"8 1\\n0 1 0 1\\n4 0 2 2\\n0 4\",\n \"5 1\\n3 3 1 2\\n2 0 3 4\\n0 1\",\n \"5 1\\n0 4 0 3\\n2 1 2 3\\n0 2\",\n \"8 1\\n0 1 0 1\\n4 0 2 2\\n0 1\",\n \"5 1\\n3 3 1 2\\n2 0 3 7\\n0 1\",\n \"8 1\\n0 2 0 1\\n4 0 2 2\\n0 1\",\n \"5 1\\n3 3 1 2\\n2 1 3 7\\n0 1\",\n \"5 1\\n2 1 3 1\\n2 1 2 2\\n0 0\",\n \"5 1\\n2 1 3 2\\n3 1 2 2\\n0 1\",\n \"5 1\\n1 1 5 2\\n2 1 2 3\\n0 1\",\n \"5 1\\n1 1 0 2\\n4 1 2 4\\n0 1\",\n \"5 1\\n2 1 1 2\\n3 1 2 2\\n0 2\",\n \"5 1\\n1 1 5 1\\n2 2 2 0\\n0 1\",\n \"5 1\\n1 1 1 2\\n4 1 3 2\\n0 1\",\n \"5 1\\n1 1 0 2\\n1 0 2 2\\n0 1\",\n \"5 1\\n1 1 2 1\\n2 0 2 0\\n0 2\",\n \"5 1\\n1 1 1 2\\n6 0 2 2\\n0 1\",\n \"5 1\\n1 1 10 1\\n4 0 2 0\\n0 2\",\n \"10 1\\n1 1 10 1\\n3 0 2 0\\n0 1\"\n ],\n \"outputs\": [\n \"4.18\",\n \"4.175570504585\\n\",\n \"6.175570504585\\n\",\n \"5.175570504585\\n\",\n \"1.000000000000\\n\",\n \"3.351141009170\\n\",\n \"2.175570504585\\n\",\n \"4.000000000000\\n\",\n \"1.175570504585\\n\",\n \"9.000000000000\\n\",\n \"7.351141009170\\n\",\n \"3.526711513755\\n\",\n \"2.351141009170\\n\",\n \"0.000000000000\\n\",\n \"5.526711513755\\n\",\n \"1.414213562373\\n\",\n \"4.765366864730\\n\",\n \"6.765366864730\\n\",\n \"8.526711513755\\n\",\n \"9.242640687119\\n\",\n \"2.000000000000\\n\",\n \"3.175570504585\\n\",\n \"5.351141009170\\n\",\n \"3.000000000000\\n\",\n \"10.175570504585\\n\",\n \"6.684040286651\\n\",\n \"16.000000000000\\n\",\n \"4.351141009170\\n\",\n \"6.464101615138\\n\",\n \"6.351141009170\\n\",\n \"9.351141009170\\n\",\n \"7.368080573303\\n\",\n \"17.175570504585\\n\",\n \"11.351141009170\\n\",\n \"6.526711513755\\n\",\n \"5.000000000000\\n\",\n \"12.351141009170\\n\",\n 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\"1.000000000000\\n\",\n \"9.000000000000\\n\",\n \"0.000000000000\\n\",\n \"0.000000000000\\n\",\n \"0.000000000000\\n\",\n \"0.000000000000\\n\",\n \"3.175570504585\\n\",\n \"0.000000000000\\n\",\n \"0.000000000000\\n\",\n \"3.175570504585\\n\",\n \"0.000000000000\\n\",\n \"3.175570504585\\n\",\n \"1.000000000000\\n\",\n \"3.351141009170\\n\",\n \"5.175570504585\\n\",\n \"1.000000000000\\n\",\n \"2.175570504585\\n\",\n \"4.000000000000\\n\",\n \"1.175570504585\\n\",\n \"1.000000000000\\n\",\n \"1.000000000000\\n\",\n \"1.175570504585\\n\",\n \"9.000000000000\\n\",\n \"9.000000000000\\n\"\n ]\n}"},"problem":{"kind":"string","value":"In a forest, there lived a spider named Tim. Tim was so smart that he created a huge, well-structured web. Surprisingly, his web forms a set of equilateral and concentric N-sided polygons whose edge lengths form an arithmetic sequence.\n\n\n\nFigure 1: An example web of Tim\n\nCorresponding vertices of the N-sided polygons lie on a straight line, each apart from neighboring ver- tices by distance 1. Neighboring vertices are connected by a thread (shown in the figure as solid lines), on which Tim can walk (you may regard Tim as a point). Radial axes are numbered from 1 to N in a rotational order, so you can denote by (r, i) the vertex on axis i and apart from the center of the web by distance r. You may consider the web as infinitely large, i.e. consisting of infinite number of N-sided polygons, since the web is so gigantic.\n\nTim’s web is thus marvelous, but currently has one problem: due to rainstorms, some of the threads are damaged and Tim can’t walk on those parts.\n\nNow, a bug has been caught on the web. Thanks to the web having so organized a structure, Tim accu- rately figures out where the bug is, and heads out for that position. You, as a biologist, are interested in whether Tim is smart enough to move through the shortest possible route. To judge that, however, you need to know the length of the shortest route yourself, and thereby decided to write a program which calculates that length.\n\n\n\nInput\n\nThe input consists of multiple test cases. Each test case begins with a line containing two integers N (3 ≤ N ≤ 100) and X (0 ≤ X ≤ 100), where N is as described above and X denotes the number of damaged threads. Next line contains four integers rS, iS, rT, and iT, meaning that Tim is starting at (rS, iS) and the bug is at (rT, iT). This line is followed by X lines, each containing four integers rA, iA, rB, and iB, meaning that a thread connecting (rA, iA) and (rB, iB) is damaged. Here (rA, iA) and (rB, iB) will be always neighboring to each other. Also, for all vertices (r, i) given above, you may assume 1 ≤ r ≤ 107 and 1 ≤ i ≤ N.\n\nThere will be at most 200 test cases. You may also assume that Tim is always able to reach where the bug is.\n\nThe input is terminated by a line containing two zeros.\n\nOutput\n\nFor each test case, print the length of the shortest route in a line. You may print any number of digits after the decimal point, but the error must not be greater than 0.01.\n\nExample\n\nInput\n\n5 1\n2 1 3 2\n2 1 2 2\n0 0\n\n\nOutput\n\n4.18"}}},{"rowIdx":82,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2 2 2 1\\n0 0 0\",\n \"2 2 2 0\\n0 0 0\",\n \"2 1 2 0\\n-1 -1 0\",\n \"2 0 2 0\\n-1 0 0\",\n \"4 2 2 0\\n0 0 1\",\n \"3 1 2 0\\n-1 0 -1\",\n \"1 2 1 0\\n-2 -1 0\",\n \"2 2 3 0\\n-1 -1 -1\",\n \"1 1 4 0\\n0 1 -1\",\n \"3 2 0 0\\n-1 -1 -1\",\n \"1 0 1 0\\n0 1 -1\",\n \"1 -1 1 0\\n0 1 -1\",\n \"1 0 0 0\\n0 0 -1\",\n \"1 1 1 0\\n0 0 -1\",\n \"1 2 0 0\\n0 0 -1\",\n \"1 2 4 0\\n-1 -1 0\",\n \"-1 2 0 0\\n-2 0 -1\",\n \"2 1 2 1\\n0 0 0\",\n \"1 2 8 0\\n-1 -1 0\",\n \"1 -2 1 0\\n-1 0 -1\",\n \"2 3 3 0\\n0 0 -1\",\n \"2 2 8 0\\n-1 -1 -1\",\n \"4 1 4 0\\n0 2 0\",\n \"8 1 4 0\\n0 2 -1\",\n \"8 1 6 0\\n0 2 0\",\n \"8 2 6 0\\n0 2 0\",\n \"13 2 6 0\\n0 2 0\",\n \"13 2 12 0\\n0 2 0\",\n \"13 2 22 0\\n-1 2 0\",\n \"26 2 22 0\\n-1 2 0\",\n \"36 2 22 0\\n-1 2 0\",\n \"36 2 43 0\\n-1 2 0\",\n \"5 2 43 0\\n-1 2 0\",\n \"0 4 -1 0\\n1 -2 -1\",\n \"5 2 47 0\\n-1 4 0\",\n \"5 4 47 0\\n-1 4 0\",\n \"5 8 47 0\\n-1 4 0\",\n \"5 8 88 0\\n-1 4 0\",\n \"3 8 88 0\\n-2 8 -1\",\n \"3 9 88 0\\n-2 8 -1\",\n \"3 9 82 0\\n-2 8 -1\",\n \"3 4 1 0\\n-1 -1 -1\",\n \"4 3 3 0\\n-1 0 1\",\n \"7 1 2 0\\n-1 0 1\",\n \"6 2 2 0\\n0 0 2\",\n \"4 4 2 0\\n0 -1 -2\",\n \"15 1 4 0\\n0 2 -1\",\n \"36 2 44 0\\n-1 2 0\",\n \"10 2 43 0\\n-1 2 0\",\n \"5 2 37 0\\n-1 4 0\",\n \"3 8 47 0\\n-1 4 0\",\n \"5 8 35 0\\n-1 4 0\",\n \"9 8 88 0\\n-2 8 -1\",\n \"0 9 82 0\\n-2 8 -1\",\n \"1 9 82 0\\n-2 8 -1\",\n \"5 4 1 0\\n-1 -1 -1\",\n \"4 2 1 1\\n0 0 0\",\n \"6 2 6 0\\n-1 0 1\",\n \"1 5 2 0\\n-2 1 0\",\n \"0 3 13 0\\n-1 1 2\",\n \"2 2 2 0\\n-1 0 0\",\n \"2 2 2 0\\n-1 -1 0\",\n \"2 1 2 0\\n-1 0 0\",\n \"2 2 2 0\\n0 0 1\",\n \"1 2 2 0\\n-1 -1 0\",\n \"2 1 2 0\\n-1 -1 1\",\n \"2 1 2 0\\n-1 0 -1\",\n \"2 0 2 0\\n0 0 0\",\n \"1 2 2 0\\n-2 -1 0\",\n \"1 2 2 0\\n0 0 1\",\n \"3 1 2 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1 5 1 2 1 1 4 1 1 5 2 2 1 1 2 4\\n\",\n \"18 1\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\",\n \"18 1\\n8 2 3 1 8 3 3 2 7 5 8 2 7 1 4 3 1 3\\n\",\n \"11 4\\n1 4 3 4 3 3 4 1 1 3 4\\n\",\n \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 1 1 3 3 3 3 2\\n\",\n \"1 316327\\n500000\\n\",\n \"18 5\\n2 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\\n\",\n \"9 2\\n1 2 1 2 1 2 1 3 0\\n\",\n \"18 1\\n3 3 1 3 1 1 3 4 2 2 3 1 2 1 4 1 4 3\\n\",\n \"18 2\\n5 3 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 2\\n\",\n \"18 1\\n5 4 7 9 2 5 1 2 5 8 8 3 2 4 4 6 3 7\\n\",\n \"29 3\\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 6 1 4 2 2 3 4 2 4 2\\n\",\n \"39 1\\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 3 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 2 4\\n\",\n \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 1 1 3 3 3 5 2\\n\",\n \"3 2\\n6 2 0\\n\",\n \"9 2\\n2 2 1 2 1 2 1 3 0\\n\",\n \"39 1\\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 3 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 1 4\\n\",\n \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 0 1 3 3 3 5 1\\n\",\n \"2 0\\n1 2\\n\",\n \"18 5\\n4 4 4 6 6 4 1 1 1 1 3 3 4 5 6 1 1 3\\n\",\n \"13 4\\n1 4 3 4 3 3 4 1 1 1 4 3 4\\n\",\n \"18 1\\n8 2 3 1 7 3 3 2 7 5 8 2 7 1 4 3 1 3\\n\",\n \"11 4\\n1 4 3 4 3 3 4 2 1 3 4\\n\",\n \"6 9\\n9 9 1 9 9 9\\n\",\n \"18 5\\n1 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\\n\",\n \"18 5\\n4 4 4 6 6 4 1 1 1 1 3 4 4 5 6 1 1 3\\n\",\n \"18 1\\n3 3 1 3 1 1 3 4 2 2 3 1 3 1 4 1 4 3\\n\",\n \"18 2\\n5 0 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 2\\n\",\n \"13 4\\n1 4 3 4 2 3 4 1 1 1 4 3 4\\n\",\n \"18 1\\n5 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\\n\",\n \"29 3\\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 6 1 4 2 2 3 4 2 4 3\\n\",\n \"18 1\\n8 2 3 1 7 3 3 2 7 5 8 2 7 2 4 3 1 3\\n\",\n \"11 8\\n1 4 3 4 3 3 4 2 1 3 4\\n\",\n \"18 2\\n3 3 2 2 3 2 1 2 2 1 3 0 1 3 3 3 5 2\\n\",\n \"6 9\\n9 9 1 18 9 9\\n\",\n \"18 5\\n1 4 9 2 8 3 8 9 5 5 8 1 1 6 6 5 9 8\\n\",\n \"9 2\\n2 2 1 2 2 2 1 3 0\\n\",\n \"18 0\\n3 3 1 3 1 1 3 4 2 2 3 1 3 1 4 1 4 3\\n\",\n \"18 2\\n5 0 4 2 6 4 3 4 1 5 4 1 3 3 2 3 4 2\\n\",\n \"13 7\\n1 4 3 4 2 3 4 1 1 1 4 3 4\\n\",\n \"18 1\\n3 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\\n\",\n \"18 1\\n8 2 3 1 7 2 3 2 7 5 8 2 7 2 4 3 1 3\\n\",\n \"11 8\\n1 4 3 4 3 3 4 4 1 3 4\\n\",\n \"6 9\\n9 9 1 18 3 9\\n\",\n \"18 5\\n1 4 9 2 8 3 8 9 5 5 8 1 1 6 6 5 9 6\\n\",\n \"9 2\\n2 3 1 2 2 2 1 3 0\\n\",\n \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 3 2 3 4 2\\n\",\n \"13 7\\n1 4 3 4 2 3 4 1 1 1 5 3 4\\n\",\n \"18 1\\n2 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\\n\",\n \"18 1\\n8 2 3 1 7 2 3 2 7 5 8 4 7 2 4 3 1 3\\n\",\n \"11 8\\n1 4 3 4 3 3 2 4 1 3 4\\n\",\n \"18 2\\n3 3 2 2 3 2 1 2 2 2 3 0 1 3 3 3 5 1\\n\",\n \"6 9\\n9 9 1 18 3 13\\n\",\n \"18 5\\n1 4 9 2 8 3 8 9 8 5 8 1 1 6 6 5 9 6\\n\",\n \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 3 2 3 6 2\\n\",\n \"13 7\\n1 4 3 5 2 3 4 1 1 1 5 3 4\\n\",\n \"18 1\\n2 4 7 9 2 5 1 2 5 8 0 2 2 4 4 6 3 7\\n\",\n \"11 8\\n1 0 3 4 3 3 2 4 1 3 4\\n\",\n \"18 2\\n3 3 3 2 3 2 1 2 2 2 3 0 1 3 3 3 5 1\\n\",\n \"6 9\\n9 9 1 18 3 7\\n\",\n \"18 5\\n1 4 9 2 8 3 8 9 8 5 8 1 1 9 6 5 9 6\\n\",\n \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 5 2 3 6 2\\n\",\n \"13 3\\n1 4 3 5 2 3 4 1 1 1 5 3 4\\n\",\n \"18 1\\n2 0 7 9 2 5 1 2 5 8 0 2 2 4 4 6 3 7\\n\",\n \"11 8\\n1 0 3 4 3 3 2 4 1 0 4\\n\",\n \"18 2\\n3 3 3 2 3 2 0 2 2 2 3 0 1 3 3 3 5 1\\n\",\n \"6 9\\n9 9 1 1 3 7\\n\",\n \"18 5\\n1 4 9 2 8 3 8 9 8 5 8 1 1 9 6 4 9 6\\n\",\n \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 8 2 3 6 2\\n\",\n \"13 3\\n1 4 3 5 2 3 4 1 1 1 5 3 3\\n\",\n \"11 14\\n1 0 3 4 3 3 2 4 1 0 4\\n\",\n \"18 2\\n3 3 3 2 3 2 0 2 2 2 6 0 1 3 3 3 5 1\\n\",\n \"18 5\\n1 4 9 2 7 3 8 9 8 5 8 1 1 9 6 4 9 6\\n\",\n \"18 2\\n5 0 2 2 6 4 3 4 1 5 4 1 3 8 2 2 6 2\\n\",\n \"13 5\\n1 4 3 5 2 3 4 1 1 1 5 3 4\\n\",\n \"18 5\\n1 4 9 2 7 3 8 9 8 5 8 1 1 9 6 6 9 6\\n\",\n \"18 2\\n5 0 1 2 6 4 3 4 1 5 4 1 3 8 2 2 6 2\\n\"\n ],\n \"outputs\": [\n \"2\\n\",\n \"6\\n\",\n \"1\\n\",\n \"5\\n\",\n \"1\\n\",\n \"5\\n\",\n \"2\\n\",\n \"12\\n\",\n \"6\\n\",\n \"9\\n\",\n \"6\\n\",\n \"6\\n\",\n \"7\\n\",\n \"4\\n\",\n \"12\\n\",\n \"19\\n\",\n \"18\\n\",\n \"5\\n\",\n \"6\\n\",\n \"11\\n\",\n \"1\\n\",\n \"6\\n\",\n \"4\\n\",\n \"8\\n\",\n \"7\\n\",\n \"3\\n\",\n \"12\\n\",\n \"19\\n\",\n \"10\\n\",\n \"2\\n\",\n \"5\\n\",\n \"20\\n\",\n \"9\\n\",\n \"1\\n\",\n \"6\\n\",\n \"8\\n\",\n \"6\\n\",\n \"6\\n\",\n \"6\\n\",\n \"6\\n\",\n \"7\\n\",\n \"8\\n\",\n \"7\\n\",\n \"8\\n\",\n \"4\\n\",\n \"12\\n\",\n \"5\\n\",\n \"4\\n\",\n \"10\\n\",\n \"5\\n\",\n \"5\\n\",\n \"6\\n\",\n \"7\\n\",\n \"6\\n\",\n \"5\\n\",\n \"4\\n\",\n \"6\\n\",\n \"5\\n\",\n \"4\\n\",\n \"5\\n\",\n \"5\\n\",\n \"7\\n\",\n \"4\\n\",\n \"5\\n\",\n \"5\\n\",\n \"4\\n\",\n \"10\\n\",\n \"3\\n\",\n \"5\\n\",\n \"7\\n\",\n \"4\\n\",\n \"5\\n\",\n \"4\\n\",\n \"9\\n\",\n \"3\\n\",\n \"5\\n\",\n \"7\\n\",\n \"6\\n\",\n \"5\\n\",\n \"3\\n\",\n \"9\\n\",\n \"4\\n\",\n \"4\\n\",\n \"7\\n\",\n \"7\\n\",\n \"3\\n\",\n \"8\\n\",\n \"4\\n\",\n \"8\\n\",\n \"5\\n\",\n \"4\\n\",\n \"7\\n\"\n ]\n}"},"problem":{"kind":"string","value":"You are given array a of length n. You can choose one segment [l, r] (1 ≤ l ≤ r ≤ n) and integer value k (positive, negative or even zero) and change a_l, a_{l + 1}, ..., a_r by k each (i.e. a_i := a_i + k for each l ≤ i ≤ r).\n\nWhat is the maximum possible number of elements with value c that can be obtained after one such operation?\n\nInput\n\nThe first line contains two integers n and c (1 ≤ n ≤ 5 ⋅ 10^5, 1 ≤ c ≤ 5 ⋅ 10^5) — the length of array and the value c to obtain.\n\nThe second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 5 ⋅ 10^5) — array a.\n\nOutput\n\nPrint one integer — the maximum possible number of elements with value c which can be obtained after performing operation described above.\n\nExamples\n\nInput\n\n\n6 9\n9 9 9 9 9 9\n\n\nOutput\n\n\n6\n\n\nInput\n\n\n3 2\n6 2 6\n\n\nOutput\n\n\n2\n\nNote\n\nIn the first example we can choose any segment and k = 0. The array will stay same.\n\nIn the second example we can choose segment [1, 3] and k = -4. The array will become [2, -2, 2]."}}},{"rowIdx":84,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"3 2\\n2 6\\n4 3\\n1 5\",\n \"3 4\\n1 4 7 10\\n2 5 8 11\\n3 6 9 12\",\n \"3 2\\n2 5\\n4 3\\n1 5\",\n \"3 2\\n2 6\\n4 3\\n2 5\",\n \"3 2\\n1 6\\n4 3\\n2 5\",\n \"3 2\\n1 6\\n4 4\\n2 5\",\n \"3 4\\n1 4 7 10\\n2 6 8 11\\n3 6 9 12\",\n \"3 2\\n2 5\\n3 3\\n1 5\",\n \"3 2\\n2 6\\n4 3\\n2 6\",\n \"3 2\\n1 6\\n4 3\\n2 6\",\n \"3 2\\n1 6\\n4 3\\n1 5\",\n \"3 4\\n1 4 8 10\\n2 5 8 11\\n3 6 9 12\",\n \"3 4\\n1 4 7 10\\n2 6 8 9\\n3 6 9 12\",\n \"3 4\\n1 4 7 10\\n1 6 8 11\\n3 6 9 12\",\n \"3 4\\n1 4 5 10\\n2 5 8 11\\n3 6 9 12\",\n \"3 4\\n2 4 7 10\\n2 5 8 11\\n3 6 9 12\",\n \"3 4\\n2 4 7 10\\n1 6 8 11\\n3 6 9 12\",\n \"3 4\\n2 4 7 10\\n1 5 8 11\\n3 6 9 12\",\n \"3 4\\n2 4 7 10\\n1 6 8 11\\n3 5 9 12\",\n \"3 4\\n2 4 7 10\\n2 6 8 11\\n3 5 9 12\",\n \"3 2\\n1 6\\n4 4\\n1 5\",\n \"3 4\\n1 4 7 10\\n1 6 8 9\\n3 6 9 12\",\n \"3 4\\n1 4 7 10\\n2 5 8 11\\n3 5 9 12\",\n \"3 2\\n2 6\\n3 3\\n2 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9 12\",\n \"3 4\\n1 4 8 10\\n2 5 8 11\\n1 6 9 9\",\n \"3 4\\n2 4 7 11\\n2 6 8 11\\n1 7 9 12\",\n \"3 2\\n4 5\\n4 1\\n1 5\"\n ],\n \"outputs\": [\n \"2 6\\n4 3\\n5 1\\n2 1\\n4 3\\n5 6\",\n \"1 4 7 10\\n5 8 11 2\\n9 12 3 6\\n1 4 3 2\\n5 8 7 6\\n9 12 11 10\",\n \"5 2 \\n3 4 \\n1 5 \\n1 2 \\n3 4 \\n5 5 \\n\",\n \"6 2 \\n3 4 \\n2 5 \\n2 2 \\n3 4 \\n6 5 \\n\",\n \"6 1 \\n3 4 \\n2 5 \\n2 1 \\n3 4 \\n6 5 \\n\",\n \"6 1 \\n4 4 \\n2 5 \\n2 1 \\n4 4 \\n6 5 \\n\",\n \"10 4 7 1 \\n8 11 2 6 \\n3 6 12 9 \\n3 4 2 1 \\n8 6 7 6 \\n10 11 12 9 \\n\",\n \"5 2 \\n3 3 \\n1 5 \\n1 2 \\n3 3 \\n5 5 \\n\",\n \"6 2 \\n3 4 \\n2 6 \\n2 2 \\n3 4 \\n6 6 \\n\",\n \"6 1 \\n3 4 \\n2 6 \\n2 1 \\n3 4 \\n6 6 \\n\",\n \"6 1 \\n3 4 \\n1 5 \\n1 1 \\n3 4 \\n6 5 \\n\",\n \"10 4 8 1 \\n8 11 2 5 \\n3 6 12 9 \\n3 4 2 1 \\n8 6 8 5 \\n10 11 12 9 \\n\",\n \"10 4 7 1 \\n8 9 2 6 \\n3 6 12 9 \\n3 4 2 1 \\n8 6 7 6 \\n10 9 12 9 \\n\",\n \"10 4 7 1 \\n8 11 1 6 \\n3 6 12 9 \\n3 4 1 1 \\n8 6 7 6 \\n10 11 12 9 \\n\",\n \"10 4 5 1 \\n8 11 2 5 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\\n\",\n \"10 4 5 2 \\n8 11 2 6 \\n3 6 12 9 \\n3 4 2 2 \\n8 6 5 6 \\n10 11 12 9 \\n\",\n \"10 4 7 2 \\n8 11 2 6 \\n1 7 12 9 \\n1 4 2 2 \\n8 7 7 6 \\n10 11 12 9 \\n\",\n \"5 2 \\n4 4 \\n1 5 \\n1 2 \\n4 4 \\n5 5 \\n\",\n \"10 4 7 2 \\n8 11 3 6 \\n3 6 12 9 \\n3 4 3 2 \\n8 6 7 6 \\n10 11 12 9 \\n\",\n \"10 4 8 2 \\n5 10 1 6 \\n3 6 12 9 \\n3 4 1 2 \\n5 6 8 6 \\n10 10 12 9 \\n\",\n \"10 4 8 2 \\n8 11 2 6 \\n3 7 11 9 \\n3 4 2 2 \\n8 7 8 6 \\n10 11 11 9 \\n\",\n \"10 4 5 4 \\n8 11 2 5 \\n3 6 12 9 \\n3 4 2 4 \\n8 6 5 5 \\n10 11 12 9 \\n\",\n \"10 4 7 1 \\n8 9 1 6 \\n3 6 9 9 \\n3 4 1 1 \\n8 6 7 6 \\n10 9 9 9 \\n\",\n \"10 4 7 2 \\n8 12 2 6 \\n1 7 12 9 \\n1 4 2 2 \\n8 7 7 6 \\n10 12 12 9 \\n\",\n \"5 2 \\n4 4 \\n1 6 \\n1 2 \\n4 4 \\n5 6 \\n\",\n \"11 4 7 2 \\n8 11 3 6 \\n3 6 12 9 \\n3 4 3 2 \\n8 6 7 6 \\n11 11 12 9 \\n\",\n \"10 4 7 2 \\n8 11 2 6 \\n3 6 12 9 \\n3 4 2 2 \\n8 6 7 6 \\n10 11 12 9 \\n\",\n \"6 2 \\n3 3 \\n2 6 \\n2 2 \\n3 3 \\n6 6 \\n\",\n \"10 1 5 2 \\n8 11 2 5 \\n3 6 12 9 \\n3 1 2 2 \\n8 6 5 5 \\n10 11 12 9 \\n\",\n \"10 4 7 2 \\n8 11 1 8 \\n3 6 12 12 \\n3 4 1 2 \\n8 6 7 8 \\n10 11 12 12 \\n\",\n \"5 1 \\n3 3 \\n2 5 \\n2 1 \\n3 3 \\n5 5 \\n\",\n \"10 4 7 4 \\n5 11 2 5 \\n3 6 12 9 \\n3 4 2 4 \\n5 6 7 5 \\n10 11 12 9 \\n\",\n \"10 4 5 2 \\n8 11 1 8 \\n3 6 12 9 \\n3 4 1 2 \\n8 6 5 8 \\n10 11 12 9 \\n\",\n \"10 1 7 1 \\n8 9 2 6 \\n3 6 9 9 \\n3 1 2 1 \\n8 6 7 6 \\n10 9 9 9 \\n\",\n \"9 4 5 2 \\n8 11 2 6 \\n3 6 12 9 \\n3 4 2 2 \\n8 6 5 6 \\n9 11 12 9 \\n\",\n \"10 4 8 2 \\n8 11 3 6 \\n3 7 11 9 \\n3 4 3 2 \\n8 7 8 6 \\n10 11 11 9 \\n\",\n \"6 1 \\n3 3 \\n2 6 \\n2 1 \\n3 3 \\n6 6 \\n\",\n \"10 4 7 3 \\n8 11 1 8 \\n3 6 12 12 \\n3 4 1 3 \\n8 6 7 8 \\n10 11 12 12 \\n\",\n \"9 4 5 2 \\n8 11 2 6 \\n2 6 12 9 \\n2 4 2 2 \\n8 6 5 6 \\n9 11 12 9 \\n\",\n \"6 2 \\n3 4 \\n1 6 \\n1 2 \\n3 4 \\n6 6 \\n\",\n \"10 4 7 1 \\n8 9 2 6 \\n3 7 12 9 \\n3 4 2 1 \\n8 7 7 6 \\n10 9 12 9 \\n\",\n \"10 4 7 1 \\n8 11 1 6 \\n1 6 12 9 \\n1 4 1 1 \\n8 6 7 6 \\n10 11 12 9 \\n\",\n \"10 4 7 2 \\n7 11 1 6 \\n3 5 12 9 \\n3 4 1 2 \\n7 5 7 6 \\n10 11 12 9 \\n\",\n \"10 4 7 1 \\n8 9 1 6 \\n2 5 12 9 \\n2 4 1 1 \\n8 5 7 6 \\n10 9 12 9 \\n\",\n \"5 1 \\n3 3 \\n2 6 \\n2 1 \\n3 3 \\n5 6 \\n\",\n \"10 4 7 1 \\n8 12 2 7 \\n3 5 12 9 \\n3 4 2 1 \\n8 5 7 7 \\n10 12 12 9 \\n\",\n \"10 4 7 1 \\n8 9 2 6 \\n3 6 9 12 \\n3 4 2 1 \\n8 6 7 6 \\n10 9 9 12 \\n\",\n \"10 4 7 2 \\n8 11 2 6 \\n3 7 11 9 \\n3 4 2 2 \\n8 7 7 6 \\n10 11 11 9 \\n\",\n \"10 4 5 4 \\n8 11 2 5 \\n3 6 12 10 \\n3 4 2 4 \\n8 6 5 5 \\n10 11 12 10 \\n\",\n \"10 4 7 2 \\n8 9 1 6 \\n3 6 9 9 \\n3 4 1 2 \\n8 6 7 6 \\n10 9 9 9 \\n\",\n \"10 4 7 1 \\n5 11 1 6 \\n1 6 12 9 \\n1 4 1 1 \\n5 6 7 6 \\n10 11 12 9 \\n\",\n \"10 4 7 1 \\n5 11 2 6 \\n1 6 12 9 \\n1 4 2 1 \\n5 6 7 6 \\n10 11 12 9 \\n\",\n \"5 2 \\n3 4 \\n2 5 \\n2 2 \\n3 4 \\n5 5 \\n\",\n \"5 1 \\n3 3 \\n1 5 \\n1 1 \\n3 3 \\n5 5 \\n\",\n \"10 4 5 2 \\n8 11 1 6 \\n3 6 12 9 \\n3 4 1 2 \\n8 6 5 6 \\n10 11 12 9 \\n\",\n \"10 4 7 4 \\n8 11 1 5 \\n3 6 12 9 \\n3 4 1 4 \\n8 6 7 5 \\n10 11 12 9 \\n\",\n \"6 1 \\n4 3 \\n1 5 \\n1 1 \\n4 3 \\n6 5 \\n\",\n \"11 4 8 2 \\n8 10 1 6 \\n3 6 12 9 \\n3 4 1 2 \\n8 6 8 6 \\n11 10 12 9 \\n\",\n \"10 4 8 1 \\n8 11 2 5 \\n1 6 9 9 \\n1 4 2 1 \\n8 6 8 5 \\n10 11 9 9 \\n\",\n \"11 4 7 2 \\n8 11 2 6 \\n1 7 12 9 \\n1 4 2 2 \\n8 7 7 6 \\n11 11 12 9 \\n\",\n \"5 4 \\n4 1 \\n1 5 \\n1 1 \\n4 4 \\n5 5 \\n\"\n ]\n}"},"problem":{"kind":"string","value":"We have a grid with N rows and M columns of squares. Each integer from 1 to NM is written in this grid once. The number written in the square at the i-th row from the top and the j-th column from the left is A_{ij}.\n\nYou need to rearrange these numbers as follows:\n\n1. First, for each of the N rows, rearrange the numbers written in it as you like.\n2. Second, for each of the M columns, rearrange the numbers written in it as you like.\n3. Finally, for each of the N rows, rearrange the numbers written in it as you like.\n\n\n\nAfter rearranging the numbers, you want the number written in the square at the i-th row from the top and the j-th column from the left to be M\\times (i-1)+j. Construct one such way to rearrange the numbers. The constraints guarantee that it is always possible to achieve the objective.\n\nConstraints\n\n* 1 \\leq N,M \\leq 100\n* 1 \\leq A_{ij} \\leq NM\n* A_{ij} are distinct.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN M\nA_{11} A_{12} ... A_{1M}\n:\nA_{N1} A_{N2} ... A_{NM}\n\n\nOutput\n\nPrint one way to rearrange the numbers in the following format:\n\n\nB_{11} B_{12} ... B_{1M}\n:\nB_{N1} B_{N2} ... B_{NM}\nC_{11} C_{12} ... C_{1M}\n:\nC_{N1} C_{N2} ... C_{NM}\n\n\nHere B_{ij} is the number written in the square at the i-th row from the top and the j-th column from the left after Step 1, and C_{ij} is the number written in that square after Step 2.\n\nExamples\n\nInput\n\n3 2\n2 6\n4 3\n1 5\n\n\nOutput\n\n2 6\n4 3\n5 1\n2 1\n4 3\n5 6\n\n\nInput\n\n3 4\n1 4 7 10\n2 5 8 11\n3 6 9 12\n\n\nOutput\n\n1 4 7 10\n5 8 11 2\n9 12 3 6\n1 4 3 2\n5 8 7 6\n9 12 11 10"}}},{"rowIdx":85,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2 2 1000000007\\n*/\\n/*\\n\",\n \"2 2 1000000007\\n**\\n\\\\\\\\\",\n \"2 2 3\\n**\\n**\\n\",\n \"20 19 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Box consists of grid of size n × m. Each cell of the grid contains a mirror put in the shape of '\\' or ' / ' (45 degree to the horizontal or vertical line). But mirrors in some cells have been destroyed. You want to put new mirrors into these grids so that the following two conditions are satisfied:\n\n 1. If you put a light ray horizontally/vertically into the middle of any unit segment that is side of some border cell, the light will go out from the neighboring unit segment to the segment you put the ray in.\n 2. each unit segment of the grid of the mirror box can be penetrated by at least one light ray horizontally/vertically put into the box according to the rules of the previous paragraph \n\n\n\nAfter you tried putting some mirrors, you find out that there are many ways of doing so. How many possible ways are there? The answer might be large, so please find the result modulo prime number MOD.\n\nInput\n\nThe first line contains three integers n, m, MOD (1 ≤ n, m ≤ 100, 3 ≤ MOD ≤ 109 + 7, MOD is prime), m, n indicates the dimensions of a box and MOD is the number to module the answer.\n\nThe following n lines each contains a string of length m. Each string contains only ' / ', '\\', '*', where '*' denotes that the mirror in that grid has been destroyed. \n\nIt is guaranteed that the number of '*' is no more than 200.\n\nOutput\n\nOutput the answer modulo MOD.\n\nExamples\n\nInput\n\n2 2 1000000007\n*/\n/*\n\n\nOutput\n\n1\n\n\nInput\n\n2 2 1000000007\n**\n\\\\\n\nOutput\n\n1\n\nInput\n\n2 2 3\n**\n**\n\n\nOutput\n\n2\n\nNote\n\nThe only way for sample 1 is shown on the left picture from the statement.\n\nThe only way for sample 2 is shown on the right picture from the statement.\n\nFor the third sample, there are 5 possibilities that are listed below: \n\n1.\n\n\n\n\n\n2.\n\n\n\n\n\n3.\n\n\n\n\n\n4.\n\n\n\n\n\n5.\n\n\n\n\n\nThe answer is then module by 3 so the output should be 2."}}},{"rowIdx":86,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"6 3\\n5 6\\n1 4\\n4 6\\n\",\n \"5 3\\n1 3\\n2 4\\n2 5\\n\",\n \"1000 10\\n3 998\\n2 1000\\n1 999\\n2 1000\\n3 998\\n2 1000\\n3 998\\n1 1000\\n2 1000\\n3 999\\n\",\n 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\"010101\\n\",\n \"0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101\\n\"\n ]\n}"},"problem":{"kind":"string","value":"Sonya decided to organize an exhibition of flowers. Since the girl likes only roses and lilies, she decided that only these two kinds of flowers should be in this exhibition.\n\nThere are n flowers in a row in the exhibition. Sonya can put either a rose or a lily in the i-th position. Thus each of n positions should contain exactly one flower: a rose or a lily.\n\nShe knows that exactly m people will visit this exhibition. The i-th visitor will visit all flowers from l_i to r_i inclusive. The girl knows that each segment has its own beauty that is equal to the product of the number of roses and the number of lilies.\n\nSonya wants her exhibition to be liked by a lot of people. That is why she wants to put the flowers in such way that the sum of beauties of all segments would be maximum possible.\n\nInput\n\nThe first line contains two integers n and m (1≤ n, m≤ 10^3) — the number of flowers and visitors respectively.\n\nEach of the next m lines contains two integers l_i and r_i (1≤ l_i≤ r_i≤ n), meaning that i-th visitor will visit all flowers from l_i to r_i inclusive.\n\nOutput\n\nPrint the string of n characters. The i-th symbol should be «0» if you want to put a rose in the i-th position, otherwise «1» if you want to put a lily.\n\nIf there are multiple answers, print any.\n\nExamples\n\nInput\n\n5 3\n1 3\n2 4\n2 5\n\n\nOutput\n\n01100\n\nInput\n\n6 3\n5 6\n1 4\n4 6\n\n\nOutput\n\n110010\n\nNote\n\nIn the first example, Sonya can put roses in the first, fourth, and fifth positions, and lilies in the second and third positions;\n\n * in the segment [1…3], there are one rose and two lilies, so the beauty is equal to 1⋅ 2=2; \n * in the segment [2…4], there are one rose and two lilies, so the beauty is equal to 1⋅ 2=2; \n * in the segment [2…5], there are two roses and two lilies, so the beauty is equal to 2⋅ 2=4. \n\n\n\nThe total beauty is equal to 2+2+4=8.\n\nIn the second example, Sonya can put roses in the third, fourth, and sixth positions, and lilies in the first, second, and fifth positions;\n\n * in the segment [5…6], there are one rose and one lily, so the beauty is equal to 1⋅ 1=1; \n * in the segment [1…4], there are two roses and two lilies, so the beauty is equal to 2⋅ 2=4; \n * in the segment [4…6], there are two roses and one lily, so the beauty is equal to 2⋅ 1=2. \n\n\n\nThe total beauty is equal to 1+4+2=7."}}},{"rowIdx":87,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"15\\n57\\n62\\n47\\n45\\n42\\n74\\n90\\n75\\n54\\n50\\n66\\n63\\n77\\n87\\n51\",\n \"2\\n1\\n2\",\n \"7\\n10\\n15\\n13\\n18\\n11\\n14\\n19\",\n \"15\\n57\\n62\\n37\\n45\\n42\\n74\\n90\\n75\\n54\\n50\\n66\\n63\\n77\\n87\\n51\",\n \"2\\n0\\n2\",\n \"7\\n10\\n15\\n13\\n18\\n11\\n24\\n19\",\n \"15\\n57\\n62\\n74\\n45\\n42\\n74\\n90\\n75\\n54\\n50\\n66\\n63\\n77\\n87\\n51\",\n \"2\\n-1\\n2\",\n \"7\\n10\\n15\\n18\\n18\\n11\\n24\\n19\",\n \"15\\n57\\n62\\n74\\n45\\n42\\n74\\n90\\n75\\n54\\n50\\n66\\n63\\n77\\n143\\n51\",\n \"2\\n-1\\n3\",\n \"7\\n10\\n15\\n29\\n18\\n11\\n24\\n19\",\n \"15\\n57\\n62\\n74\\n45\\n42\\n74\\n90\\n75\\n54\\n50\\n66\\n63\\n77\\n143\\n7\",\n 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The values of D_i are all distinct. Does a tree with N vertices that satisfies the following conditions exist?\n\n* The vertices are numbered 1,2,..., N.\n* The edges are numbered 1,2,..., N-1, and Edge i connects Vertex u_i and v_i.\n* For each vertex i, the sum of the distances from i to the other vertices is D_i, assuming that the length of each edge is 1.\n\n\n\nIf such a tree exists, construct one such tree.\n\nConstraints\n\n* 2 \\leq N \\leq 100000\n* 1 \\leq D_i \\leq 10^{12}\n* D_i are all distinct.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nD_1\nD_2\n:\nD_N\n\n\nOutput\n\nIf a tree with n vertices that satisfies the conditions does not exist, print `-1`.\n\nIf a tree with n vertices that satisfies the conditions exist, print n-1 lines. The i-th line should contain u_i and v_i with a space in between. If there are multiple trees that satisfy the conditions, any such tree will be accepted.\n\nExamples\n\nInput\n\n7\n10\n15\n13\n18\n11\n14\n19\n\n\nOutput\n\n1 2\n1 3\n1 5\n3 4\n5 6\n6 7\n\n\nInput\n\n2\n1\n2\n\n\nOutput\n\n-1\n\n\nInput\n\n15\n57\n62\n47\n45\n42\n74\n90\n75\n54\n50\n66\n63\n77\n87\n51\n\n\nOutput\n\n1 10\n1 11\n2 8\n2 15\n3 5\n3 9\n4 5\n4 10\n5 15\n6 12\n6 14\n7 13\n9 12\n11 13"}}},{"rowIdx":88,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"4 5 3 1 5\\n\",\n \"5 1 2 1 2\\n\",\n \"3 3 1 1 1\\n\",\n \"2 313 856 964 421\\n\",\n \"61 464 623 89 548\\n\",\n \"37 261 207 1 1000\\n\",\n \"4 202 512 995 375\\n\",\n \"3 3 1 6 9\\n\",\n \"213 480 811 134 745\\n\",\n \"1 10 2 6 10\\n\",\n \"6 5 7 10 4\\n\",\n \"2 7 6 2 3\\n\",\n \"29 344 406 900 1\\n\",\n \"1 2 8 8 5\\n\",\n \"1 1 1 1 1\\n\",\n \"424 41 41 909 909\\n\",\n \"641 31 29 161 802\\n\",\n \"12 462 8 311 327\\n\",\n \"15 14 32 65 28\\n\",\n \"1 2 8 9 8\\n\",\n \"9 5 7 8 7\\n\",\n \"637 324 69 612 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During the competition, they have to type a text consisting of s characters. The first participant types one character in v1 milliseconds and has ping t1 milliseconds. The second participant types one character in v2 milliseconds and has ping t2 milliseconds.\n\nIf connection ping (delay) is t milliseconds, the competition passes for a participant as follows: \n\n 1. Exactly after t milliseconds after the start of the competition the participant receives the text to be entered. \n 2. Right after that he starts to type it. \n 3. Exactly t milliseconds after he ends typing all the text, the site receives information about it. \n\n\n\nThe winner is the participant whose information on the success comes earlier. If the information comes from both participants at the same time, it is considered that there is a draw.\n\nGiven the length of the text and the information about participants, determine the result of the game.\n\nInput\n\nThe first line contains five integers s, v1, v2, t1, t2 (1 ≤ s, v1, v2, t1, t2 ≤ 1000) — the number of characters in the text, the time of typing one character for the first participant, the time of typing one character for the the second participant, the ping of the first participant and the ping of the second participant.\n\nOutput\n\nIf the first participant wins, print \"First\". If the second participant wins, print \"Second\". In case of a draw print \"Friendship\".\n\nExamples\n\nInput\n\n5 1 2 1 2\n\n\nOutput\n\nFirst\n\n\nInput\n\n3 3 1 1 1\n\n\nOutput\n\nSecond\n\n\nInput\n\n4 5 3 1 5\n\n\nOutput\n\nFriendship\n\nNote\n\nIn the first example, information on the success of the first participant comes in 7 milliseconds, of the second participant — in 14 milliseconds. So, the first wins.\n\nIn the second example, information on the success of the first participant comes in 11 milliseconds, of the second participant — in 5 milliseconds. So, the second wins.\n\nIn the third example, information on the success of the first participant comes in 22 milliseconds, of the second participant — in 22 milliseconds. So, it is be a draw."}}},{"rowIdx":89,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2\\n31\\n4 1\\n160\\n9 2\\n\\nSAMPLE\",\n \"2\\n31\\n4 1\\n98\\n9 2\\n\\nSAMPLE\",\n \"2\\n31\\n7 1\\n98\\n17 2\\n\\nSAMOLE\",\n \"2\\n6\\n7 1\\n98\\n17 2\\n\\nSAMOLE\",\n \"2\\n6\\n4 2\\n98\\n24 3\\n\\nSAMOLE\",\n \"2\\n6\\n4 2\\n152\\n24 3\\n\\nSAMOLE\",\n \"2\\n12\\n4 1\\n152\\n24 3\\n\\nSAMOLE\",\n \"2\\n12\\n4 1\\n72\\n24 3\\n\\nELOMAS\",\n \"2\\n12\\n4 1\\n11\\n24 3\\n\\nEKOMAS\",\n \"2\\n12\\n4 1\\n11\\n19 3\\n\\nEKOMAS\",\n \"2\\n12\\n7 1\\n20\\n19 3\\n\\nEKOMAS\",\n \"2\\n12\\n7 1\\n20\\n19 6\\n\\nEKPLAS\",\n \"2\\n26\\n9 0\\n20\\n26 0\\n\\nEKPLAS\",\n \"2\\n26\\n9 0\\n33\\n10 0\\n\\nEKPLAS\",\n \"2\\n39\\n9 0\\n33\\n10 0\\n\\nEKPLAS\",\n \"2\\n39\\n9 0\\n33\\n2 0\\n\\nEKPLAS\",\n \"2\\n39\\n9 0\\n53\\n2 0\\n\\nEKPLAS\",\n \"2\\n28\\n9 0\\n53\\n2 0\\n\\nEKPALS\",\n \"2\\n28\\n9 0\\n53\\n3 0\\n\\nEKPBLR\",\n \"2\\n28\\n9 0\\n86\\n3 0\\n\\nEKPBLR\",\n \"2\\n10\\n3 0\\n86\\n3 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Suddenly, a block in the ground opens and she falls into it! Gudi slides down and lands in a dark room. A mysterious voice announces: \nIntruders are not allowed inside the castle. To proceed, you must\nsolve my puzzle. Here is a string S indexed from 1 to N,\nconsisting of digits from 0-9. If you summon the spell \"Sera\", the\nstring will be rotated clockwise by H positions. If you summon the\nspell \"Xhaka\", the number A will be added to all the even-indexed\ndigits of the string. For example, if H = 1 A = 3 \"Sera\" and\n\"Xhaka\" on the string \"781\" will result in strings \"\"178\" and \"711\"\nrespectively i.e. digits post 9 are cycled back to 0. The objective is\nto obtain the lexicographically smallest string possible as a result\nof applying any of the two spells any number of times in any order. Find the string\nand I shall set you free \n\nInput\nThe first line contains an integer T. T testcases follow.\nFirst line of each test contains the string S.\nThe next line contains two space-separated integers A and H. \n\nOutput\nPrint the answer to each testcase in a new line.\n\nConstraints\n 1 ≤ T ≤ 10\n 1 ≤ N, H ≤ 6\n 1 ≤ A ≤ 10\n\nSAMPLE INPUT\n2\n31\n4 1\n160\n9 2\n\nSAMPLE OUTPUT\n11\n000\n\nExplanation\n\nFor the first testcase, we can summon the spells as:\n31 --(Sera)- -> 13 --(Xhaka)- -> 17 --(Xhaka)- -> 11, and it is the smallest possible answer."}}},{"rowIdx":90,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"5 4 10 1 6\\n1 1 5\\n1 5 5\\n1 3 2\\n1 5 2\\n2 1\\n2 2\\n\",\n \"5 2 2 1 8\\n1 1 2\\n1 5 3\\n1 2 1\\n2 2\\n1 4 2\\n1 3 2\\n2 1\\n2 3\\n\",\n \"1 1 2 1 1\\n2 1\\n\",\n \"1 1 2 0 1\\n2 1\\n\",\n \"5 4 10 1 6\\n1 1 5\\n1 5 5\\n1 3 2\\n1 5 1\\n2 1\\n2 2\\n\",\n \"5 2 2 1 8\\n1 1 2\\n1 5 3\\n1 2 1\\n2 2\\n1 4 0\\n1 3 2\\n2 1\\n2 3\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 2 1\\n2 2\\n1 4 2\\n1 3 2\\n2 1\\n2 3\\n\",\n \"5 2 2 1 8\\n1 1 2\\n1 5 3\\n1 2 1\\n2 2\\n1 4 2\\n1 3 2\\n2 1\\n2 2\\n\",\n \"5 4 2 1 8\\n1 1 2\\n1 5 3\\n1 2 1\\n2 2\\n1 4 2\\n1 3 2\\n2 1\\n2 2\\n\",\n \"5 4 10 1 6\\n1 1 4\\n1 5 5\\n1 3 2\\n1 5 2\\n2 1\\n2 2\\n\",\n \"5 3 2 1 8\\n1 1 2\\n1 5 3\\n1 2 1\\n2 2\\n1 4 0\\n1 3 2\\n2 1\\n2 3\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 4 1\\n2 2\\n1 4 2\\n1 3 2\\n2 1\\n2 3\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 1 1\\n2 2\\n1 4 2\\n1 5 2\\n2 1\\n2 3\\n\",\n \"5 4 10 1 6\\n1 1 5\\n1 5 3\\n1 3 2\\n1 5 2\\n2 1\\n2 2\\n\",\n \"5 4 1 1 8\\n1 1 2\\n1 5 3\\n1 2 1\\n2 2\\n1 4 2\\n1 3 2\\n2 1\\n2 2\\n\",\n \"5 4 10 1 6\\n1 2 4\\n1 5 5\\n1 3 2\\n1 5 2\\n2 1\\n2 2\\n\",\n \"5 3 2 1 8\\n1 1 0\\n1 5 3\\n1 2 1\\n2 2\\n1 4 0\\n1 3 2\\n2 1\\n2 3\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 5 1\\n2 2\\n1 4 2\\n1 3 2\\n2 1\\n2 3\\n\",\n \"5 4 20 1 6\\n1 1 4\\n1 2 5\\n1 3 2\\n1 5 1\\n2 1\\n2 2\\n\",\n \"5 2 2 2 8\\n1 1 1\\n1 5 3\\n1 1 1\\n2 2\\n1 4 2\\n1 5 2\\n2 1\\n2 3\\n\",\n \"1 1 3 0 1\\n2 1\\n\",\n \"2 1 3 0 1\\n2 1\\n\",\n \"1 1 2 2 1\\n2 1\\n\",\n \"5 4 10 1 6\\n1 1 4\\n1 5 5\\n1 3 2\\n1 5 1\\n2 1\\n2 2\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 2 1\\n2 2\\n1 4 2\\n1 5 2\\n2 1\\n2 3\\n\",\n \"2 1 3 0 1\\n2 2\\n\",\n \"1 1 2 4 1\\n2 1\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 2 1\\n2 2\\n1 4 4\\n1 5 2\\n2 1\\n2 3\\n\",\n \"1 1 2 3 1\\n2 1\\n\",\n \"1 2 3 0 1\\n2 1\\n\",\n \"1 1 1 2 1\\n2 1\\n\",\n \"5 4 20 1 6\\n1 1 4\\n1 5 5\\n1 3 2\\n1 5 1\\n2 1\\n2 2\\n\",\n \"2 1 6 0 1\\n2 2\\n\",\n \"1 1 1 4 1\\n2 1\\n\",\n \"1 0 1 2 1\\n2 1\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 1 1\\n2 2\\n1 4 2\\n1 5 3\\n2 1\\n2 3\\n\",\n \"2 1 11 0 1\\n2 2\\n\",\n \"2 1 1 4 1\\n2 1\\n\",\n \"1 0 1 2 1\\n2 2\\n\",\n \"5 2 2 1 8\\n1 2 1\\n1 5 3\\n1 1 1\\n2 2\\n1 4 2\\n1 5 3\\n2 1\\n2 3\\n\",\n \"2 1 0 4 1\\n2 1\\n\",\n \"1 0 1 4 1\\n2 2\\n\",\n \"2 1 0 5 1\\n2 1\\n\",\n \"2 1 0 2 1\\n2 1\\n\",\n \"1 1 2 1 1\\n2 2\\n\",\n \"1 1 2 0 1\\n2 2\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 2 2\\n2 2\\n1 4 2\\n1 3 2\\n2 1\\n2 3\\n\",\n \"5 2 2 1 8\\n1 1 2\\n1 5 3\\n1 2 1\\n2 2\\n1 4 0\\n1 3 2\\n2 1\\n2 2\\n\",\n \"2 1 3 0 1\\n2 3\\n\",\n \"2 1 2 4 1\\n2 1\\n\",\n \"5 2 2 1 8\\n1 1 1\\n1 5 3\\n1 2 1\\n2 2\\n1 4 4\\n1 5 1\\n2 1\\n2 3\\n\",\n \"1 1 2 3 1\\n2 2\\n\",\n \"1 1 1 0 1\\n2 1\\n\",\n \"2 0 11 0 1\\n2 2\\n\",\n \"1 0 2 4 1\\n2 2\\n\"\n ],\n \"outputs\": [\n \"7\\n1\\n\",\n \"3\\n6\\n4\\n\",\n \"0\\n\",\n \"0\\n\",\n \"6\\n1\\n\",\n \"3\\n4\\n4\\n\",\n \"3\\n6\\n4\\n\",\n \"3\\n6\\n5\\n\",\n \"1\\n2\\n1\\n\",\n \"7\\n1\\n\",\n \"3\\n2\\n2\\n\",\n \"4\\n6\\n3\\n\",\n \"3\\n4\\n3\\n\",\n \"5\\n1\\n\",\n \"1\\n1\\n1\\n\",\n \"7\\n0\\n\",\n \"2\\n2\\n1\\n\",\n \"3\\n6\\n3\\n\",\n \"1\\n1\\n\",\n \"4\\n4\\n4\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"6\\n1\\n\",\n \"3\\n4\\n4\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n4\\n4\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"6\\n1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n4\\n3\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n4\\n4\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n6\\n4\\n\",\n \"3\\n4\\n3\\n\",\n \"0\\n\",\n \"0\\n\",\n \"3\\n4\\n4\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\"\n ]\n}"},"problem":{"kind":"string","value":"A factory produces thimbles in bulk. Typically, it can produce up to a thimbles a day. However, some of the machinery is defective, so it can currently only produce b thimbles each day. The factory intends to choose a k-day period to do maintenance and construction; it cannot produce any thimbles during this time, but will be restored to its full production of a thimbles per day after the k days are complete.\n\nInitially, no orders are pending. The factory receives updates of the form di, ai, indicating that ai new orders have been placed for the di-th day. Each order requires a single thimble to be produced on precisely the specified day. The factory may opt to fill as many or as few of the orders in a single batch as it likes.\n\nAs orders come in, the factory owner would like to know the maximum number of orders he will be able to fill if he starts repairs on a given day pi. Help the owner answer his questions.\n\nInput\n\nThe first line contains five integers n, k, a, b, and q (1 ≤ k ≤ n ≤ 200 000, 1 ≤ b < a ≤ 10 000, 1 ≤ q ≤ 200 000) — the number of days, the length of the repair time, the production rates of the factory, and the number of updates, respectively.\n\nThe next q lines contain the descriptions of the queries. Each query is of one of the following two forms: \n\n * 1 di ai (1 ≤ di ≤ n, 1 ≤ ai ≤ 10 000), representing an update of ai orders on day di, or \n * 2 pi (1 ≤ pi ≤ n - k + 1), representing a question: at the moment, how many orders could be filled if the factory decided to commence repairs on day pi? \n\n\n\nIt's guaranteed that the input will contain at least one query of the second type.\n\nOutput\n\nFor each query of the second type, print a line containing a single integer — the maximum number of orders that the factory can fill over all n days.\n\nExamples\n\nInput\n\n5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3\n\n\nOutput\n\n3\n6\n4\n\n\nInput\n\n5 4 10 1 6\n1 1 5\n1 5 5\n1 3 2\n1 5 2\n2 1\n2 2\n\n\nOutput\n\n7\n1\n\nNote\n\nConsider the first sample.\n\nWe produce up to 1 thimble a day currently and will produce up to 2 thimbles a day after repairs. Repairs take 2 days.\n\nFor the first question, we are able to fill 1 order on day 1, no orders on days 2 and 3 since we are repairing, no orders on day 4 since no thimbles have been ordered for that day, and 2 orders for day 5 since we are limited to our production capacity, for a total of 3 orders filled.\n\nFor the third question, we are able to fill 1 order on day 1, 1 order on day 2, and 2 orders on day 5, for a total of 4 orders."}}},{"rowIdx":91,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"7 2\\nabacaba\\naa\\n\",\n \"15 6\\nqwertyhgfdsazxc\\nqa\\n\",\n \"7 3\\nasddsaf\\nsd\\n\",\n \"4 2\\nbbaa\\nab\\n\",\n \"200 100\\ncxqtpwtozcnavklpcksprgecocdraaryxzztqkcfzsrhdrzabtwdukzmsgpnvvgigbtyaxubrngiomfatojjvnvhogqqlujsrglodzwmpyjijtzdzcczlxvhmkkefuereazzwfqbndaccpvlupgixdezadhvwdfzxqzmnkcgwktubylaiezruthgdzqqdrsrorvganxf\\nwt\\n\",\n \"200 20\\nbcbabacbaaaccbbaaabcabccaacaccccbbcbcacaacbaaababcbcaccbbbbcabccaaabbbbaabbbacbbbcacaaccbbbcbbcbbabbcbbcaaacccaccacbccbaccaccaababbccbcccaacbabccbbacbccbccaabaaacaabaaacabcacccbcccaacaccabcaabcbbaacaa\\naa\\n\",\n \"2 1\\naa\\nsb\\n\",\n \"200 100\\nktlrcnrfmafobkjlianalpfkbfqmfjfbknqsocotoscohffjmbjsbbridajqsiegdgishnshsapmriacllkkkdklgghdqekqbdlcolroalqofkekrdtparekephodbbpehmpttdtqoejmiecdfblnlhsalahtekmrhtdkabshcarcidnqbpqoregtfdhqdjdpprtkabi\\nll\\n\",\n \"200 20\\nepajbenfcpoajfftqhjnsafpcsjdenebneehortdglpprkjeampeomldcierqdhlsfnhdlbodaneglrhhoggrdgfnbnlpdgphbienmdarrlaqggticlipopftangkddprrpitdepmhftbeihpknkhjstqbpsemdoomrrghkrqnpnsbtjafmdnqdiiblkskgadtstfnpa\\nao\\n\",\n \"200 150\\nkegdqehqjvqcbcrzovuueubttwyimeddqhazvdfvsmjvbozipwtpgfukiflhtpvdonfnaclrlxkqwnkmeoydwclgjfqanltdcijpiqpbbcmglionapitprpovmmxbkdoqylehyzasfiwlnyujffmcljztmakzwwoarfzgvuofujfxocltljbknjyvxzdrwgrgydpsuwv\\nht\\n\",\n \"200 1\\nstjfrqjrbjdooiolrmhtfieofdafjpqpltiarfkgfnqggqbmljnrlsohplehtjsghsdeofkpgjrnmkohlirgeqsctbdjbqojdnjtmlhjmostdlplfqgsloahpjipkinpelstrstpplqtddeajbigmaatcmtolbkemacaetpbdiclfodsgmmkaoneqfeothhamjsdphhh\\nce\\n\",\n \"200 150\\nshjhthdtsclitsndedjdjfifsrmenhamjcfalglldleihmmjqjfcksbedssiaacgqgspoojlgcretioiaakgngkintpjgjngodjqrifbmptemedchnngkplrmbteetnjasfaiqmomgktlkljgrccqtilgprrqctrefmchsnokanksoceinfanhrdrrkhhofhnchhcjef\\nej\\n\",\n \"200 20\\nhbadbbhfcafhcecgfcecbbaagbegbahcdacgcfbefafhbhcehffhfbfahfgcghhhefhcadgeghdagbadhgabfgchgbgebgdffbhebhgccgefhgadchghhfbhdeeahagghgegbebfbabedefdgdbbcbagfdebbdddfddacfefabbhceahhfhebecbbfegbahfgaghdhca\\nde\\n\",\n \"11 4\\nbdfbdbccdad\\nab\\n\",\n \"200 1\\ncccbaacabcbbabbccbcaaabbbacacccbacaaababcabbaabacabaacbaacbaaccbcaabccabbaabcacabcaaaaaabaccbcacbbacabbaaccacabbcbcaaacaaccaccbabaaccbbccbaabbabbbaaaaacbacbcbaacbccabccbaacbacaaabbcbaaaacbccbbababacac\\nac\\n\",\n \"200 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1\\nheeaccgddefffgbegdfdefefabdgcabegecbbffagfcegdbaedgdeafahahebbegeebfgbfdefbddegbgbaebcfgedhdfgcfdbafggffbaebddehabhdedffbfebbcdccgcbbffdbbabddabdahgbadgeehdachhceefcfacdccfhbbaehegaebccebfgahfedahfdgf\\nch\\n\",\n \"200 190\\nghcebcdabheeeaeabfghdbegecabebhbahdhfchabchchbdcbcaebaebdbgebebhdadgegdahhdaaabehhgghchadfbggbgecahagdfceeffchfddecfgcdbbdhhecfhdfefdbeagcgaedahdebfffhecfcbbcdceghbfcggeaegcdhdchhebffhgchbgacddabcfbcg\\nha\\n\",\n \"200 20\\nbbbbaaaccacdddeebdbddaadeedcbbdcaedccebcbbabccecacaaacdcaeaaaadaadbaabbeceecacdadebdddadeeadeedccdaaaeeabdbaabeccbedcaaccbbdbabbcdbdbcadeceadaacaaaabaadedecaaaabceeecadbaaacceedaebaedbcbcaabcdabcbdbca\\ncd\\n\",\n \"200 0\\naeceedcbdeedaaaededcdeceeabdcaddaccaaccdbdeeeddaededcbbceeeeebbcbcbcbeddadcaeaabbecbdceabcbbdeaeecedeeecaccbacebaaecadbaccbadcbdbebcaeebecdddbaaaaeacbbacbbbedabeaaccbddacedccdaaaeaeebbbabebcebccbbdbba\\nac\\n\",\n \"2 1\\nas\\nsa\\n\",\n \"2 0\\nas\\nas\\n\",\n \"200 0\\nesiqcqkirmeamjmggfdgrkdjirlesspqqdprrapiaasmserepidgbisilehqmgiddgfssqfmmdsiisdlkhpeqnieghbfpantckqngrehsjcqreplogtljajppamnhlbpbmrmmrirmboacjjpnrdonkachnfcndbmmjfkateltmemofalfplhgrsecpkgmajnpstgpheb\\ngb\\n\",\n \"200 100\\nbcacabeccaceeedbbaacedacadeebbecedebbedeaccdbabeedbccbebabcaccdeeccbdddbabdeadaedadbbddbaedbbadbcbbbdbdaceeaddeaebbbaabedabceebcccbbdcbcdbbedbdccaeacdccdcdaeaccbaebabbecaeeccbdbbaeeccbacaaebadccdcdbbb\\ndc\\n\",\n \"200 190\\nddeaecceeacbccbdbdaaecbeccddbdcdaaeababdccbdeedcaddaeaacbcdebccdaabbdeecdabadaadebaacbebcecdcecbccbaedbeaacddbccdcecbedcdaaccceeebeeceedaadceeedcebeecbcbddeaacddadddeecbacbaddabdeabbcccedbbbabdadcadeb\\ndc\\n\",\n \"200 1\\nbbddbbcddeaaeacbdaabccdcacbddaaeaeddadcaedccdbadecabdeabecdbdddcacebaaeddecbedccdacedecabbadcacaaebbaaaeadccebbabddddbecebadaadeceaccdaceabadcebeaadacbadacbbbcdcacbdaaeadabaecdbcbbdbbbdabdeceeeacaadae\\ned\\n\",\n \"200 150\\nbbbacaabaabaccbbcbbaacbcabacbcaaabcccabaacabaacbcbcccacbccccbaabbccccacccccbcaccbcbcaaaccbbbbbbabbcbcbcacababcccaccbcaabbbacaaacbcacaacbabbcbaacacabcccbbcccbbacbaabbccbaaabccccbbababaccacaccaaacbbcbab\\naa\\n\",\n \"200 1\\nhfgeibjadejebicjdbaebagbjhfegebddcdjdffchiehcghabddgbigjfahaachhdebeihbdcdbcgecifghdejhcehbfhihiebgigfdebjebaiidfffdbcfedbiiaffddijabegdhighgaaeefebabaagjaajdcebicddfdjdegdhfefaagbhiiigbeajaachajejfae\\nbi\\n\",\n \"200 100\\nbbbcccabbccabcccacabacbacaaabccbccbbcaabcbbbaaccbcbcaabbbbcbaaaabaccccbbabbaccacbaacababcbbbbcacaaabaccccbcbbaabcaaabbccbccbbcccabbcbbcccbbccccbcccbcbaabbbcbabcccbbbbcabacaccbcabccbacbbacbcabbacccaccc\\nab\\n\",\n \"200 150\\njbihceccaifigibbjechghaceaffchfjbhajifehfgcadcahgfecahagefjbjdjfdcdehiaicicdgfcadiafbjhigfcidbhfcchfacaibjeijagdiceaadggjcahdfghifebcabccdahbgheacifeiidaagceechdfadhebdaehcjdebccjbjdahhfacihijgdgihhfb\\nfd\\n\",\n \"200 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190\\ncbccbbccaabacbbcbccbaccbcaababaacbbaaabccacababaacabbccacabacbcccbcabacabbacbbbcacbbcbbbbcccbbacbbbabcbccbcbbcbcabbabaacaacbacbccbccccaccccbacbacbabcbbaabcbacbbbcaccaaaccabcbbcbaaaacacacccbcacacbcabbc\\nbb\\n\",\n \"200 150\\nhbbfcgafgcfcgcaadbcgefbgafbdfdachggccbacgcddghbeeadafgbfggddefeaagchddbfebddaghaghbcfgebaadeaageefbgghgachabfcbadadhgbbegegehcgfhdghaedcffffbaghfdhfdhdgfcdfaaadbdgebffcegdfggeaheghafddfaeebeagfcbdhddh\\ndg\\n\",\n \"200 200\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\naa\\n\",\n \"200 100\\nhageafgacbdbffeahgchedebcdgdgbahcfhbgfghdfgdaefahhbcgabcbhggbbfbfdcffhcaddebdbhhgdheefabgfcdgbhaddgbbhdbedhhgegfebdeeehdhggcgbacfhebaebdddfdeacfhbdgfhdbefdeaefccbdhfefdaaeegahabbgbedagcaaccdhccaabdafh\\nhd\\n\",\n \"200 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1\\ncccbaacabcbbabbccbcaaabbbacacccbacaaababcabbaabacabaacbaacbaaccbcaabccabbaabcacabcaaaaaabaccbcacbbacabbaaccacabbcbcaaacaaccaccbabaaccbbccbaabbabbbaaaaacbacbcbaacbccabbcbaacbacaaabbcbaaaacbccbcababacac\\nac\\n\",\n \"200 20\\ngfbaiabgcjdigbjhcijaegddgacafajgghdfhfadfgecdggabiiechfiaedbhfeedbhcjfghdfiijebiddchbcbijjbdegdehhefcgaigjhcjchffdgfegdajhhbdhhjjcdggabfbfgfaffdfcjedeibahbdgfgajeejghhdajdbcfchchbgjcgbhfdgihacidbcijbe\\nbi\\n\",\n \"200 0\\naaaaabbbbaccbacabaacaaaccccaabbabaacbabcbabbcbcbbaaaacccaabaabbbcbccccbbccaaacbabbabbbaaaccabaabcababacccbcaccccbbacbaccaccccaabaabaabbabcaaacbcbaaabacaaccbacaabacbcababccccaabaaaabcbcbbaabcabcaccccbb\\nca\\n\",\n \"2 2\\nas\\nas\\n\",\n \"200 1\\nheeaccgddefffgbegdfdefefabdgcabegecbbffagfcegdbaedgdeafahahebbegeebfgbfdefbddegbgbaebcfgedhdfgcfdbafggffbaebddehabhdedffbfebbcdccgcbbffdbbabddabdahgbadheehdachhceefcfacdccfhbbaehegaebccebfgahfedahfdgf\\nch\\n\",\n \"200 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1\\nuysvnyfvmwnhjdtieprejgtxpbybqcmhpbdbbrnstutmeshhezgaulvssbaioozyxwooxcuzfwxrojqrwtucoxojtklzqrivvcnjehivpyszkkkecqeyztsnvwxitgcpsxbbpcvwxjejgdcqvpgmgqiqxrzijbzjuulkhvawhpiiryyntrhowocqzeoakcvmomckuyrn\\nxh\\n\",\n \"200 14\\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\\nba\\n\",\n \"200 98\\nhddhdbcfgaebeeafddfahgehaeggfdgecffbegdbdaaafdcfgdhdfhdfhgabffffcdeahgdhfgchegegebbghdadabcfbahcaghggbfeegaaedaabegfcbhgahgaddbefbddhcgaaefeddggfbgfadaeebhgddcgcabccgghcadfdbfagbfegcbdaacgcfcgfagcfbbh\\ndg\\n\",\n \"11 0\\nbdfbdbccdad\\nab\\n\",\n \"2 1\\nar\\nsa\\n\",\n \"2 0\\nar\\nas\\n\",\n \"200 0\\nesiqcqkirmeamjmggfdgrkdjirlesspqqdprrapiaasmserepidgbisilehqmgiddgfssqfmmdsiisdlkhpeqnieghbfpantckqngrehsjcqreplogtljajppamnhlbpbmrmmrirmboacjjpnrdonkachnfcndbmmjfkateltmemofalfplhgrsecpkgmajnpstgpheb\\nbg\\n\",\n \"200 190\\nddeaecceeacbccbdbdaaecbeccddbdcdaaeababdccbdeedcaddaeaacbcdebccdaabbdeecdabadaadebaacbebcecdcecbccbaedbeaacddbccdcecbedcdaaccceeebeeceedaadceeedcebeecbcbddeaacddadddeecbacbaddabdeabbcccedbbbabdadcadeb\\ncd\\n\",\n \"15 8\\nqwertyhgfdsazxc\\nqa\\n\",\n \"4 1\\nbbaa\\nab\\n\",\n \"2 1\\nab\\nbs\\n\",\n \"200 33\\nbbbbaaaccacdddeebdbddaadeedcbbdcaedccebcbbabccecacaaacdcaeaaaadaadbaabbeceecacdadebdddadeeadeedccdaaaeeabdbaabeccbedcaaccbbdbabbcdbdbcadeceadaacaaaabaadedecaaaabceeecadbaaacceedaebaedbcbcaabcdabcbdbca\\nce\\n\",\n \"2 1\\nar\\nas\\n\",\n \"2 0\\nar\\n`s\\n\",\n \"200 190\\ncbccbbccaabacbbcbccbaccbcaababaacbbaaabccacababaacabbccacabacbcccbcabacabbacbbbcacbbcbbbbcccbbacbbbabcbccacbbcbcabbabaacaacb`cbccbccccaccccbacbacbabcbbaabcbacbbbcaccaaaccabcbbcbaaaacacacccbcacacbcabbc\\nbb\\n\"\n ],\n \"outputs\": [\n \"15\\n\",\n \"16\\n\",\n \"10\\n\",\n \"3\\n\",\n \"3125\\n\",\n \"3741\\n\",\n \"0\\n\",\n \"6216\\n\",\n \"318\\n\",\n \"6380\\n\",\n \"25\\n\",\n \"7065\\n\",\n \"674\\n\",\n \"10\\n\",\n \"2464\\n\",\n \"19503\\n\",\n \"600\\n\",\n \"2206\\n\",\n \"10000\\n\",\n \"1\\n\",\n \"167\\n\",\n \"10000\\n\",\n \"1435\\n\",\n \"713\\n\",\n \"0\\n\",\n \"1\\n\",\n \"59\\n\",\n \"6428\\n\",\n \"10000\\n\",\n \"608\\n\",\n \"19900\\n\",\n \"282\\n\",\n \"8984\\n\",\n \"8355\\n\",\n \"32\\n\",\n \"10000\\n\",\n \"19900\\n\",\n \"10000\\n\",\n \"19900\\n\",\n \"9177\\n\",\n \"19900\\n\",\n \"5415\\n\",\n \"10000\\n\",\n \"4106\\n\",\n \"9927\\n\",\n \"232\\n\",\n \"276\\n\",\n \"32\\n\",\n \"9938\\n\",\n \"274\\n\",\n \"3179\\n\",\n \"0\\n\",\n \"6216\\n\",\n \"25\\n\",\n \"6956\\n\",\n \"2474\\n\",\n \"555\\n\",\n \"2181\\n\",\n \"1\\n\",\n \"178\\n\",\n \"10000\\n\",\n \"2023\\n\",\n \"564\\n\",\n \"8911\\n\",\n \"281\\n\",\n \"1943\\n\",\n \"1575\\n\",\n \"46\\n\",\n \"5100\\n\",\n \"19900\\n\",\n \"9585\\n\",\n \"4966\\n\",\n \"260\\n\",\n \"300\\n\",\n \"9734\\n\",\n \"652\\n\",\n \"21\\n\",\n \"8\\n\",\n \"2979\\n\",\n \"3368\\n\",\n \"35\\n\",\n \"7035\\n\",\n \"2158\\n\",\n \"193\\n\",\n \"24\\n\",\n \"605\\n\",\n \"6754\\n\",\n \"303\\n\",\n \"1984\\n\",\n \"1440\\n\",\n \"44\\n\",\n \"1351\\n\",\n \"5635\\n\",\n \"0\\n\",\n \"0\\n\",\n \"0\\n\",\n \"25\\n\",\n \"10000\\n\",\n \"25\\n\",\n \"1\\n\",\n \"0\\n\",\n \"1943\\n\",\n \"1\\n\",\n \"0\\n\",\n \"19900\\n\"\n ]\n}"},"problem":{"kind":"string","value":"You are given two strings s and t consisting of lowercase Latin letters. The length of t is 2 (i.e. this string consists only of two characters).\n\nIn one move, you can choose any character of s and replace it with any lowercase Latin letter. More formally, you choose some i and replace s_i (the character at the position i) with some character from 'a' to 'z'.\n\nYou want to do no more than k replacements in such a way that maximizes the number of occurrences of t in s as a subsequence.\n\nRecall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.\n\nInput\n\nThe first line of the input contains two integers n and k (2 ≤ n ≤ 200; 0 ≤ k ≤ n) — the length of s and the maximum number of moves you can make. The second line of the input contains the string s consisting of n lowercase Latin letters. The third line of the input contains the string t consisting of two lowercase Latin letters.\n\nOutput\n\nPrint one integer — the maximum possible number of occurrences of t in s as a subsequence if you replace no more than k characters in s optimally.\n\nExamples\n\nInput\n\n\n4 2\nbbaa\nab\n\n\nOutput\n\n\n3\n\n\nInput\n\n\n7 3\nasddsaf\nsd\n\n\nOutput\n\n\n10\n\n\nInput\n\n\n15 6\nqwertyhgfdsazxc\nqa\n\n\nOutput\n\n\n16\n\n\nInput\n\n\n7 2\nabacaba\naa\n\n\nOutput\n\n\n15\n\nNote\n\nIn the first example, you can obtain the string \"abab\" replacing s_1 with 'a' and s_4 with 'b'. Then the answer is 3.\n\nIn the second example, you can obtain the string \"ssddsdd\" and get the answer 10.\n\nIn the fourth example, you can obtain the string \"aaacaaa\" and get the answer 15."}}},{"rowIdx":92,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n7 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n7 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n14 6 5 4 3 2 1\\n\",\n \"2\\n3 1\\n7 6 3 5 4 2 1\\n3 2\\n14 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 1\\n23 6 5 4 3 2 1\\n\",\n \"2\\n3 1\\n7 6 3 5 4 2 1\\n3 1\\n23 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n14 9 5 6 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n17 6 8 4 5 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n14 6 8 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n13 6 8 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n23 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n14 6 3 5 4 2 1\\n3 2\\n23 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n21 6 8 4 3 2 1\\n\",\n \"2\\n3 2\\n11 6 3 5 4 2 1\\n3 2\\n7 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n14 12 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n17 6 8 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n14 9 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n10 9 5 4 3 2 1\\n\",\n \"2\\n3 2\\n14 6 3 5 4 2 1\\n3 2\\n23 9 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n17 5 8 4 3 2 1\\n\",\n \"2\\n3 2\\n14 6 3 5 4 2 1\\n3 2\\n23 13 5 4 3 2 1\\n\",\n \"2\\n3 2\\n14 10 3 5 4 2 1\\n3 2\\n23 13 5 4 3 2 1\\n\",\n \"2\\n3 2\\n11 6 3 5 4 2 1\\n3 2\\n21 6 8 4 3 2 1\\n\",\n \"2\\n3 2\\n15 6 3 5 4 2 1\\n3 2\\n23 9 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n18 9 5 6 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 1\\n14 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n9 5 8 4 3 2 1\\n\",\n \"2\\n3 2\\n14 6 3 5 4 2 1\\n3 2\\n23 13 6 4 3 2 1\\n\",\n \"2\\n3 2\\n11 6 3 5 4 2 1\\n3 2\\n21 6 5 4 3 2 1\\n\",\n \"2\\n3 2\\n14 6 3 5 4 2 1\\n3 2\\n21 13 6 4 3 2 1\\n\",\n \"2\\n3 2\\n14 10 3 5 4 2 1\\n3 2\\n23 12 5 4 3 2 1\\n\",\n \"2\\n3 2\\n14 10 3 5 4 2 1\\n3 2\\n23 12 9 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n13 5 8 4 3 2 1\\n\",\n \"2\\n3 2\\n14 6 3 5 4 2 1\\n3 2\\n44 13 5 4 3 2 1\\n\",\n \"2\\n3 2\\n11 6 3 5 4 2 1\\n3 2\\n21 7 8 4 3 2 1\\n\",\n \"2\\n3 2\\n15 6 3 5 4 2 1\\n3 2\\n23 7 5 4 3 2 1\\n\",\n \"2\\n3 2\\n7 6 3 5 4 2 1\\n3 2\\n18 9 10 6 3 2 1\\n\",\n \"2\\n3 1\\n14 10 3 5 4 2 1\\n3 2\\n23 12 9 4 3 2 1\\n\",\n \"2\\n3 2\\n14 6 3 5 4 2 1\\n3 1\\n44 13 5 4 3 2 1\\n\"\n ],\n \"outputs\": [\n \"10\\n1 1 3 3 \\n8\\n1 1 1 3 \\n\",\n \"10\\n1 1 3 3 \\n8\\n1 1 1 3 \\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"1\\n1 1 1 1 1 1\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n1\\n1 1 1 1 1 1\\n\",\n \"1\\n1 1 1 1 1 1\\n1\\n1 1 1 1 1 1\\n\",\n \"10\\n1 1 3 3\\n9\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n10\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n9\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n1\\n1 1 1 1 1 1\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n10\\n1 1 1 3\\n\",\n \"1\\n1 1 1 1 1 1\\n8\\n1 1 1 3\\n\",\n \"10\\n1 1 3 3\\n1\\n1 1 1 1 1 1\\n\"\n ]\n}"},"problem":{"kind":"string","value":"Drazil likes heap very much. So he created a problem with heap:\n\nThere is a max heap with a height h implemented on the array. The details of this heap are the following:\n\nThis heap contains exactly 2^h - 1 distinct positive non-zero integers. All integers are distinct. These numbers are stored in the array a indexed from 1 to 2^h-1. For any 1 < i < 2^h, a[i] < a[\\left ⌊{i/2}\\right ⌋].\n\nNow we want to reduce the height of this heap such that the height becomes g with exactly 2^g-1 numbers in heap. To reduce the height, we should perform the following action 2^h-2^g times:\n\nChoose an index i, which contains an element and call the following function f in index i:\n\n\n\nNote that we suppose that if a[i]=0, then index i don't contain an element.\n\nAfter all operations, the remaining 2^g-1 element must be located in indices from 1 to 2^g-1. Now Drazil wonders what's the minimum possible sum of the remaining 2^g-1 elements. Please find this sum and find a sequence of the function calls to achieve this value.\n\nInput\n\nThe first line of the input contains an integer t (1 ≤ t ≤ 70 000): the number of test cases.\n\nEach test case contain two lines. The first line contains two integers h and g (1 ≤ g < h ≤ 20). The second line contains n = 2^h-1 distinct positive integers a[1], a[2], …, a[n] (1 ≤ a[i] < 2^{20}). For all i from 2 to 2^h - 1, a[i] < a[\\left ⌊{i/2}\\right ⌋].\n\nThe total sum of n is less than 2^{20}.\n\nOutput\n\nFor each test case, print two lines.\n\nThe first line should contain one integer denoting the minimum sum after reducing the height of heap to g. The second line should contain 2^h - 2^g integers v_1, v_2, …, v_{2^h-2^g}. In i-th operation f(v_i) should be called.\n\nExample\n\nInput\n\n\n2\n3 2\n7 6 3 5 4 2 1\n3 2\n7 6 5 4 3 2 1\n\n\nOutput\n\n\n10\n3 2 3 1\n8\n2 1 3 1"}}},{"rowIdx":93,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"5\",\n \"1\",\n \"4\",\n \"2\",\n \"3\",\n \"8\",\n \"11\",\n \"10\",\n \"7\",\n \"6\",\n \"12\",\n \"14\",\n \"9\",\n \"19\",\n \"16\",\n \"15\",\n \"13\",\n \"23\",\n \"32\",\n \"58\",\n \"99\",\n \"34\",\n \"54\",\n \"35\",\n \"40\",\n \"67\",\n \"41\",\n \"62\",\n \"49\",\n \"24\",\n \"17\",\n \"18\",\n \"21\",\n \"25\",\n \"20\",\n \"30\",\n \"56\",\n \"29\",\n \"66\",\n \"27\",\n \"22\",\n \"105\",\n \"43\",\n \"38\",\n \"28\",\n \"89\",\n \"26\",\n \"46\",\n \"39\",\n \"79\",\n \"45\",\n \"51\",\n \"102\",\n \"31\",\n \"69\",\n \"60\",\n \"108\",\n \"53\",\n \"48\",\n \"74\",\n \"44\",\n \"47\",\n \"70\",\n \"120\",\n \"36\",\n \"42\",\n \"109\",\n \"52\",\n \"81\",\n \"59\",\n \"77\",\n \"68\",\n \"50\",\n \"143\",\n \"122\",\n \"106\",\n \"87\",\n \"103\",\n \"112\",\n \"134\",\n \"75\",\n \"61\",\n \"188\",\n \"73\",\n \"170\",\n \"149\",\n \"125\",\n \"86\",\n \"214\",\n \"37\",\n \"118\",\n \"95\",\n \"76\",\n \"291\",\n \"123\",\n \"72\",\n \"133\",\n \"190\",\n \"96\",\n \"101\",\n \"57\"\n ],\n \"outputs\": [\n \"130000\",\n \"105000\\n\",\n \"123000\\n\",\n \"111000\\n\",\n \"117000\\n\",\n \"152000\\n\",\n \"177000\\n\",\n \"168000\\n\",\n \"144000\\n\",\n \"137000\\n\",\n \"186000\\n\",\n \"206000\\n\",\n \"160000\\n\",\n \"265000\\n\",\n \"228000\\n\",\n \"217000\\n\",\n \"196000\\n\",\n \"324000\\n\",\n \"507000\\n\",\n \"1823000\\n\",\n \"13530000\\n\",\n \"560000\\n\",\n \"1499000\\n\",\n \"588000\\n\",\n \"753000\\n\",\n \"2833000\\n\",\n \"791000\\n\",\n \"2218000\\n\",\n \"1173000\\n\",\n \"341000\\n\",\n \"240000\\n\",\n \"252000\\n\",\n \"293000\\n\",\n \"359000\\n\",\n \"279000\\n\",\n \"459000\\n\",\n \"1653000\\n\",\n \"437000\\n\",\n \"2698000\\n\",\n \"396000\\n\",\n \"308000\\n\",\n \"18135000\\n\",\n \"873000\\n\",\n \"682000\\n\",\n \"416000\\n\",\n \"8303000\\n\",\n \"377000\\n\",\n \"1012000\\n\",\n \"717000\\n\",\n \"5094000\\n\",\n \"963000\\n\",\n \"1294000\\n\",\n \"15664000\\n\",\n \"482000\\n\",\n \"3124000\\n\",\n \"2011000\\n\",\n \"20995000\\n\",\n \"1427000\\n\",\n \"1117000\\n\",\n \"3990000\\n\",\n \"917000\\n\",\n \"1063000\\n\",\n \"3281000\\n\",\n \"37712000\\n\",\n \"618000\\n\",\n \"831000\\n\",\n \"22045000\\n\",\n \"1359000\\n\",\n \"5617000\\n\",\n \"1915000\\n\",\n \"4620000\\n\",\n \"2975000\\n\",\n \"1232000\\n\",\n \"115848000\\n\",\n \"41578000\\n\",\n \"19042000\\n\",\n \"7530000\\n\",\n \"16448000\\n\",\n \"25522000\\n\",\n \"74673000\\n\",\n \"4190000\\n\",\n \"2112000\\n\",\n \"1040975000\\n\",\n \"3800000\\n\",\n \"432541000\\n\",\n \"155251000\\n\",\n \"48132000\\n\",\n \"7171000\\n\",\n \"3701387000\\n\",\n \"649000\\n\",\n \"34205000\\n\",\n \"11129000\\n\",\n \"4400000\\n\",\n \"158467928000\\n\",\n \"43657000\\n\",\n \"3619000\\n\",\n \"71117000\\n\",\n \"1147676000\\n\",\n \"11686000\\n\",\n \"14918000\\n\",\n \"1736000\\n\"\n ]\n}"},"problem":{"kind":"string","value":"Your friend who lives in undisclosed country is involved in debt. He is borrowing 100,000-yen from a loan shark. The loan shark adds 5% interest of the debt and rounds it to the nearest 1,000 above week by week.\n\nWrite a program which computes the amount of the debt in n weeks.\n\n\n\nInput\n\nAn integer n (0 ≤ n ≤ 100) is given in a line.\n\nOutput\n\nPrint the amout of the debt in a line.\n\nExample\n\nInput\n\n5\n\n\nOutput\n\n130000"}}},{"rowIdx":94,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"3\\na\\naa\\naa\\na\\n\",\n \"5\\nba\\na\\nabab\\na\\naba\\nbaba\\nab\\naba\\n\",\n \"2\\na\\nc\\n\",\n \"5\\na\\na\\nab\\nba\\naba\\naba\\nbaba\\nabab\\n\",\n \"4\\nab\\na\\nb\\nbab\\nab\\naba\\n\",\n \"5\\na\\naa\\naaa\\naaaa\\nb\\nba\\nbaa\\nbaaa\\n\",\n \"4\\na\\nba\\naba\\nb\\nba\\nbab\\n\",\n \"4\\na\\nb\\nab\\nab\\nbab\\naba\\n\",\n \"5\\nbaba\\nabab\\na\\nab\\naba\\na\\nba\\naba\\n\",\n \"4\\nzn\\nz\\nn\\nnzn\\nzn\\nznz\\n\",\n \"4\\nb\\nab\\nbab\\na\\nab\\naba\\n\",\n \"4\\nb\\nbb\\nbba\\nbbb\\nba\\na\\n\",\n \"8\\na\\nha\\naha\\nhaha\\nahaha\\nhahaha\\nahahaha\\nh\\nha\\nhah\\nhaha\\nhahah\\nhahaha\\nhahahah\\n\",\n \"3\\na\\na\\nba\\nab\\n\",\n \"4\\nza\\na\\nz\\naza\\nza\\nzaz\\n\",\n \"4\\na\\nab\\nbab\\nb\\nab\\naba\\n\",\n \"5\\nabab\\nbaba\\nb\\nb\\nbab\\nbab\\nba\\nab\\n\",\n \"3\\na\\nza\\naz\\na\\n\",\n \"4\\nc\\ncb\\nb\\nbcb\\ncb\\ncbc\\n\",\n \"4\\na\\nc\\nac\\nab\\naba\\nbac\\n\",\n \"3\\na\\nb\\naa\\nab\\n\",\n \"5\\nc\\ncd\\ncdc\\ncdcc\\nb\\ncb\\nccb\\ndccb\\n\",\n \"3\\na\\naa\\nba\\nb\\n\",\n \"5\\nbaaa\\nbaa\\nba\\nb\\naaaa\\naaa\\naa\\na\\n\",\n \"4\\nb\\nbb\\nbbb\\na\\nba\\nbba\\n\",\n \"4\\naba\\na\\nba\\nb\\nba\\nbab\\n\",\n \"4\\nbab\\nab\\na\\nab\\naba\\nb\\n\",\n \"2\\nz\\nz\\n\",\n \"3\\nb\\nb\\nab\\nba\\n\",\n \"5\\nba\\na\\na\\naba\\nbaba\\nab\\naba\\nabab\\n\",\n \"5\\nb\\nb\\nba\\nab\\nbab\\nbab\\nabab\\nbaba\\n\",\n \"5\\nh\\nhwh\\nwhwh\\nhw\\nh\\nwh\\nhwh\\nhwhw\\n\",\n \"3\\nba\\nab\\na\\na\\n\",\n \"5\\nba\\na\\nbaba\\nabab\\na\\naba\\nab\\naba\\n\",\n \"5\\nxy\\nyx\\nx\\nx\\nxyx\\nxyx\\nyxyx\\nxyxy\\n\",\n \"3\\nah\\nha\\nh\\nh\\n\",\n \"5\\nba\\na\\nbaba\\na\\naba\\nabab\\nab\\naba\\n\",\n \"18\\nd\\nh\\ndj\\nxh\\ndjs\\njxh\\ndjsh\\nzjxh\\ndjshf\\nkzjxh\\ndjshfk\\nhkzjxh\\ndjshfkj\\nkhkzjxh\\ndjshfkje\\nskhkzjxh\\ndjshfkjeh\\ndskhkzjxh\\ndjshfkjehd\\nhdskhkzjxh\\ndjshfkjehds\\nehdskhkzjxh\\ndjshfkjehdsk\\njehdskhkzjxh\\ndjshfkjehdskh\\nkjehdskhkzjxh\\ndjshfkjehdskhk\\nfkjehdskhkzjxh\\ndjshfkjehdskhkz\\nhfkjehdskhkzjxh\\ndjshfkjehdskhkzj\\nshfkjehdskhkzjxh\\ndjshfkjehdskhkzjx\\njshfkjehdskhkzjxh\\n\",\n \"4\\nbab\\naba\\nab\\nab\\na\\nb\\n\",\n \"3\\na\\nb\\naa\\nba\\n\",\n \"2\\nz\\n{\\n\",\n \"3\\na\\naa\\nab\\nb\\n\",\n \"2\\n`\\nc\\n\",\n \"2\\n_\\nc\\n\",\n \"2\\n_\\nb\\n\",\n \"2\\n^\\nc\\n\",\n \"2\\n^\\nb\\n\",\n \"2\\n]\\nb\\n\",\n \"2\\n^\\na\\n\",\n \"2\\n_\\na\\n\",\n \"2\\n_\\n`\\n\",\n \"2\\n`\\na\\n\",\n \"2\\n`\\n`\\n\",\n \"2\\n]\\na\\n\",\n \"2\\n^\\nd\\n\",\n \"2\\n_\\nd\\n\",\n \"2\\n`\\nd\\n\",\n \"2\\n`\\ne\\n\",\n \"2\\na\\ne\\n\",\n \"2\\nb\\ne\\n\",\n \"2\\nc\\ne\\n\",\n \"2\\nb\\nf\\n\",\n \"2\\nc\\nf\\n\",\n \"2\\nd\\nf\\n\",\n \"2\\nd\\ne\\n\",\n \"2\\nd\\nd\\n\",\n \"2\\nc\\nd\\n\",\n \"2\\nc\\nc\\n\",\n \"2\\ny\\nz\\n\",\n \"2\\na\\nb\\n\",\n \"2\\n\\\\\\na\\n\",\n \"2\\n_\\n_\\n\",\n \"2\\n`\\nb\\n\",\n \"2\\n]\\nd\\n\",\n \"2\\n]\\nc\\n\",\n \"2\\n^\\n`\\n\",\n \"2\\n^\\n_\\n\",\n \"2\\n\\\\\\nc\\n\",\n \"2\\n]\\n`\\n\",\n \"2\\na\\na\\n\",\n \"2\\n\\\\\\nd\\n\",\n \"2\\na\\nd\\n\",\n \"2\\n_\\ne\\n\",\n \"2\\nb\\nd\\n\",\n \"2\\na\\nf\\n\",\n \"2\\n`\\nf\\n\",\n \"2\\ne\\ne\\n\",\n \"2\\n\\\\\\n`\\n\",\n \"2\\nb\\ng\\n\",\n \"2\\ne\\nf\\n\",\n \"2\\nb\\nc\\n\",\n \"2\\na\\ng\\n\",\n \"2\\ny\\n{\\n\",\n \"2\\n^\\ne\\n\",\n \"2\\n[\\na\\n\",\n \"2\\n]\\ne\\n\",\n \"2\\n\\\\\\ne\\n\",\n \"2\\n^\\n^\\n\",\n \"2\\n\\\\\\nb\\n\",\n \"2\\n[\\nd\\n\",\n \"2\\n\\\\\\n_\\n\",\n \"2\\nb\\nb\\n\",\n \"2\\nb\\nh\\n\",\n \"2\\n_\\nf\\n\",\n \"2\\n\\\\\\nf\\n\",\n \"2\\n[\\ne\\n\",\n \"2\\n`\\ng\\n\",\n \"2\\n]\\n_\\n\",\n \"2\\ne\\ng\\n\",\n \"2\\n[\\n`\\n\",\n \"2\\nc\\nh\\n\",\n \"2\\nf\\nf\\n\",\n \"2\\na\\nh\\n\",\n \"2\\ny\\n|\\n\",\n \"2\\n^\\nf\\n\",\n \"2\\n]\\nf\\n\",\n \"2\\n[\\nf\\n\",\n \"2\\n[\\nc\\n\",\n \"2\\nZ\\nf\\n\",\n \"2\\n\\\\\\n^\\n\",\n \"2\\nc\\ng\\n\",\n \"2\\n]\\ng\\n\",\n \"2\\n\\\\\\ng\\n\"\n ],\n \"outputs\": [\n \"PPSS\",\n \"SPPSPSPS\",\n \"PS\",\n \"PSPSPSSP\",\n \"PPSSSP\",\n \"SSSSPPPP\",\n \"SPSPSP\",\n \"PSPSSP\",\n \"SPPPPSSS\",\n \"PPSSSP\",\n \"SPSPSP\",\n \"PPSPSS\",\n \"SPSPSPSPSPSPSP\",\n \"PSSP\",\n \"PSPSSP\",\n \"PPSSSP\",\n \"SPPSPSPS\",\n \"PSPS\",\n \"PPSSSP\",\n \"PSSPPS\",\n \"PSPS\",\n \"PPPPSSSS\",\n \"SSPP\",\n \"PPPPSSSS\",\n \"PPPSSS\",\n \"SSPPSP\",\n \"SPPSPS\",\n \"PS\",\n \"PSSP\",\n \"SPSPSPSP\",\n \"PSPSPSSP\",\n \"PPSPSSSP\",\n \"SPPS\",\n \"SPSPSPPS\",\n \"PSPSPSSP\",\n \"SPPS\",\n \"SPSSPPPS\",\n \"PSPSPSPSPSPSPSPSPSPSPSPSPSPSPSPSPS\",\n \"SPPSPS\",\n \"SPSP\",\n \"PS\",\n \"PPSS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\",\n \"PS\"\n ]\n}"},"problem":{"kind":"string","value":"Ivan wants to play a game with you. He picked some string s of length n consisting only of lowercase Latin letters. \n\nYou don't know this string. Ivan has informed you about all its improper prefixes and suffixes (i.e. prefixes and suffixes of lengths from 1 to n-1), but he didn't tell you which strings are prefixes and which are suffixes.\n\nIvan wants you to guess which of the given 2n-2 strings are prefixes of the given string and which are suffixes. It may be impossible to guess the string Ivan picked (since multiple strings may give the same set of suffixes and prefixes), but Ivan will accept your answer if there is at least one string that is consistent with it. Let the game begin!\n\nInput\n\nThe first line of the input contains one integer number n (2 ≤ n ≤ 100) — the length of the guessed string s.\n\nThe next 2n-2 lines are contain prefixes and suffixes, one per line. Each of them is the string of length from 1 to n-1 consisting only of lowercase Latin letters. They can be given in arbitrary order.\n\nIt is guaranteed that there are exactly 2 strings of each length from 1 to n-1. It is also guaranteed that these strings are prefixes and suffixes of some existing string of length n.\n\nOutput\n\nPrint one string of length 2n-2 — the string consisting only of characters 'P' and 'S'. The number of characters 'P' should be equal to the number of characters 'S'. The i-th character of this string should be 'P' if the i-th of the input strings is the prefix and 'S' otherwise.\n\nIf there are several possible answers, you can print any.\n\nExamples\n\nInput\n\n\n5\nba\na\nabab\na\naba\nbaba\nab\naba\n\n\nOutput\n\n\nSPPSPSPS\n\n\nInput\n\n\n3\na\naa\naa\na\n\n\nOutput\n\n\nPPSS\n\n\nInput\n\n\n2\na\nc\n\n\nOutput\n\n\nPS\n\nNote\n\nThe only string which Ivan can guess in the first example is \"ababa\".\n\nThe only string which Ivan can guess in the second example is \"aaa\". Answers \"SPSP\", \"SSPP\" and \"PSPS\" are also acceptable.\n\nIn the third example Ivan can guess the string \"ac\" or the string \"ca\". The answer \"SP\" is also acceptable."}}},{"rowIdx":95,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"98765432109876543210\\n58\",\n \"30\\n4\",\n \"1000000009\\n1\",\n \"98765432109876543210\\n66\",\n \"30\\n1\",\n \"1000000009\\n2\",\n \"98765432109876543210\\n18\",\n \"1000000009\\n4\",\n \"98765432109876543210\\n11\",\n \"1000000009\\n5\",\n \"98765432109876543210\\n12\",\n \"1000000009\\n9\",\n \"98765432109876543210\\n10\",\n \"1000000009\\n7\",\n \"98765432109876543210\\n15\",\n \"1000000009\\n12\",\n \"98765432109876543210\\n4\",\n \"1000000009\\n15\",\n \"98765432109876543210\\n8\",\n \"1000000009\\n29\",\n \"98765432109876543210\\n7\",\n \"1000000009\\n56\",\n \"98765432109876543210\\n5\",\n \"1000000009\\n66\",\n \"98765432109876543210\\n3\",\n \"98765432109876543210\\n1\",\n \"98765432109876543210\\n39\",\n \"30\\n2\",\n \"98765432109876543210\\n19\",\n \"1000000009\\n3\",\n \"98765432109876543210\\n13\",\n \"98765432109876543210\\n6\",\n 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\"979267466\\n\",\n \"26117982\\n\",\n \"42126975\\n\"\n ]\n}"},"problem":{"kind":"string","value":"Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:\n\n* The sum of the digits in base ten is a multiple of D.\n\nConstraints\n\n* All values in input are integers.\n* 1 \\leq K < 10^{10000}\n* 1 \\leq D \\leq 100\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nK\nD\n\n\nOutput\n\nPrint the number of integers satisfying the condition, modulo 10^9 + 7.\n\nExamples\n\nInput\n\n30\n4\n\n\nOutput\n\n6\n\n\nInput\n\n1000000009\n1\n\n\nOutput\n\n2\n\n\nInput\n\n98765432109876543210\n58\n\n\nOutput\n\n635270834"}}},{"rowIdx":96,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"3\\n8 3\\n0 1\\n4 8\",\n \"1\\n1 1\",\n \"2\\n1 2\\n3 2\",\n \"2\\n1 3\\n3 1\",\n \"1\\n0 0\",\n \"2\\n1 5\\n5 1\",\n \"3\\n8 3\\n-1 1\\n5 8\",\n \"2\\n0 2\\n3 1\",\n \"2\\n0 1\\n3 2\",\n \"2\\n1 4\\n5 2\",\n \"3\\n8 3\\n-1 0\\n4 8\",\n \"1\\n2 2\",\n \"1\\n-1 -1\",\n \"2\\n1 0\\n1 2\",\n \"2\\n2 3\\n2 1\",\n \"1\\n3 3\",\n \"1\\n-2 -2\",\n \"2\\n1 0\\n2 3\",\n \"2\\n-1 2\\n4 1\",\n \"2\\n2 3\\n3 2\",\n \"1\\n-3 -3\",\n \"2\\n2 1\\n2 3\",\n \"2\\n0 2\\n4 2\",\n \"2\\n0 0\\n2 2\",\n \"2\\n0 4\\n5 1\",\n \"2\\n2 5\\n5 2\",\n \"2\\n1 3\\n4 2\",\n \"2\\n1 1\\n1 1\",\n \"2\\n-2 2\\n4 0\",\n \"2\\n2 2\\n3 3\",\n \"2\\n1 2\\n2 1\",\n \"2\\n2 0\\n1 3\",\n \"2\\n1 1\\n0 0\",\n \"2\\n-2 1\\n4 1\",\n \"2\\n0 1\\n1 0\",\n \"3\\n11 3\\n-1 1\\n2 8\",\n \"2\\n0 3\\n4 1\",\n \"2\\n0 2\\n2 0\",\n \"2\\n2 2\\n2 2\",\n \"1\\n-6 -6\",\n \"2\\n2 2\\n1 1\",\n \"1\\n-4 -4\",\n \"2\\n-1 0\\n2 1\",\n \"2\\n-4 1\\n6 1\",\n \"2\\n1 1\\n2 2\",\n \"2\\n0 0\\n1 1\",\n \"2\\n2 1\\n1 2\",\n \"2\\n0 1\\n2 1\",\n \"2\\n2 4\\n3 1\",\n \"2\\n2 2\\n4 4\",\n \"2\\n0 0\\n4 4\",\n \"2\\n3 0\\n0 3\",\n \"2\\n1 2\\n0 -1\",\n \"2\\n1 0\\n0 1\",\n \"2\\n1 -1\\n1 3\",\n \"2\\n1 4\\n3 0\",\n \"2\\n1 0\\n3 4\",\n \"2\\n0 0\\n3 3\",\n \"2\\n0 -1\\n1 2\",\n \"2\\n1 3\\n2 0\",\n \"2\\n2 0\\n0 2\",\n \"2\\n1 -1\\n0 2\",\n \"2\\n0 0\\n0 0\",\n \"2\\n-1 1\\n1 -1\",\n \"2\\n1 1\\n3 3\",\n \"2\\n-1 -1\\n1 1\",\n \"2\\n4 4\\n2 2\",\n \"1\\n4 4\",\n \"2\\n2 0\\n2 4\",\n \"2\\n0 1\\n0 -1\",\n \"2\\n-1 2\\n2 -1\",\n \"2\\n2 2\\n0 0\",\n \"2\\n1 2\\n1 0\",\n \"2\\n-1 -1\\n0 0\",\n \"2\\n0 3\\n3 0\",\n \"2\\n0 3\\n2 -1\",\n \"2\\n2 -1\\n-1 2\",\n \"2\\n0 2\\n1 -1\",\n \"2\\n-1 1\\n2 0\",\n \"2\\n2 1\\n-1 0\",\n \"2\\n-1 2\\n3 0\",\n \"2\\n1 5\\n6 2\",\n \"2\\n1 0\\n4 5\",\n \"2\\n1 2\\n4 3\",\n \"2\\n2 4\\n2 0\",\n \"1\\n0 0\",\n \"1\\n-1 -1\",\n \"1\\n2 2\",\n \"2\\n0 2\\n4 2\",\n \"1\\n-2 -2\",\n \"1\\n-3 -3\",\n \"2\\n0 3\\n4 1\",\n \"2\\n1 2\\n1 0\",\n \"2\\n1 4\\n4 1\",\n \"1\\n4 4\",\n \"2\\n0 1\\n3 2\",\n \"1\\n3 3\",\n \"1\\n-4 -4\",\n \"2\\n1 2\\n2 1\",\n \"2\\n0 0\\n3 3\",\n \"2\\n1 4\\n3 0\",\n \"2\\n1 1\\n3 3\",\n \"2\\n1 3\\n3 1\"\n ],\n \"outputs\": [\n \"9\",\n \"0\",\n \"2\",\n \"3\\n\",\n \"0\\n\",\n \"5\\n\",\n 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\"0\\n\",\n \"0\\n\",\n \"3\\n\",\n \"2\\n\",\n \"4\\n\",\n \"0\\n\",\n \"1\\n\",\n \"0\\n\",\n \"0\\n\",\n \"2\\n\",\n \"0\\n\",\n \"4\\n\",\n \"0\\n\",\n \"3\\n\"\n ]\n}"},"problem":{"kind":"string","value":"You are given sequences A and B consisting of non-negative integers. The lengths of both A and B are N, and the sums of the elements in A and B are equal. The i-th element in A is A_i, and the i-th element in B is B_i.\n\nTozan and Gezan repeats the following sequence of operations:\n\n* If A and B are equal sequences, terminate the process.\n* Otherwise, first Tozan chooses a positive element in A and decrease it by 1.\n* Then, Gezan chooses a positive element in B and decrease it by 1.\n* Then, give one candy to Takahashi, their pet.\n\n\n\nTozan wants the number of candies given to Takahashi until the process is terminated to be as large as possible, while Gezan wants it to be as small as possible. Find the number of candies given to Takahashi when both of them perform the operations optimally.\n\nConstraints\n\n* 1 \\leq N \\leq 2 × 10^5\n* 0 \\leq A_i,B_i \\leq 10^9(1\\leq i\\leq N)\n* The sums of the elements in A and B are equal.\n* All values in input are integers.\n\nInput\n\nInput is given from Standard Input in the following format:\n\n\nN\nA_1 B_1\n:\nA_N B_N\n\n\nOutput\n\nPrint the number of candies given to Takahashi when both Tozan and Gezan perform the operations optimally.\n\nExamples\n\nInput\n\n2\n1 2\n3 2\n\n\nOutput\n\n2\n\n\nInput\n\n3\n8 3\n0 1\n4 8\n\n\nOutput\n\n9\n\n\nInput\n\n1\n1 1\n\n\nOutput\n\n0"}}},{"rowIdx":97,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"3\\njohn johanna\\nira ira\\nkayla jayla\",\n \"3\\njohn johanna\\nira ria\\nkayla jayla\",\n \"3\\njohn johanna\\nria ria\\nkayla jayla\",\n \"3\\njogn johanna\\nria qia\\nkayma jayla\",\n \"3\\nipoh o`gomka\\nbjr bjr\\njmya` aayjk\",\n \"3\\njohn johanna\\nria ria\\nkayma jayla\",\n \"3\\njohn johanna\\nria qia\\nkayma jayla\",\n \"3\\nngoj johanna\\nria qia\\nkayma jayla\",\n \"3\\nngoj johanna\\nria qi`\\nkayma jayla\",\n \"3\\nngoj joganna\\nria qi`\\nkayma jayla\",\n \"3\\nngoj joganna\\nria qi`\\nkaxma jayla\",\n \"3\\nngpj joganna\\nria qi`\\nkaxma jayla\",\n \"3\\njpgn joganna\\nria qi`\\nkaxma jayla\",\n \"3\\njpgn joganna\\nair qi`\\nkaxma jayla\",\n \"3\\njpgn joganna\\nari qi`\\nkaxma jayla\",\n \"3\\njpgn jog`nna\\nari qi`\\nkaxma jayla\",\n \"3\\njpgn jog`nna\\nari qi`\\namxak jayla\",\n \"3\\njgpn jog`nna\\nari qi`\\namxak jayla\",\n \"3\\njgpn jog`nna\\nari qi`\\namxak alyaj\",\n \"3\\nnpgj jog`nna\\nari qi`\\namxak jayla\",\n \"3\\npngj jog`nna\\nari qi`\\namxak jayla\",\n \"3\\npngj jog`nna\\nari qi`\\nkmxaa jayla\",\n \"3\\npngj ann`goj\\nari qi`\\nkmxaa jayla\",\n \"3\\npngj ann`goj\\nari qj`\\nkmxaa jayla\",\n \"3\\njgnp ann`goj\\nari qj`\\nkmxaa jayla\",\n \"3\\njgnp ann`goj\\nari qi`\\nkmxaa jayla\",\n \"3\\njgnp ann`gok\\nari qi`\\nkmxaa jayla\",\n \"3\\njgnp ann`gok\\nari qi`\\nkmxaa layja\",\n \"3\\njgnp ann`gok\\nari qi`\\naaxmk layja\",\n \"3\\njgnp ann`gok\\nari qj`\\naaxmk layja\",\n \"3\\npngj ann`gok\\nari qj`\\naaxmk layja\",\n \"3\\npnhj ann`gok\\nari qj`\\naaxmk layja\",\n \"3\\npnhj ann`gok\\nari qj`\\naaxmk ajyal\",\n \"3\\npnhj ann`gok\\naqi qj`\\naaxmk ajyal\",\n \"3\\njhnp ann`gok\\nari qj`\\naaxmk layja\",\n \"3\\njhnp ann`gok\\nair qj`\\naaxmk layja\",\n \"3\\njhnp ann`gok\\nria qj`\\naaxmk layja\",\n \"3\\njhnp ann`gok\\nrja qj`\\naaxmk layja\",\n \"3\\njhnp ann`gok\\najr qj`\\naaxmk layja\",\n \"3\\njhnp ann`gok\\najr rj`\\naaxmk layja\",\n \"3\\njhnp ann`gok\\najr rj`\\naaxmk kayja\",\n \"3\\njhnp ann`gok\\najr rj`\\nkmxaa kayja\",\n \"3\\njhnp ann`gok\\najr `jr\\nkmxaa kayja\",\n \"3\\njhnp ann`gok\\najr `jr\\naaxmk kayja\",\n \"3\\njgnp ann`gok\\najr `jr\\naaxmk kayja\",\n \"3\\njhnp annog`k\\najr `jr\\naaxmk kayja\",\n \"3\\njhnp annog`k\\nrja `jr\\naaxmk kayja\",\n \"3\\njhnp aknog`n\\nrja `jr\\naaxmk kayja\",\n \"3\\njhnp aknog`n\\nrja `jr\\n`axmk kayja\",\n \"3\\njhnp akmog`n\\nrja `jr\\n`axmk kayja\",\n \"3\\npnhj akmog`n\\nrja `jr\\n`axmk kayja\",\n \"3\\npnhj akmog`n\\nrja `jr\\nkmxa` kayja\",\n \"3\\npnhj akmog`n\\nrja ajr\\nkmxa` kayja\",\n \"3\\npnhj akmog`n\\nrjb ajr\\nkmxa` kayja\",\n \"3\\npnhj akmog`n\\nrjb ajr\\njmxa` kayja\",\n \"3\\nnphj akmog`n\\nrjb ajr\\njmxa` kayja\",\n \"3\\nnphj akmog`n\\nbjr ajr\\njmxa` kayja\",\n \"3\\nnpjh akmog`n\\nbjr ajr\\njmxa` kayja\",\n \"3\\nnpjh akmog`n\\nbjr ajr\\njmya` kayja\",\n \"3\\nnpjh n`gomka\\nbjr ajr\\njmya` kayja\",\n \"3\\njpnh n`gomka\\nbjr ajr\\njmya` kayja\",\n \"3\\njpoh n`gomka\\nbjr ajr\\njmya` kayja\",\n \"3\\njpoh n`gomka\\nbjr ajr\\n`aymj kayja\",\n \"3\\njpoh n`gomka\\nbjr ajr\\njmya` aayjk\",\n \"3\\njpoh n`gomka\\nbjr rja\\njmya` aayjk\",\n \"3\\nhopj n`gomka\\nbjr rja\\njmya` aayjk\",\n \"3\\njpoh n`gomka\\nbjr rjb\\njmya` aayjk\",\n \"3\\njpoh o`gomka\\nbjr rjb\\njmya` aayjk\",\n \"3\\nipoh o`gomka\\nbjr rjb\\njmya` aayjk\",\n \"3\\nipoh o`gomka\\nbjr rjb\\njmya` kjyaa\",\n \"3\\nipoh oagomka\\nbjr bjr\\njmya` aayjk\",\n \"3\\nipoh obgomka\\nbjr bjr\\njmya` aayjk\",\n \"3\\nipoh obgomka\\nbjr bjr\\njmyb` aayjk\",\n \"3\\nipoh obgomka\\nbjr bjr\\nimyb` aayjk\",\n \"3\\nhopi obgomka\\nbjr bjr\\nimyb` aayjk\",\n \"3\\nhopi obgomka\\nbjr bjr\\nimyb` aayjl\",\n \"3\\nnhoj johanna\\nira ira\\nkayla jayla\",\n \"3\\njohn johanna\\nria ria\\nkaylb jayla\",\n \"3\\njnhn johanna\\nria qia\\nkayma jayla\",\n \"3\\njogn johanna\\nira qia\\nkayma jayla\",\n \"3\\nngoj johanna\\nria aiq\\nkayma jayla\",\n \"3\\nngoj johanna\\nria qi`\\nkayma jaylb\",\n \"3\\njogn joganna\\nria qi`\\nkayma jayla\",\n \"3\\nngoj joganna\\nria qi`\\nkaxma alyaj\",\n \"3\\nngoj jogann`\\nria qi`\\nkaxma jayla\",\n \"3\\njpgn jogann`\\nria qi`\\nkaxma jayla\",\n \"3\\njogn joganna\\nair qi`\\nkaxma jayla\",\n \"3\\nnpgj joganna\\nari qi`\\nkaxma jayla\",\n \"3\\njpgn jog`nna\\nari qi`\\nkaxma jazla\",\n \"3\\njpgn jog`nna\\nira qi`\\namxak jayla\",\n \"3\\njgpn jog`mna\\nari qi`\\namxak jayla\",\n \"3\\njgpn jog`nna\\nari `iq\\namxak alyaj\",\n \"3\\njgpn jog`nna\\nari qi`\\namxak jayma\",\n \"3\\npngj jog`nna\\nari qi`\\namxak alyaj\",\n \"3\\npngj jog`nna\\nari qi`\\njmxaa jayla\",\n \"3\\npngj ann`goj\\nari qi`\\nkmxaa jayl`\",\n \"3\\npngj ano`gnj\\nari qj`\\nkmxaa jayla\",\n \"3\\njngp ann`goj\\nari qj`\\nkmxaa jayla\",\n \"3\\njgnp ann`goj\\nari qi`\\namxak jayla\",\n \"3\\njgnp ann`gok\\nira qi`\\nkmxaa jayla\",\n \"3\\njgnp bnn`gok\\nari qi`\\nkmxaa layja\"\n ],\n \"outputs\": [\n \"YES\\nYES\\nNO\\n\",\n \"YES\\nNO\\nNO\\n\",\n \"YES\\nYES\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nYES\\nNO\\n\",\n \"YES\\nYES\\nNO\\n\",\n \"YES\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nYES\\nNO\\n\",\n \"NO\\nYES\\nNO\\n\",\n \"NO\\nYES\\nNO\\n\",\n \"NO\\nYES\\nNO\\n\",\n \"NO\\nYES\\nNO\\n\",\n \"NO\\nYES\\nNO\\n\",\n \"NO\\nYES\\nNO\\n\",\n \"YES\\nYES\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"YES\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"YES\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\",\n \"NO\\nNO\\nNO\\n\"\n ]\n}"},"problem":{"kind":"string","value":"In an attempt to control the rise in population, Archer was asked to come up with a plan. This time he is targeting marriages. Archer, being as intelligent as he is, came up with the following plan:\nA man with name M is allowed to marry a woman with name W, only if M is a subsequence of W or W is a subsequence of M.\nA is said to be a subsequence of B, if A can be obtained by deleting some elements of B without changing the order of the remaining elements.\nYour task is to determine whether a couple is allowed to marry or not, according to Archer's rule.\n\nInput\nThe first line contains an integer T, the number of test cases. T test cases follow. Each test case contains two space separated strings M and W.\n\nOutput\nFor each test case print \"YES\" if they are allowed to marry, else print \"NO\". (quotes are meant for clarity, please don't print them)\n\nConstraints\n\n1 ≤ T ≤ 100\n1 ≤ |M|, |W| ≤ 25000 (|A| denotes the length of the string A.)\nAll names consist of lowercase English letters only.\n\n\nExample\n\nInput:\n3\njohn johanna\nira ira\nkayla jayla\n\nOutput:\nYES\nYES\nNO\n\nExplanation\nCase 1: Consider S = \"johanna\". So, S[0] = 'j', S[1] = 'o', S[2] = 'h' and so on. If we remove the indices [3, 4, 6] or [3, 5, 6] from S, it becomes \"john\". Hence \"john\" is a subsequence of S, so the answer is \"YES\".\nCase 2: Any string is a subsequence of it self, as it is formed after removing \"0\" characters. Hence the answer is \"YES\".\nCase 3: \"jayla\" can not be attained from \"kayla\" as removing any character from \"kayla\" would make the string length smaller than \"jayla\", also there is no 'j' in \"kayla\". Similar reasoning can be applied to see why \"kayla\" can't be attained from \"jayla\". Hence the answer is \"NO\"."}}},{"rowIdx":98,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"7 2\\n1 2\\n1 3\\n1 4\\n3 5\\n3 6\\n3 7\\n2 7\\n\",\n \"6 4\\n1 2\\n2 3\\n2 4\\n4 5\\n4 6\\n2 4 5 6\\n\",\n \"10 3\\n10 5\\n3 2\\n6 8\\n1 5\\n10 4\\n6 1\\n9 8\\n2 9\\n7 3\\n3 9 1\\n\",\n \"16 8\\n16 12\\n16 15\\n15 9\\n15 13\\n16 3\\n15 2\\n15 10\\n1 2\\n6 16\\n5 15\\n2 7\\n15 4\\n14 15\\n11 16\\n8 5\\n5 10 14 6 8 3 1 9\\n\",\n \"8 5\\n2 5\\n1 8\\n6 7\\n3 4\\n6 8\\n8 5\\n5 3\\n1 6 7 3 8\\n\",\n \"15 2\\n7 12\\n13 11\\n6 8\\n2 15\\n10 9\\n5 1\\n13 5\\n5 4\\n14 3\\n8 9\\n8 4\\n4 7\\n12 14\\n5 2\\n7 4\\n\",\n \"31 29\\n10 14\\n16 6\\n23 22\\n25 23\\n2 27\\n24 17\\n20 8\\n5 2\\n8 24\\n16 5\\n10 26\\n8 7\\n5 29\\n20 16\\n13 9\\n13 21\\n24 30\\n13 1\\n10 15\\n23 3\\n25 10\\n2 25\\n20 13\\n25 11\\n8 12\\n30 28\\n20 18\\n5 4\\n23 19\\n16 31\\n13 14 3 30 5 6 26 22 25 1 23 7 31 12 16 28 17 2 8 18 24 4 20 21 15 11 9 29 10\\n\",\n \"13 11\\n4 11\\n2 7\\n4 13\\n8 12\\n8 9\\n8 6\\n3 8\\n4 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She is the hidden identity of Super M, the Byteforces’ superhero. Byteforces is a country that consists of n cities, connected by n - 1 bidirectional roads. Every road connects exactly two distinct cities, and the whole road system is designed in a way that one is able to go from any city to any other city using only the given roads. There are m cities being attacked by humans. So Ari... we meant Super M have to immediately go to each of the cities being attacked to scare those bad humans. Super M can pass from one city to another only using the given roads. Moreover, passing through one road takes her exactly one kron - the time unit used in Byteforces. \n\n\n\nHowever, Super M is not on Byteforces now - she is attending a training camp located in a nearby country Codeforces. Fortunately, there is a special device in Codeforces that allows her to instantly teleport from Codeforces to any city of Byteforces. The way back is too long, so for the purpose of this problem teleportation is used exactly once.\n\nYou are to help Super M, by calculating the city in which she should teleport at the beginning in order to end her job in the minimum time (measured in krons). Also, provide her with this time so she can plan her way back to Codeforces.\n\nInput\n\nThe first line of the input contains two integers n and m (1 ≤ m ≤ n ≤ 123456) - the number of cities in Byteforces, and the number of cities being attacked respectively.\n\nThen follow n - 1 lines, describing the road system. Each line contains two city numbers ui and vi (1 ≤ ui, vi ≤ n) - the ends of the road i.\n\nThe last line contains m distinct integers - numbers of cities being attacked. These numbers are given in no particular order.\n\nOutput\n\nFirst print the number of the city Super M should teleport to. If there are many possible optimal answers, print the one with the lowest city number.\n\nThen print the minimum possible time needed to scare all humans in cities being attacked, measured in Krons.\n\nNote that the correct answer is always unique.\n\nExamples\n\nInput\n\n7 2\n1 2\n1 3\n1 4\n3 5\n3 6\n3 7\n2 7\n\n\nOutput\n\n2\n3\n\n\nInput\n\n6 4\n1 2\n2 3\n2 4\n4 5\n4 6\n2 4 5 6\n\n\nOutput\n\n2\n4\n\nNote\n\nIn the first sample, there are two possibilities to finish the Super M's job in 3 krons. They are:\n\n and .\n\nHowever, you should choose the first one as it starts in the city with the lower number."}}},{"rowIdx":99,"cells":{"tests":{"kind":"string","value":"{\n \"inputs\": [\n \"3\\n4 28 27 11\\n15 20 42 5\\n11 24 33 14\\n5\\n4 28 27 11\\n12 11 34 2\\n7 26 14 16\\n14 16 19 12\\n17 28 27 21\\n2\\n300000 1000000 600000 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 42 5\\n11 24 33 14\\n5\\n4 28 27 11\\n12 11 34 2\\n7 26 14 16\\n14 16 19 12\\n17 28 27 21\\n2\\n322297 1000000 600000 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 24 33 14\\n5\\n4 28 27 11\\n12 11 34 2\\n7 26 14 16\\n14 16 19 12\\n17 28 50 21\\n2\\n322297 1000000 828907 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 42 5\\n19 24 33 14\\n5\\n4 28 27 11\\n12 11 34 2\\n7 26 14 16\\n14 16 19 12\\n17 28 27 6\\n2\\n322297 1000000 600000 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 42 5\\n19 24 33 14\\n5\\n4 28 27 11\\n12 11 34 2\\n7 26 14 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300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n19 24 33 14\\n0\\n4 4 27 11\\n15 11 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 27 21\\n2\\n322297 1000000 828907 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 40 33 14\\n5\\n4 27 27 11\\n12 21 34 2\\n7 26 14 25\\n14 16 19 12\\n17 28 93 21\\n2\\n322297 1000000 828907 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 42 5\\n19 24 33 14\\n5\\n4 28 27 15\\n12 11 28 2\\n7 26 10 16\\n14 16 19 12\\n17 31 27 6\\n2\\n322297 1000000 600000 0\\n0 1002237 1100000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n19 24 33 14\\n0\\n4 4 27 11\\n15 11 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 27 21\\n2\\n322297 1000100 828907 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 40 33 14\\n5\\n4 27 27 11\\n5 21 34 2\\n7 26 14 25\\n14 16 19 12\\n17 28 93 21\\n2\\n322297 1000000 828907 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 42 5\\n19 24 33 14\\n5\\n4 28 27 15\\n12 11 28 2\\n7 26 10 16\\n14 16 19 12\\n17 31 27 6\\n2\\n232522 1000000 600000 0\\n0 1002237 1100000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n19 38 33 14\\n0\\n4 4 27 11\\n15 11 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 27 21\\n2\\n322297 1000100 828907 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 40 33 14\\n5\\n4 27 27 11\\n5 21 34 2\\n7 26 14 25\\n14 16 19 12\\n17 28 93 21\\n2\\n322297 1000000 390784 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n19 38 33 6\\n0\\n4 4 27 11\\n15 11 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 27 21\\n2\\n322297 1000100 828907 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 40 33 14\\n5\\n4 27 27 11\\n5 21 34 2\\n7 26 14 25\\n14 16 19 12\\n17 44 93 21\\n2\\n322297 1000000 390784 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n19 38 33 6\\n0\\n4 4 27 11\\n15 11 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 2 21\\n2\\n322297 1000100 828907 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 40 33 14\\n5\\n4 27 27 11\\n10 21 34 2\\n7 26 14 25\\n14 16 19 12\\n17 44 93 21\\n2\\n322297 1000000 390784 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n19 38 33 6\\n0\\n4 4 27 11\\n15 11 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 2 21\\n2\\n322297 1000100 418950 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 8\\n19 40 33 14\\n5\\n4 27 27 11\\n10 21 34 2\\n7 26 14 25\\n14 16 19 12\\n17 44 93 21\\n2\\n322297 1000000 390784 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n19 38 33 6\\n0\\n4 4 27 11\\n15 18 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 2 21\\n2\\n322297 1000100 418950 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n19 38 33 6\\n0\\n4 4 27 11\\n15 18 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 0 21\\n2\\n322297 1000100 418950 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n30 38 33 6\\n0\\n4 4 27 11\\n15 18 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 0 21\\n2\\n322297 1000100 14190 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n30 38 33 6\\n0\\n4 4 27 11\\n15 18 34 2\\n7 26 14 16\\n14 12 19 12\\n17 22 0 21\\n2\\n322297 1000100 14190 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n0 38 33 6\\n0\\n4 4 27 11\\n15 18 34 2\\n7 26 14 16\\n14 12 19 12\\n17 22 0 21\\n2\\n322297 1000100 14190 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n0 38 33 6\\n0\\n4 4 27 11\\n15 18 34 1\\n7 26 14 16\\n14 12 19 12\\n17 22 0 21\\n2\\n322297 1000100 14190 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n0 38 33 4\\n0\\n4 4 27 11\\n15 18 34 1\\n7 26 14 16\\n14 12 19 12\\n17 22 0 21\\n2\\n322297 1000100 14190 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n0 38 7 4\\n0\\n4 4 27 11\\n15 18 34 1\\n7 26 14 16\\n14 12 19 12\\n17 22 0 21\\n2\\n322297 1000100 14190 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n23 20 42 5\\n0 38 7 4\\n0\\n4 4 27 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14 16\\n2 16 19 12\\n17 28 27 21\\n2\\n322297 1000100 600000 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 24 33 14\\n5\\n4 28 27 11\\n12 11 66 2\\n7 26 14 16\\n14 16 19 12\\n17 28 27 21\\n2\\n322297 1010000 828907 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 24 50 14\\n5\\n4 28 27 15\\n12 11 34 2\\n7 26 14 16\\n14 16 19 12\\n17 28 50 21\\n2\\n267741 1000000 828907 0\\n-1 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 70 9\\n11 24 33 14\\n5\\n5 28 27 11\\n12 11 34 2\\n7 26 14 16\\n14 16 19 12\\n17 28 27 21\\n2\\n300000 1000000 600000 0\\n0 600000 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 42 5\\n19 24 55 14\\n5\\n4 28 27 11\\n12 11 34 2\\n7 26 14 16\\n14 16 19 12\\n17 28 27 6\\n2\\n322297 1000000 600000 0\\n0 1002237 1000000 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 42 5\\n19 24 33 14\\n5\\n4 16 27 11\\n12 11 34 2\\n7 26 14 16\\n14 12 19 12\\n17 28 27 21\\n2\\n322297 1000000 828907 0\\n0 600000 1000000 256152\\n0\",\n \"3\\n4 28 27 17\\n15 20 42 5\\n19 24 33 14\\n5\\n4 28 27 11\\n12 11 66 2\\n11 26 14 16\\n14 16 19 12\\n17 28 27 21\\n2\\n322297 1000000 828907 0\\n-1 600000 1000001 300000\\n0\",\n \"3\\n4 28 27 11\\n15 20 42 9\\n11 24 33 14\\n5\\n5 28 27 11\\n12 11 34 2\\n7 26 19 16\\n14 16 19 12\\n17 28 27 21\\n2\\n550504 1000000 600000 0\\n0 600000 1000000 300000\\n0\"\n ],\n \"outputs\": [\n \"8\\n6\\n6\",\n \"8\\n6\\n6\\n\",\n \"8\\n7\\n6\\n\",\n \"8\\n8\\n6\\n\",\n \"8\\n8\\n4\\n\",\n \"8\\n5\\n6\\n\",\n \"8\\n9\\n6\\n\",\n \"8\\n\",\n \"8\\n11\\n4\\n\",\n \"8\\n12\\n4\\n\",\n \"6\\n\",\n \"4\\n8\\n6\\n\",\n \"8\\n7\\n4\\n\",\n \"8\\n10\\n4\\n\",\n \"6\\n8\\n6\\n\",\n \"8\\n8\\n\",\n \"8\\n6\\n2\\n\",\n \"6\\n7\\n6\\n\",\n \"6\\n8\\n4\\n\",\n \"8\\n6\\n4\\n\",\n \"10\\n\",\n \"8\\n10\\n6\\n\",\n \"6\\n10\\n6\\n\",\n \"8\\n9\\n4\\n\",\n \"5\\n8\\n6\\n\",\n \"4\\n\",\n \"4\\n9\\n6\\n\",\n \"7\\n\",\n \"8\\n13\\n4\\n\",\n \"4\\n10\\n6\\n\",\n \"8\\n9\\n\",\n \"3\\n10\\n6\\n\",\n \"6\\n8\\n\",\n 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\"8\\n7\\n6\\n\",\n \"8\\n7\\n6\\n\",\n \"8\\n6\\n6\\n\",\n \"8\\n7\\n6\\n\",\n \"8\\n6\\n6\\n\",\n \"8\\n8\\n6\\n\",\n \"8\\n6\\n6\\n\",\n \"8\\n8\\n4\\n\",\n \"8\\n5\\n6\\n\",\n \"8\\n6\\n6\\n\",\n \"8\\n7\\n6\\n\"\n ]\n}"},"problem":{"kind":"string","value":"There are a number of rectangles on the x-y plane. The four sides of the rectangles are parallel to either the x-axis or the y-axis, and all of the rectangles reside within a range specified later. There are no other constraints on the coordinates of the rectangles.\n\nThe plane is partitioned into regions surrounded by the sides of one or more rectangles. In an example shown in Figure C.1, three rectangles overlap one another, and the plane is partitioned into eight regions.\n\nRectangles may overlap in more complex ways. For example, two rectangles may have overlapped sides, they may share their corner points, and/or they may be nested. Figure C.2 illustrates such cases.\n\nYour job is to write a program that counts the number of the regions on the plane partitioned by the rectangles.\n\n\n\nInput\n\nThe input consists of multiple datasets. Each dataset is formatted as follows.\n\n\nn\nl1 t1 r1 b1\nl2 t2 r2 b2\n:\nln tn rn bn\n\n\nA dataset starts with n (1 ≤ n ≤ 50), the number of rectangles on the plane. Each of the following n lines describes a rectangle. The i-th line contains four integers, li, ti, ri, and bi, which are the coordinates of the i-th rectangle; (li, ti) gives the x-y coordinates of the top left corner, and (ri, bi) gives that of the bottom right corner of the rectangle (0 ≤ li < ri ≤ 106, 0 ≤ bi < ti ≤ 106, for 1 ≤ i ≤ n). The four integers are separated by a space.\n\nThe input is terminated by a single zero.\n\nOutput\n\nFor each dataset, output a line containing the number of regions on the plane partitioned by the sides of the rectangles.\n\n\nFigure C.1. Three rectangles partition the plane into eight regions. This corresponds to the first dataset of the sample input. The x- and y-axes are shown for illustration purposes only, and therefore they do not partition the plane.\n\nFigure C.2. Rectangles overlapping in more complex ways. This corresponds to the second dataset.\n\nExample\n\nInput\n\n3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0\n\n\nOutput\n\n8\n6\n6"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":0,"numItemsPerPage":100,"numTotalItems":13315,"offset":0,"length":100}},"jwt":"eyJhbGciOiJFZERTQSJ9.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc2ODEyNDkyMCwic3ViIjoiL2RhdGFzZXRzL2F4b24tcmwvQ29kZUNvbnRlc3QiLCJleHAiOjE3NjgxMjg1MjAsImlzcyI6Imh0dHBzOi8vaHVnZ2luZ2ZhY2UuY28ifQ.fYc32lSSJSYsOVYxdZAp4aHPGSHJbqfFlKoxrUI5Lrzi84vmsYEM9q8z_wDjEomoDWGDdrK9RQjKJdqG_-02Bw","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"train","numRows":13315,"numBytesParquet":573746925},{"config":"default","split":"test","numRows":165,"numBytesParquet":5399101},{"config":"default","split":"valid","numRows":117,"numBytesParquet":3713179}]},"discussionsStats":{"closed":0,"open":1,"total":1},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">
tests
dict | problem
stringlengths 29
13k
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|---|---|
{
"inputs": [
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"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\na`b\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\nc\nc\n",
"5\n2 4\nabac\nbabz\n2 4\na`aa\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nbbb\n2 2\nba\nbb\n2 1\na\nc\nc\n",
"5\n2 3\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nbbb\n2 2\nba\nbb\n2 1\na\nc\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbba\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naa`\naab\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbca\n3 3\nbba\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbaby\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabbc\nbabz\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbaa\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbaby\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naac\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbba\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaba\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaba\nbbbb\n3 3\nbba\naaa\naab\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbaa\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nd\n",
"5\n2 4\nabac\nbaby\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naad\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabab\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\naab\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nb\n",
"5\n2 4\nabac\naabz\n2 4\naaaa\nacbb\n3 3\nbaa\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n"
],
"outputs": [
"zbac\n-1\naaa\nab\na\n",
"zbac\n-1\naaa\nab\na\n",
"-1\n-1\naaa\nab\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"zbac\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\naab\nba\na\n",
"-1\n-1\n-1\nb`\na\n",
"-1\n-1\nbaa\nba\na\n",
"zbac\n-1\naaa\nab\na\n",
"-1\n-1\naaa\nab\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naaa\nab\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naaa\nba\na\n"
]
}
|
You are given n strings a_1, a_2, …, a_n: all of them have the same length m. The strings consist of lowercase English letters.
Find any string s of length m such that each of the given n strings differs from s in at most one position. Formally, for each given string a_i, there is no more than one position j such that a_i[j] ≠ s[j].
Note that the desired string s may be equal to one of the given strings a_i, or it may differ from all the given strings.
For example, if you have the strings abac and zbab, then the answer to the problem might be the string abab, which differs from the first only by the last character, and from the second only by the first.
Input
The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case starts with a line containing two positive integers n (1 ≤ n ≤ 10) and m (1 ≤ m ≤ 10) — the number of strings and their length.
Then follow n strings a_i, one per line. Each of them has length m and consists of lowercase English letters.
Output
Print t answers to the test cases. Each answer (if it exists) is a string of length m consisting of lowercase English letters. If there are several answers, print any of them. If the answer does not exist, print "-1" ("minus one", without quotes).
Example
Input
5
2 4
abac
zbab
2 4
aaaa
bbbb
3 3
baa
aaa
aab
2 2
ab
bb
3 1
a
b
c
Output
abab
-1
aaa
ab
z
Note
The first test case was explained in the statement.
In the second test case, the answer does not exist.
|
{
"inputs": [
"5\n00100\n",
"6\n111010\n",
"5\n10001\n",
"7\n1100010\n",
"18\n110100000000000000\n",
"70\n0010011001010100000110011001011111101011010110110101110101111011101010\n",
"7\n0000000\n",
"17\n00100000000000000\n",
"16\n1101010010000000\n",
"3\n111\n",
"4\n0000\n",
"4\n0110\n",
"3\n010\n",
"4\n1001\n",
"337\n0000000000000000000000000000000000000010000000000000000000000000000000010000000000001000000000100100000000000000000000000000000000000000000000000000000000100000000000000010000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000001000100000000000000000000000000000000000100010000000100\n",
"2\n11\n",
"6\n110011\n",
"4\n1100\n",
"15\n110101101111111\n",
"3\n101\n",
"6\n111111\n",
"10\n1000000000\n",
"8\n10011001\n",
"10\n1000101001\n",
"100\n1111111111111111111111111111111111111111111111111111111111111111111111111111101111111111111111111111\n",
"7\n0100011\n",
"12\n101101010010\n",
"1\n0\n",
"14\n00101111111111\n",
"100\n1001001000011010001101000011100101101110101001110110010001110011011100111000010010011011101000011101\n",
"149\n11110101110111101111110110001111110101111011111111111111101111110000101101110110111101011111011111111000111011011110111111001011111111111010110111110\n",
"35\n11111111111111111111111111111111110\n",
"8\n00000110\n",
"14\n10101001101010\n",
"6\n000000\n",
"23\n10010101010101010101001\n",
"100\n0000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n",
"18\n111100000000000000\n",
"70\n0010011001010100000110011001011110101011010110110101110101111011101010\n",
"7\n0000010\n",
"17\n01100000000000000\n",
"3\n001\n",
"337\n0000000000000000000000000000000000000010000000000000000000000000000000010000000000001000000000100100000000000000000000000000000000000000000000000000000000100000000001000010000000000000000000000000000000000000000000000000000000000000000000000010000000000000000000000000000000000000001000100000000000000000000000000000000000100010000000100\n",
"15\n110001101111111\n",
"10\n1010000000\n",
"10\n1100101001\n",
"100\n1111111111111111111111111111111111111111111111111111111111111111011111111111101111111111111111111111\n",
"12\n101111010010\n",
"100\n1001001000011010001101000011100101101110101001110110010001110011011100111000010010011011101000011100\n",
"149\n11110101110111101111110110001111110101111011111111111111101111110000101101110110111101011111011111111000111011011110111110001011111111111010110111110\n",
"35\n11110111111111111111111111111111110\n",
"70\n0010011001010100000110011001011110101011010110111101110101111011101010\n",
"4\n0101\n",
"337\n0000000000000000000000000000000000000010000000000000000000000000000000010000000000001000000000100100000000000000000000000000000000000000000000000000000000100000000001000010000000000000000000000000000000000000000000000000000000000000000100000010000000000000000000000000000000000000001000100000000000000000000000000000000000100010000000100\n",
"100\n1111111111111111111111111111111111111111111111111111111111111111011111111111101111111111111111101111\n",
"12\n111111010010\n",
"100\n1001001000011010001101000011100101101110101001110110010001110011011000111000010010011011101000011100\n",
"35\n11110111111111111111111101111111110\n",
"16\n1100010010000000\n",
"4\n0010\n",
"4\n0100\n",
"3\n110\n",
"4\n1000\n",
"6\n110010\n",
"4\n0001\n",
"3\n100\n",
"6\n101111\n",
"8\n10011011\n",
"7\n0000011\n",
"14\n00101101111111\n",
"8\n00000111\n",
"14\n10101011101010\n",
"6\n100000\n",
"23\n10010100010101010101001\n",
"100\n0000000000100000000000000000000000000000000000000000000000000000010000000000000000000000000000000000\n",
"5\n10100\n",
"6\n011010\n",
"5\n10011\n",
"7\n1100011\n",
"18\n111100000000010000\n",
"7\n1000000\n",
"17\n01100010000000000\n",
"16\n1100110010000000\n",
"3\n011\n",
"4\n0011\n",
"3\n000\n",
"4\n1101\n",
"6\n111000\n",
"4\n1110\n",
"15\n110001101111110\n",
"6\n100111\n",
"10\n1010000100\n",
"8\n10011010\n",
"10\n1100101101\n",
"7\n0100001\n",
"14\n00101101111101\n",
"149\n11110101110111101111110110001111110101111011111111111111101111110000101101110110111001011111011111111000111011011110111110001011111111111010110111110\n",
"8\n00000011\n",
"14\n10001011101010\n",
"6\n100010\n",
"23\n10010100010111010101001\n",
"100\n0000000000100000000000000000000000000010000000000000000000000000010000000000000000000000000000000000\n",
"5\n00000\n",
"6\n011011\n",
"5\n10000\n",
"7\n1101011\n",
"18\n111100000010010000\n",
"70\n0000011001010100000110011001011110101011010110111101110101111011101010\n",
"7\n1001000\n",
"17\n01000010000000000\n",
"16\n1100110010000100\n",
"4\n0111\n"
],
"outputs": [
"2",
"1",
"1",
"2",
"8",
"32",
"3",
"8",
"7",
"1",
"2",
"2",
"0",
"2",
"160",
"1",
"3",
"2",
"7",
"0",
"3",
"4",
"4",
"3",
"49",
"2",
"6",
"0",
"6",
"49",
"73",
"17",
"4",
"2",
"3",
"4",
"49",
"9\n",
"33\n",
"2\n",
"8\n",
"1\n",
"161\n",
"7\n",
"3\n",
"4\n",
"50\n",
"5\n",
"48\n",
"74\n",
"16\n",
"34\n",
"0\n",
"162\n",
"49\n",
"6\n",
"47\n",
"15\n",
"8\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"2\n",
"3\n",
"3\n",
"7\n",
"3\n",
"1\n",
"2\n",
"5\n",
"50\n",
"1\n",
"2\n",
"2\n",
"3\n",
"8\n",
"3\n",
"8\n",
"7\n",
"1\n",
"2\n",
"1\n",
"1\n",
"2\n",
"1\n",
"7\n",
"3\n",
"4\n",
"2\n",
"5\n",
"3\n",
"6\n",
"74\n",
"4\n",
"2\n",
"1\n",
"6\n",
"49\n",
"2\n",
"3\n",
"2\n",
"2\n",
"9\n",
"33\n",
"3\n",
"8\n",
"8\n",
"1\n"
]
}
|
Vasya and Petya have invented a new game. Vasya takes a stripe consisting of 1 × n square and paints the squares black and white. After that Petya can start moves — during a move he may choose any two neighboring squares of one color and repaint these two squares any way he wants, perhaps in different colors. Petya can only repaint the squares in white and black colors. Petya’s aim is to repaint the stripe so that no two neighboring squares were of one color. Help Petya, using the given initial coloring, find the minimum number of moves Petya needs to win.
Input
The first line contains number n (1 ≤ n ≤ 1000) which represents the stripe’s length. The second line contains exactly n symbols — the line’s initial coloring. 0 corresponds to a white square, 1 corresponds to a black one.
Output
If Petya cannot win with such an initial coloring, print -1. Otherwise print the minimum number of moves Petya needs to win.
Examples
Input
6
111010
Output
1
Input
5
10001
Output
1
Input
7
1100010
Output
2
Input
5
00100
Output
2
Note
In the first sample Petya can take squares 1 and 2. He repaints square 1 to black and square 2 to white.
In the second sample Petya can take squares 2 and 3. He repaints square 2 to white and square 3 to black.
|
{
"inputs": [
"5\ninsert A\ninsert T\ninsert C\nfind G\nfind A",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert A\ninsert U\ninsert C\nfind G\nfind A",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AGF\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert B\ninsert T\ninsert C\nfind G\nfind A",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind BCC\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TUT\nfind T",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind S",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind UTT\nfind S",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAB\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TUT\nfind T",
"13\ninsert AA@\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCD\ninsert CCC\nfind CCC\ninsert T\nfind UTT\nfind S",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind BAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind DCC\ninsert T\nfind TTT\nfind S",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AGG\ninsert TTS\nfind AAA\nfind CCC\nfind DCC\ninsert CCC\nfind BCC\ninsert T\nfind TTT\nfind T",
"13\ninsert @AA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind BCC\nfind CBC\ninsert CCC\nfind CCB\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert AHF\ninsert TTT\nfind BAA\nfind CCC\nfind CCB\ninsert CCC\nfind BCC\ninsert U\nfind UTT\nfind T",
"13\ninsert @AA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind BCC\nfind CBC\ninsert CCC\nfind CCB\ninsert T\nfind STT\nfind T",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert GGA\ninsert TTT\nfind AA@\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert S\nfind TTT\nfind T",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert UTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind DCC\ninsert T\nfind TTT\nfind S",
"5\ninsert A\ninsert U\ninsert F\nfind F\nfind B",
"5\ninsert A\ninsert U\ninsert D\nfind G\nfind A",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert A\ninsert T\ninsert C\nfind G\nfind @",
"5\ninsert A\ninsert U\ninsert D\nfind G\nfind B",
"5\ninsert A\ninsert T\ninsert C\nfind F\nfind A",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert @\ninsert T\ninsert C\nfind G\nfind A",
"5\ninsert B\ninsert U\ninsert C\nfind G\nfind A",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AHF\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert B\ninsert T\ninsert C\nfind G\nfind B",
"5\ninsert A\ninsert U\ninsert D\nfind G\nfind C",
"5\ninsert A\ninsert T\ninsert C\nfind E\nfind A",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert B\ninsert U\ninsert D\nfind G\nfind A",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert AHF\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert B\ninsert S\ninsert C\nfind G\nfind B",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind BCC\ninsert T\nfind TTT\nfind T",
"5\ninsert B\ninsert T\ninsert C\nfind G\nfind @",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert A\ninsert U\ninsert E\nfind G\nfind B",
"5\ninsert A\ninsert T\ninsert C\nfind F\nfind B",
"5\ninsert B\ninsert U\ninsert B\nfind G\nfind A",
"5\ninsert B\ninsert T\ninsert C\nfind H\nfind B",
"5\ninsert A\ninsert T\ninsert B\nfind E\nfind A",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCB\ninsert T\nfind TTT\nfind T",
"5\ninsert B\ninsert U\ninsert D\nfind H\nfind A",
"13\ninsert AAA\ninsert ABD\ninsert AGA\ninsert AHF\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCD\ninsert CCC\nfind CCC\ninsert T\nfind UTT\nfind S",
"5\ninsert B\ninsert T\ninsert B\nfind H\nfind B",
"13\ninsert AAA\ninsert ABC\ninsert AFA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCB\ninsert T\nfind TTT\nfind T",
"5\ninsert A\ninsert T\ninsert C\nfind G\nfind ?",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AHF\ninsert TTT\nfind AAA\nfind DCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert A\ninsert T\ninsert C\nfind E\nfind B",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert AHF\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert U\nfind TTT\nfind T",
"5\ninsert B\ninsert T\ninsert C\nfind H\nfind @",
"5\ninsert B\ninsert V\ninsert B\nfind G\nfind A",
"5\ninsert A\ninsert T\ninsert C\nfind H\nfind B",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind BCC\nfind CCC\ninsert CCC\nfind CCB\ninsert T\nfind TTT\nfind T",
"5\ninsert A\ninsert T\ninsert B\nfind H\nfind B",
"5\ninsert B\ninsert V\ninsert A\nfind G\nfind A",
"5\ninsert A\ninsert T\ninsert C\nfind I\nfind B",
"5\ninsert A\ninsert T\ninsert B\nfind I\nfind B",
"5\ninsert A\ninsert T\ninsert C\nfind I\nfind C",
"5\ninsert A\ninsert U\ninsert C\nfind H\nfind A",
"5\ninsert B\ninsert U\ninsert D\nfind G\nfind B",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind DCC\ninsert CCC\nfind BCC\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert AAC\ninsert AFA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CBC\ninsert CCC\nfind CCC\ninsert T\nfind TUT\nfind T",
"5\ninsert @\ninsert U\ninsert C\nfind G\nfind A",
"13\ninsert AAA\ninsert ABC\ninsert AG@\ninsert AHF\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert C\ninsert S\ninsert C\nfind G\nfind B",
"5\ninsert A\ninsert T\ninsert D\nfind G\nfind @",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert FGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert @\ninsert T\ninsert B\nfind E\nfind A",
"5\ninsert C\ninsert T\ninsert B\nfind H\nfind B",
"13\ninsert AA@\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AA@\nfind CCC\nfind CCD\ninsert CCC\nfind CCC\ninsert T\nfind UTT\nfind S",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AHF\ninsert TTT\nfind AAA\nfind DCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind UTT\nfind T",
"5\ninsert B\ninsert V\ninsert B\nfind G\nfind B",
"5\ninsert @\ninsert T\ninsert C\nfind H\nfind B",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind BCC\nfind CBC\ninsert CCC\nfind CCB\ninsert T\nfind TTT\nfind T",
"5\ninsert B\ninsert V\ninsert A\nfind F\nfind A",
"5\ninsert A\ninsert T\ninsert B\nfind I\nfind C",
"5\ninsert B\ninsert U\ninsert E\nfind G\nfind B",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind DCC\ninsert CCC\nfind BCC\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert AAC\ninsert AFA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert DCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert C\ninsert T\ninsert C\nfind H\nfind B",
"13\ninsert BA@\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AA@\nfind CCC\nfind CCD\ninsert CCC\nfind CCC\ninsert T\nfind UTT\nfind S",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AHG\ninsert TTT\nfind AAA\nfind DCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind UTT\nfind T",
"5\ninsert B\ninsert W\ninsert B\nfind G\nfind B",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind BCC\nfind CBC\ninsert CCC\nfind BCC\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert ABC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind BCC\nfind CBC\ninsert CCC\nfind BCB\ninsert T\nfind TTT\nfind T",
"13\ninsert ABA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert A\ninsert T\ninsert B\nfind G\nfind A",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TUT\nfind T",
"5\ninsert ?\ninsert T\ninsert C\nfind G\nfind A",
"5\ninsert B\ninsert V\ninsert C\nfind G\nfind A",
"13\ninsert AAA\ninsert AAC\ninsert AGA\ninsert AHF\ninsert TTT\nfind AAB\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"13\ninsert AAA\ninsert CAA\ninsert AGA\ninsert AGG\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert S\nfind TTT\nfind S",
"5\ninsert A\ninsert T\ninsert C\nfind D\nfind A",
"13\ninsert AAA\ninsert @BC\ninsert AGA\ninsert GGA\ninsert TTT\nfind AAA\nfind CCC\nfind CCC\ninsert CCC\nfind CCC\ninsert T\nfind TTT\nfind T",
"5\ninsert A\ninsert T\ninsert C\nfind F\nfind @",
"5\ninsert A\ninsert U\ninsert E\nfind G\nfind A"
],
"outputs": [
"no\nyes",
"yes\nno\nno\nyes\nyes\nyes",
"no\nyes\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"yes\nno\nno\nno\nyes\nyes\n",
"yes\nno\nno\nyes\nno\nyes\n",
"yes\nno\nno\nyes\nyes\nno\n",
"yes\nno\nno\nyes\nno\nno\n",
"no\nno\nno\nyes\nno\nyes\n",
"no\nno\nno\nyes\nno\nno\n",
"no\nno\nno\nyes\nyes\nyes\n",
"yes\nno\nno\nno\nyes\nno\n",
"yes\nno\nno\nno\nno\nyes\n",
"no\nno\nno\nno\nyes\nyes\n",
"no\nno\nno\nno\nno\nno\n",
"no\nno\nno\nno\nno\nyes\n",
"no\nno\nno\nyes\nyes\nno\n",
"yes\nno\nno\nno\nno\nno\n",
"yes\nno\n",
"no\nyes\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"no\nno\n",
"no\nyes\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"no\nno\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nyes\n",
"no\nno\n",
"no\nyes\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nyes\n",
"yes\nno\nno\nno\nyes\nyes\n",
"no\nno\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"no\nno\n",
"no\nno\n",
"no\nyes\n",
"no\nyes\n",
"yes\nno\nno\nno\nyes\nyes\n",
"no\nno\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"yes\nno\nno\nyes\nno\nno\n",
"no\nyes\n",
"yes\nno\nno\nno\nyes\nyes\n",
"no\nno\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"yes\nno\nno\nyes\nyes\nno\n",
"no\nno\n",
"no\nno\n",
"no\nno\n",
"yes\nno\nno\nno\nyes\nyes\n",
"no\nyes\n",
"no\nyes\n",
"no\nno\n",
"no\nyes\n",
"no\nyes\n",
"no\nyes\n",
"no\nyes\n",
"yes\nno\nno\nno\nyes\nyes\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"yes\nno\nno\nyes\nno\nyes\n",
"no\nno\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"no\nno\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"no\nyes\n",
"yes\nno\nno\nyes\nno\nno\n",
"yes\nno\nno\nyes\nno\nyes\n",
"no\nyes\n",
"no\nno\n",
"yes\nno\nno\nno\nyes\nyes\n",
"no\nyes\n",
"no\nno\n",
"no\nyes\n",
"yes\nno\nno\nno\nyes\nyes\n",
"yes\nno\nno\nno\nyes\nyes\n",
"no\nno\n",
"no\nno\nno\nyes\nno\nno\n",
"yes\nno\nno\nyes\nno\nyes\n",
"no\nyes\n",
"yes\nno\nno\nno\nyes\nyes\n",
"yes\nno\nno\nno\nyes\nyes\n",
"no\nno\nno\nyes\nyes\nyes\n",
"no\nyes\n",
"yes\nno\nno\nyes\nno\nyes\n",
"no\nno\n",
"no\nno\n",
"no\nno\nno\nyes\nyes\nyes\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nyes\n",
"yes\nno\nno\nyes\nyes\nyes\n",
"no\nno\n",
"no\nyes\n"
]
}
|
Your task is to write a program of a simple dictionary which implements the following instructions:
* insert str: insert a string str in to the dictionary
* find str: if the distionary contains str, then print 'yes', otherwise print 'no'
Notes
Template in C
Constraints
* A string consists of 'A', 'C', 'G', or 'T'
* 1 ≤ length of a string ≤ 12
* n ≤ 1000000
Input
In the first line n, the number of instructions is given. In the following n lines, n instructions are given in the above mentioned format.
Output
Print yes or no for each find instruction in a line.
Examples
Input
5
insert A
insert T
insert C
find G
find A
Output
no
yes
Input
13
insert AAA
insert AAC
insert AGA
insert AGG
insert TTT
find AAA
find CCC
find CCC
insert CCC
find CCC
insert T
find TTT
find T
Output
yes
no
no
yes
yes
yes
|
{
"inputs": [
"1 4\nSE23\n",
"5 7\n000E0T3\nT0TT0T0\n010T0T0\n2T0T0T0\n0T0S000\n",
"1 10\n9T9TSET9T9\n",
"3 3\n920\n752\nE8S\n",
"1 5\n78S6E\n",
"2 2\nE9\nS4\n",
"3 3\n000\nS0E\n000\n",
"5 1\n9\nT\nE\n6\nS\n",
"3 5\n00000\nS0E01\n00000\n",
"5 5\nS9999\nTTTT9\n99999\n9TTTT\n9999E\n",
"9 8\n38030772\n697T83S2\n8T626740\n86T02062\n05402864\nT7504180\n3T368E08\n90637446\n12709560\n",
"10 1\nS\n9\n9\n9\n9\nE\n9\n9\n9\n9\n",
"4 3\nS01\n234\n567\n89E\n",
"3 3\n920\n752\nS8E\n",
"2 2\n9E\nS4\n",
"5 5\nS9999\nTTTT9\n94028\n9TTTT\n9999E\n",
"9 8\n38030772\n697T83S2\n8T626740\n86T02062\n05402864\nT7504180\n3T368E08\n90637446\n13738808\n",
"4 3\nS01\n234\n995\n89E\n",
"5 1\n3\nT\nE\n6\nS\n",
"3 5\n00000\n10E0S\n00000\n",
"4 3\nS10\n234\n567\n89E\n",
"5 7\n000E0T3\nT0TT0T0\n010T0T1\n2T0T0T0\n0T0S000\n",
"9 8\n38030772\n698T83S2\n8T626740\n86T02062\n05402864\nT7504180\n80E863T3\n90637446\n13738808\n",
"9 8\n38030772\n698T83S2\n8T636740\n86T02062\n05402864\nT7504180\n80E863T3\n90637446\n13738808\n",
"1 10\n9T9TSET9T8\n",
"9 8\n38030772\n697T83S2\n8T626740\n86T02062\n05402864\nT7504180\n3T368E08\n55550197\n12709560\n",
"4 3\n10S\n234\n567\n89E\n",
"3 3\n296\n752\nS8E\n",
"2 2\n9E\n4S\n",
"3 5\n00000\n10E0S\n00010\n",
"4 3\nS10\n234\n372\n89E\n",
"9 8\n38030772\n698T83S2\n8T626740\n86T02062\n05402864\nT7504180\n80E863T3\n13040711\n13738808\n",
"9 8\n36149255\n698T83S2\n8T636740\n26020T68\n05402864\nT7504180\n80E863T3\n90637446\n13738808\n",
"9 8\n38030772\n697T83S2\n8T626740\n86T02062\n05402864\nT7504180\n3T368E08\n24086157\n12709560\n",
"3 3\n296\n171\nS8E\n",
"4 3\nS10\n234\n372\n99E\n",
"9 8\n38030772\n698T83S2\n8T626740\n86T02062\n05402864\nT7504180\n90E863T3\n13040711\n13738808\n",
"9 8\n38030772\n697T83S2\n8T626740\n26020T68\n05402864\nT7504180\n3T368E08\n24086157\n12709560\n",
"4 3\nS10\n234\n546\n99E\n",
"9 8\n38030772\n697T83S2\n8T626740\n86T02062\n05402864\nT7405180\n3T368E08\n90637446\n13738808\n",
"9 8\n38030772\n698T83S2\n8T626740\n86T02062\n05402864\nT7504180\n3T368E08\n90637446\n13738808\n",
"5 1\n1\nT\nE\n6\nS\n",
"9 8\n38030772\n698T83S2\n8T636740\n26020T68\n05402864\nT7504180\n80E863T3\n90637446\n13738808\n",
"9 8\n38030772\n698T83S2\n8T636740\n25020T68\n05402864\nT7504180\n80E863T3\n90637446\n13738808\n",
"1 5\nE6S87\n",
"3 3\n000\nS0E\n010\n",
"1 4\nSE33\n",
"9 8\n38030772\n698T83S2\n8T636740\n86T02062\n05402864\nT7104580\n80E863T3\n90637446\n13738808\n",
"3 3\n010\nS0E\n010\n",
"3 5\n10000\n10E0S\n00010\n",
"3 3\n010\nE0S\n010\n",
"3 5\n10100\n10E0S\n00010\n",
"9 8\n38030772\n697T83S2\n8T626740\n86T02062\n05402864\nT7504180\n90E863T3\n13040711\n13738808\n",
"3 3\n000\nE0S\n010\n"
],
"outputs": [
"2\n",
"3\n",
"0\n",
"29\n",
"6\n",
"9\n",
"0\n",
"6\n",
"1\n",
"135\n",
"194\n",
"72\n",
"45\n",
"15\n",
"13\n",
"113\n",
"202\n",
"50\n",
"6\n",
"1\n",
"45\n",
"3\n",
"271\n",
"272\n",
"0\n",
"192\n",
"42\n",
"21\n",
"9\n",
"2\n",
"39\n",
"249\n",
"276\n",
"188\n",
"22\n",
"40\n",
"250\n",
"184\n",
"43\n",
"202\n",
"202\n",
"6\n",
"272\n",
"271\n",
"6\n",
"1\n",
"3\n",
"272\n",
"2\n",
"2\n",
"2\n",
"3\n",
"249\n",
"1\n"
]
}
|
You're a mikemon breeder currently in the middle of your journey to become a mikemon master. Your current obstacle is go through the infamous Biridian Forest.
The forest
The Biridian Forest is a two-dimensional grid consisting of r rows and c columns. Each cell in Biridian Forest may contain a tree, or may be vacant. A vacant cell may be occupied by zero or more mikemon breeders (there may also be breeders other than you in the forest). Mikemon breeders (including you) cannot enter cells with trees. One of the cells is designated as the exit cell.
The initial grid, including your initial position, the exit cell, and the initial positions of all other breeders, will be given to you. Here's an example of such grid (from the first example):
<image>
Moves
Breeders (including you) may move in the forest. In a single move, breeders may perform one of the following actions:
* Do nothing.
* Move from the current cell to one of the four adjacent cells (two cells are adjacent if they share a side). Note that breeders cannot enter cells with trees.
* If you are located on the exit cell, you may leave the forest. Only you can perform this move — all other mikemon breeders will never leave the forest by using this type of movement.
After each time you make a single move, each of the other breeders simultaneously make a single move (the choice of which move to make may be different for each of the breeders).
Mikemon battle
If you and t (t > 0) mikemon breeders are located on the same cell, exactly t mikemon battles will ensue that time (since you will be battling each of those t breeders once). After the battle, all of those t breeders will leave the forest to heal their respective mikemons.
Note that the moment you leave the forest, no more mikemon battles can ensue, even if another mikemon breeder move to the exit cell immediately after that. Also note that a battle only happens between you and another breeders — there will be no battle between two other breeders (there may be multiple breeders coexisting in a single cell).
Your goal
You would like to leave the forest. In order to do so, you have to make a sequence of moves, ending with a move of the final type. Before you make any move, however, you post this sequence on your personal virtual idol Blog. Then, you will follow this sequence of moves faithfully.
Goal of other breeders
Because you post the sequence in your Blog, the other breeders will all know your exact sequence of moves even before you make your first move. All of them will move in such way that will guarantee a mikemon battle with you, if possible. The breeders that couldn't battle you will do nothing.
Your task
Print the minimum number of mikemon battles that you must participate in, assuming that you pick the sequence of moves that minimize this number. Note that you are not required to minimize the number of moves you make.
Input
The first line consists of two integers: r and c (1 ≤ r, c ≤ 1000), denoting the number of rows and the number of columns in Biridian Forest. The next r rows will each depict a row of the map, where each character represents the content of a single cell:
* 'T': A cell occupied by a tree.
* 'S': An empty cell, and your starting position. There will be exactly one occurence of this in the map.
* 'E': An empty cell, and where the exit is located. There will be exactly one occurence of this in the map.
* A digit (0-9): A cell represented by a digit X means that the cell is empty and is occupied by X breeders (in particular, if X is zero, it means that the cell is not occupied by any breeder).
It is guaranteed that it will be possible for you to go from your starting position to the exit cell through a sequence of moves.
Output
A single line denoted the minimum possible number of mikemon battles that you have to participate in if you pick a strategy that minimize this number.
Examples
Input
5 7
000E0T3
T0TT0T0
010T0T0
2T0T0T0
0T0S000
Output
3
Input
1 4
SE23
Output
2
Note
The following picture illustrates the first example. The blue line denotes a possible sequence of moves that you should post in your blog:
<image>
The three breeders on the left side of the map will be able to battle you — the lone breeder can simply stay in his place until you come while the other two breeders can move to where the lone breeder is and stay there until you come. The three breeders on the right does not have a way to battle you, so they will stay in their place.
For the second example, you should post this sequence in your Blog:
<image>
Here's what happens. First, you move one cell to the right.
<image>
Then, the two breeders directly to the right of the exit will simultaneously move to the left. The other three breeder cannot battle you so they will do nothing.
<image>
You end up in the same cell with 2 breeders, so 2 mikemon battles are conducted. After those battles, all of your opponents leave the forest.
<image>
Finally, you make another move by leaving the forest.
<image>
|
{
"inputs": [
"4\n1 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n2 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 3 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 2 4\n2 1 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n2 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 3 1\n2 1 5\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n2 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 1 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n1 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 3 1\n2 1 3\n1 2 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 1 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 2 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n1 1 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 2\n1 4 1\n1 1 1\n2 7 5\n2 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 2 3\n1 4 1\n1 2 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 4 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 3\n2 5 15\n0 1 2\n0",
"4\n1 4 2\n1 3 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 2\n2 5 15\n0 4 2\n0",
"4\n1 4 1\n1 4 2\n1 2 4\n2 4 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 3\n2 5 15\n0 1 2\n0",
"4\n1 4 1\n1 4 2\n1 2 4\n2 4 1\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 3\n2 5 15\n0 1 0\n0",
"4\n1 4 2\n1 4 2\n1 2 4\n2 4 1\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 3\n2 5 15\n0 1 0\n0",
"4\n1 4 2\n1 3 3\n2 2 1\n2 3 5\n0\n1 8 1\n7\n2 2 2\n1 4 1\n2 0 3\n2 4 1\n1 1 2\n2 5 15\n0 4 1\n0",
"4\n1 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 2 2\n0",
"4\n1 4 1\n2 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n2 2 4\n2 3 5\n1\n1 3 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 8 5\n1 4 2\n0",
"4\n2 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 2 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 1 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 15\n0 1 2\n0",
"4\n1 4 1\n1 1 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 2\n2 5 15\n0 1 2\n0",
"4\n1 5 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n1 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n2 3 1\n1 2 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 1 1\n1 1 1\n2 5 5\n1 1 2\n0",
"4\n1 4 1\n1 3 2\n1 1 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 2\n1 4 2\n1 1 1\n2 7 5\n2 4 2\n0",
"4\n1 4 1\n1 3 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n1 1 3\n1 4 2\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n2 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 1 2\n1 1 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n2 2 4\n2 3 5\n1\n1 3 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 1\n0",
"4\n2 5 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 2 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n1 1 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 2 2\n1 4 2\n1 1 1\n2 7 5\n2 4 2\n0",
"4\n1 4 2\n1 3 1\n2 2 4\n2 2 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n3 0 3\n2 4 1\n1 1 2\n2 5 15\n0 4 2\n0",
"4\n1 2 2\n1 3 1\n2 2 4\n2 3 5\n0\n2 12 1\n14\n2 2 2\n1 4 1\n2 0 3\n2 4 1\n1 1 2\n2 5 15\n0 4 1\n0",
"4\n2 3 1\n2 1 3\n2 1 4\n2 3 1\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 0\n1 4 1\n1 1 1\n1 0 9\n0 4 4\n0",
"4\n1 2 1\n2 0 1\n1 2 3\n2 3 5\n0\n1 2 0\n7\n2 2 5\n1 3 1\n2 1 3\n1 0 1\n1 2 1\n2 4 9\n0 4 2\n0",
"4\n1 4 1\n1 3 2\n1 2 4\n2 4 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n2 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 1 3\n1 4 1\n1 1 1\n2 0 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n2 2 4\n2 3 5\n1\n2 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n2 4 1\n1 2 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 3 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n2 2 4\n2 4 5\n1\n1 5 1\n7\n2 2 2\n1 3 1\n2 1 3\n1 2 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 0 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 1 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 0 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 2 2\n0",
"4\n1 4 1\n1 1 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 8 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 1 2\n1 1 1\n2 0 3\n1 1 1\n1 1 1\n2 5 5\n1 1 2\n0",
"4\n2 5 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 1 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 1 2\n2 2 4\n2 3 5\n1\n1 3 1\n7\n2 2 4\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 1\n0",
"4\n1 5 1\n1 2 2\n2 2 4\n2 3 5\n1\n1 3 1\n7\n2 2 4\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 1\n2 0 4\n2 2 5\n1\n1 5 1\n7\n2 2 2\n1 1 1\n2 0 3\n1 1 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n2 4 1\n2 2 3\n1 4 1\n1 2 1\n2 5 5\n1 3 2\n0",
"4\n2 4 1\n1 3 2\n1 1 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 2\n1 1 2\n1 1 1\n2 7 5\n2 4 2\n0",
"4\n1 4 1\n1 2 2\n2 4 4\n2 3 5\n1\n1 3 1\n7\n2 2 2\n1 4 1\n1 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 1\n0",
"4\n1 4 1\n1 1 2\n2 2 4\n2 3 5\n1\n1 3 1\n7\n2 2 4\n1 4 1\n2 2 3\n1 4 1\n1 1 1\n2 5 5\n1 4 1\n0",
"4\n1 4 1\n1 2 1\n1 2 3\n2 3 5\n0\n1 5 2\n2\n2 0 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n3 0 16\n0 4 2\n0",
"4\n1 4 1\n1 3 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 7 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 2\n1 4 1\n1 1 1\n2 7 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 3 1\n2 1 5\n1 4 1\n1 1 1\n2 5 0\n1 4 2\n0",
"4\n2 4 1\n1 3 1\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 1 2\n2 0 3\n1 1 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n0 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 9\n0 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 15\n0 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 15\n0 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 15\n0 1 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 2\n2 5 15\n0 1 2\n0",
"4\n2 4 1\n1 2 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n2 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 4\n1 3 1\n2 1 5\n1 4 1\n1 1 1\n2 5 5\n1 4 2\n0",
"4\n1 4 1\n1 3 2\n1 2 4\n2 3 5\n1\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 2\n1 4 1\n1 1 1\n2 7 5\n2 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 0 1\n2 5 5\n0 4 2\n0",
"4\n1 4 1\n1 2 1\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 9\n0 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 0 3\n1 4 1\n1 1 1\n2 5 15\n0 4 2\n0",
"4\n1 4 2\n1 2 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 15\n0 4 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n2 5 15\n0 1 0\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 3\n2 5 15\n0 1 2\n0",
"4\n1 4 1\n1 2 2\n1 2 4\n2 3 5\n0\n1 5 1\n7\n3 2 2\n1 4 1\n2 1 3\n1 4 1\n1 0 1\n2 5 5\n0 4 2\n0",
"4\n1 4 1\n1 2 1\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n3 5 9\n0 4 2\n0",
"4\n1 4 2\n1 2 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 2\n2 5 15\n0 4 2\n0",
"4\n1 4 1\n1 2 1\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 1\n3 0 9\n0 4 2\n0",
"4\n1 4 1\n1 2 1\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 0\n1 4 1\n1 1 1\n3 0 9\n0 4 2\n0",
"4\n1 4 2\n1 3 2\n1 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 0 3\n1 4 1\n1 1 2\n2 5 15\n0 4 2\n0",
"4\n1 4 1\n1 4 2\n1 2 4\n2 4 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 1 3\n1 4 1\n1 1 3\n2 5 15\n0 1 0\n0",
"4\n2 4 1\n1 2 1\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 0\n1 4 1\n1 1 1\n3 0 9\n0 4 2\n0",
"4\n1 4 2\n1 3 2\n2 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 0 3\n1 4 1\n1 1 2\n2 5 15\n0 4 2\n0",
"4\n2 4 1\n1 2 1\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 0\n1 4 1\n1 1 1\n3 0 9\n0 4 4\n0",
"4\n1 4 2\n1 3 2\n2 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 0 3\n2 4 1\n1 1 2\n2 5 15\n0 4 2\n0",
"4\n2 4 1\n2 2 1\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n2 1 0\n1 4 1\n1 1 1\n3 0 9\n0 4 4\n0",
"4\n1 4 2\n1 3 2\n2 2 4\n2 3 5\n0\n1 6 1\n7\n2 2 2\n1 4 1\n2 0 3\n2 4 1\n1 1 2\n2 5 15\n0 4 1\n0",
"4\n2 4 1\n2 2 1\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n4 1 0\n1 4 1\n1 1 1\n3 0 9\n0 4 4\n0",
"4\n1 4 2\n1 3 2\n2 2 4\n2 3 5\n0\n1 8 1\n7\n2 2 2\n1 4 1\n2 0 3\n2 4 1\n1 1 2\n2 5 15\n0 4 1\n0",
"4\n2 4 1\n2 2 2\n1 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n4 1 0\n1 4 1\n1 1 1\n3 0 9\n0 4 4\n0",
"4\n1 4 2\n1 3 3\n2 2 4\n2 3 5\n0\n1 8 1\n7\n2 2 2\n1 4 1\n2 0 3\n2 4 1\n1 1 2\n2 5 15\n0 4 1\n0",
"4\n2 4 1\n2 2 2\n2 2 4\n2 3 5\n0\n1 5 1\n7\n2 2 2\n1 4 1\n4 1 0\n1 4 1\n1 1 1\n3 0 9\n0 4 4\n0",
"4\n2 4 1\n2 2 2\n2 2 4\n2 3 5\n0\n1 5 1\n7\n4 2 2\n1 4 1\n4 1 0\n1 4 1\n1 1 1\n3 0 9\n0 4 4\n0"
],
"outputs": [
"2\n0\n6",
"7\n0\n6\n",
"12\n0\n6\n",
"2\n0\n13\n",
"12\n0\n13\n",
"6\n0\n6\n",
"7\n0\n10\n",
"5\n0\n13\n",
"12\n0\n12\n",
"11\n0\n6\n",
"7\n0\n15\n",
"12\n0\n14\n",
"11\n",
"2\n0\n6\n",
"7\n0\n18\n",
"2\n0\n14\n",
"11\n0\n12\n",
"6\n0\n13\n",
"11\n0\n18\n",
"13\n",
"12\n",
"14\n",
"9\n",
"4\n",
"7\n",
"2\n0\n9\n",
"7\n0\n13\n",
"6\n3\n6\n",
"11\n0\n14\n",
"12\n0\n15\n",
"3\n",
"10\n",
"3\n0\n6\n",
"5\n0\n6\n",
"2\n0\n11\n",
"6\n0\n23\n",
"12\n0\n21\n",
"7\n0\n12\n",
"6\n3\n11\n",
"13\n0\n15\n",
"6\n0\n24\n",
"6\n",
"5\n",
"8\n",
"2\n",
"13\n0\n6\n",
"12\n0\n8\n",
"6\n5\n6\n",
"6\n0\n10\n",
"8\n0\n18\n",
"5\n0\n14\n",
"5\n0\n9\n",
"10\n0\n14\n",
"2\n0\n10\n",
"13\n0\n14\n",
"5\n3\n11\n",
"7\n3\n6\n",
"4\n0\n14\n",
"11\n0\n17\n",
"6\n0\n15\n",
"8\n3\n11\n",
"5\n3\n17\n",
"1\n",
"12\n0\n13\n",
"12\n0\n13\n",
"7\n0\n15\n",
"12\n0\n14\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"6\n0\n6\n",
"7\n0\n10\n",
"12\n0\n13\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"11\n",
"12\n",
"14\n",
"11\n",
"12\n",
"11\n",
"12\n",
"11\n",
"12\n",
"11\n",
"12\n",
"11\n",
"12\n",
"11\n",
"11\n"
]
}
|
Tetris is a game in which falling blocks are lined up on the board and erased. Here, let's consider a game that arranges it a little.
The size of the board of this game is 5 frames wide, and it is high enough to accommodate all the blocks that appear. The falling blocks are straight and come in two types, landscape and portrait, with five lengths from 1 to 5.
An example is shown below. The figure from Step (a) to Step (e) shows how the blocks fall and disappear. From Step (a), proceed in order of Step (b) and Step (c).
When dropping a block, if somewhere in the block is caught in a block piled up like Step (a), the dropped block like Step (b) will stop at that place. Also, as a result of dropping a block, if all the frames in a horizontal line on the board are clogged with blocks, the blocks in that line will disappear as shown in Step (d). After this, the block above the disappeared line will move down one line as it is (Step (e)).
<image>
In one game, up to 1000 blocks will be dropped in order. For example, the lengths of the falling blocks are 4 frames horizontally, 3 frames horizontally, 2 frames vertically, and 3 frames vertically, and the falling locations are the 1st, 1st, 4th, and 5th frames from the left end. If there is, it will drop as shown in Step (a) to (g) in the figure below, and the last remaining block will be 2 frames.
<image>
Create a program that inputs the information of the blocks that fall in order and outputs the number of frames remaining when all the blocks fall.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
n
d1 p1 q1
d2 p2 q2
::
dn pn qn
The number of blocks n (1 ≤ n ≤ 1000) is given on the first line. The next n lines give the i-th block orientation di (1 or 2), the block length pi (1 ≤ pi ≤ 5), and the block position qi. Block orientation di is 1 for landscape orientation and 2 for portrait orientation. The block position qi is an integer from 1 to 5 from the left edge on the board, and in the case of a horizontal block, it is the position where the left edge frame falls.
The number of datasets does not exceed 20.
Output
The number of frames occupied by the last remaining block for each data set is output on one line.
Example
Input
4
1 4 1
1 3 1
2 2 4
2 3 5
1
1 5 1
7
2 2 2
1 4 1
2 1 3
1 4 1
1 1 1
2 5 5
1 4 2
0
Output
2
0
6
|
{
"inputs": [
"1\naabbcc\n\nSAMPLE",
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"10\naabbccddeeffgghhiijjkkllmmnnooppqqrrssttuuvvwwxxyyzz\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\nabcdefghijklmnopqrstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllllllllllllwww\n''''''''''''''''''''''''''''''''''''''''''''''''''''''rrrrrrrrrrrrrrrrrrrr\nsssssssssssssssssssfffffffffffffffffffffffffffffweeeeeeeeeeeeeeeeeeeeecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwwwwwfffffffffffffflsssssssssssssssossspaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"1\naabbcb\n\nSAMPLE",
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"1\naabbbb\n\nSAMPLE",
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"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuuvvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaaaaaaaaaa\nabcdefghijklmnopqrstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\n''''''''''''''''''''''''''''''''''''''''''''''''''''''rrrrrrrrrrrrrrrrrrrr\nsssssssssssssssssssfffffffffffffffffffffffffffffweeeeeeeeeeeeeeeeeeeeecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwwwwwfffffffffffffflsssssssssssssssossspaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
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"1\naabbbc\n\nPAMSLE",
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"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuuvvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaabaaaaaaa\nabcdefghijklmnopqrstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\n''''''''''''''''''''''''''''''''''('''''''''''''''''''rrrrrrrrrrrrrrrrrrrr\nsssssssssssssssssssffffffgffffffffffffffffffffffweeeeeeeeeeeeeeeeeeeeecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssssssossspaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuuvvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\n''''''''''''''''''''''''''''''''''('''''''''''''''''''rrrrrrrrrrrrrrrrrrrr\nsssssssssssssssssssffffffgffffffffffffffffffffffweeeeeeeeeeeeeeeeeeeeecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssssssossspaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"1\nacbbba\n\nO@MSME",
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"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\n''''''''''''''''''''''''''''''''''('''''''''''''''''''rrrrrrrrrrrrrrrrrrrr\nsssssssssssssssssssffffffgffffffffffffffffffffffweeeeeeeeeeeeeeeeeeeeecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssstssossspaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
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"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrrrrrrrrrrrrrrrrrrr'''''''''''''''''''(''''''''''''''''''''''''''''''''''\nsssssssssssssssssssffffffgffffffffffffffffffffffweeeeefeeeeeeeeeeeeeeecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssstssossspaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrrrrrrrrrrrrrrrrrrr'''''''''''''''''''(''''''''''''''''''''''''''''''''''\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssstssossspaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"1\nadbbba\n\nENS@LO",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaaaaaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrrrrrrrrrrrrrrrrrrr'''''''''''''''''''(''''''''''''''''''''''''''''''''''\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssstssosssqaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaa`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrrrrrrrrrrrrrrrrrrr'''''''''''''''''''(''''''''''''''''''''''''''''''''''\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssstssosssqaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"1\naebbba\n\nEMS@LO",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaa`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaaa\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''''''\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssstssosssqaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaa`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''''''\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssstssosssqaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"1\naabbbe\n\nLMS@EO",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaa`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaaawwwwwwwwswwwfffffffffffffflssssssswsssstssosssqaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaa`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaaaaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffffffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaa`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffffffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
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"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaaa`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaaaaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwwxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvvvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceeeeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffsssssssssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"1\nabbbea\n\nQES>MM",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa.................dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffssssessssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"1\nebbbaa\n\nQES>MM",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewffffffffffffffffffffffgffffffssssessssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewfffffffffffffsffffffffgffffffsssfessssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaaaaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaaaaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewfffffffffffffsffffffffgffffffsssfessssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naaaaaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewfffffffffffffsffffffffgffffffsssfessssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewfffffffffffffsffffffffgffffffsssfessssssssssssss\naaaaaaaaaaaaqsssosstsssswssssssslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewfffffffffffffsffffffffgffffffsssfessssssssssssss\naaaaaasaaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgghhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewfffffffffffffsffffffffgffffffsssfessssssssssssss\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaasaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"1\naababe\n\nFMS=MR",
"10\naabbccddkeffgfhhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nbbbbbbbceseeeeeeeeeeeeefeeeeewfffffffffffffsffffffffgffffffsssfessssssssssssss\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaasaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgfhhiijjkellmmnnooppqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssefsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaasaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"1\naabaae\n\nFMT=MR",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssefsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaasaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaaaaaaaaaaaaaaaa...............................\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssefsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaasaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"1\naaeaab\n\nFMM=TR",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaaaaaaaaaaaaaaaa...............................\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaasaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"1\nbaaeaa\n\nFMM=TR",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaasaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa.",
"1\nbaaea`\n\nFMM=TR",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaasaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawwwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwwwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nba`ea`\n\nRF=MMT",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa..........-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\n`ae`ab\n\nRF=MMT",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa....../...-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\n'''('''''''''''''''''''''''''r''''('''''''''''''''''''rrrrrrrrrrrrrrrr'rrr\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nca`ea`\n\nRF=MMT",
"10\naabbccddkeffgfhhiijjkellmmnnooqpqprrssttuvuvwxxxyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa....../...-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nca`e``\n\nRF=MMT",
"10\naabbccddkeffgxhhiijjkellmmnnooqpqprrssttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\naaaabaaaaaaaa,,,,,,,,,,,,,,,,,,,,,....................\naa`aaaaaaaaaa....../...-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\naabbccddkeffgxhhiijjkellmmnnooqpqprrssttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\n....................,,,,,,,,,,,,,,,,,,,,,aaaaaaaabaaaa\naa`aaaaaaaaaa....../...-......dddddddddddkkkkkkkkkkkkvvuvvvvvvvllmlllllllllwww\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\naabbccddkeffgxhhiijjkellmmnnooqpqprrssttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\n....................,,,,,,,,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmllvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nc``e``\n\nMMT=FR",
"10\naabbccddkeffgxhhiijjkellmmnnooqpqprrssttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaaaaaaaaaba\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmllvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\naabbccddkeffgxhhiijjkellmmnnooqpqprrssttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaabaaaaaaba\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmllvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr'''''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nb``e``\n\nRF=TMM",
"10\naabbccddkeffgxhhiijjkellmmnnooqpqprrssttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaabaaaaaaba\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmllvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nb``e`_\n\n=FRTMM",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaabaaaaaaba\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmllvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaaaaaaaaabaaaaaaba\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nb``ea_\n\nMMTRF=",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaabaaaaaaaaaaaaa...............................\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaraaaaaqsssosstsssswsssssaslffffffefffffffwwwswwwwwwxwaaaaaaaaaaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaabaaaaaaaaaaaaa...............................\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffefffffflsassssswsssstssosssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaabaaaaaaaaaaaaa...............................\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstssosssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nb``e_a\n\nMLSRF=",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaabaaaaaa`aaaaaa...............................\n,...................,,,,,,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstssosssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaabaaaaaa`aaaaaa...............................\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvvvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstssosssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\na_e``b\n\n=FRSLM",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaabaaaaaa`aaaaaa...............................\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvwvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstssosssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\nabaaaaaabaaaaaa`aaaaaa...............................\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvwvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaaa\nwwwlllllllllmklvwvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\na_e_`b\n\nRLSMF=",
"10\n`abbccddkeffgxhhiijjkellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaba\nwwwlllllllllmklvwvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccdkkeffgxhhiijjdellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaba\nwwwlllllllllmklvwvvvvvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\na^e_`b\n\nQLSMF=",
"10\n`abbccdkkeffgxhhiijjdellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaba\nwwwlllllllllmklvwvvvuvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&''''''''''''''''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccdkkeffgxhhiijjdellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaba\nwwwlllllllllmklvwvvvuvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'rrrrrrrrrrrrrrrr''&'''''''''''''(''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccdkkeffgxhhiijjdellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n...............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaba\nwwwlllllllllmklvwvvvuvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'srrrrrrrrrrrrrrr''&'''''''''''''(''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nb`_e^a\n\n=FMSKQ",
"10\n`abbccdkkeffgxhhiijjdellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n-..............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaba\nwwwlllllllllmklvwvvvuvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'srrrrrrrrrrrrrrr''&'''''''''''''(''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraaaaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"1\nc`_e^a\n\n=FMSKQ",
"10\n`abbccdkkeffgxhhiijjdellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n-..............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaba\nwwwlllllllllmklvwvvvuvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'srrrrrrrrrrrrrrr''&'''''''''''''(''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraabaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaaaaaaaaa/",
"10\n`abbccdkkeffgxhhiijjdellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n-..............................aaaaaa`aaaaaabaaaaaaba\n,...................,,,,+,.,,,,,,,,,,,,,,aaaaaaaabaaba\nwwwlllllllllmklvwvvvuvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'srrrrrrrrrrrrrrr''&'''''''''''''(''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraabaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaabaaaaaa/",
"10\n`abbccdkkeffgxhhiijjdellmmnnooqpqprrstttuvuvwxxfyyzz\naaaabaaaaaaaaaaa`aaaaaaaaaaaab`aaabaaaabaa\nabcdefghijrlmnopqkstuvwxyz\n-..............................aaaaaa`aaaaaabaaaaaaba\n,........a..........,,,,+,.,,,,,,,,,,,,,,aaaaaaaab.aba\nwwwlllllllllmklvwvvvuvuvvkkkkkkkkkkkkddddddddddd......-.../......aaaaaaaaaa`aa\nrrr'srrrrrrrrrrrrrrr''&'''''''''''''(''(''''r'''''''''''''''''''''''''('''\nssssssssssssssdfsssffffffgffffffffsfffffffffffffweeeeefeeeeeeeeeeeeesecbbbbbbb\naaaaaaaaaaaaaawxwwwwwwswwwfffffffegffffflsassssswsssstsspsssqaaaaaraabaaa\n.aaaaaaaaa............aaaaaaaaabaaaaaaaaaabaaaaaa/"
],
"outputs": [
"abc\n",
"abcdefghijklmnopqrstuvwxyz\na\nabcdefghijklmnopqrstuvwxyz\n.a\n.,a\na.dkvlw\n'r\nsfwecb\nawflsospa\n.a.a.\n",
"abcdefghijklmnopqrstuvwxyz\na\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlw\n'r\nsfwecb\nawflsospa\n.a.a.\n",
"abcb\n",
"abcdkefghijkelmnopqrstuvwxyz\na\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlw\n'r\nsfwecb\nawflsospa\n.a.a.\n",
"abcdkefghijkelmnopqrstuvwxyz\na`a\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlw\n'r\nsfwecb\nawflsospa\n.a.a.\n",
"ab\n",
"abcdkefghijkelmnopqrstuvwxyz\na`a\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlmlw\n'r\nsfwecb\nawflsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvwxyz\na`a\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlmlw\n'r\nsfwecb\nawflsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvwxyz\na`a\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlmlw\n'('r\nsfwecb\nawflsospa\n.a.a.\n",
"abc\n",
"abcdkefghijkelmnopqprstuvwxyz\na`a\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlmlw\n'('r\nsfwecb\nawswflswsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvwxyz\na`aba\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlmlw\n'('r\nsfwecb\nawswflswsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvwxyz\na`aba\nabcdefghijklmnopqrstuvwxyz\n.a\na,.\na.dkvlmlw\n'('r\nsfgfwecb\nawswflswsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvwxyz\na`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\n'('r\nsfgfwecb\nawswflswsospa\n.a.a.\n",
"acba\n",
"abcdkefghijkelmnopqprstuvwxyz\na`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\n'('r\nsfgfwecb\nawswflswstsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\n'('r\nsfgfwecb\nawswflswstsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\nr'('\nsfgfwecb\nawswflswstsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\nr'('\nsfgfwefecb\nawswflswstsospa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\nr'('\nbcefewfgfs\nawswflswstsospa\n.a.a.\n",
"adba\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\nr'('\nbcefewfgfs\nawswflswstsosqa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`a`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\nr'('\nbcefewfgfs\nawswflswstsosqa\n.a.a.\n",
"aeba\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`a`aba\nabcdefghijrlmnopqkstuvwxyz\n.a\na,.\na.dkvlmlw\nr'r'('r'\nbcefewfgfs\nawswflswstsosqa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`a`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\na,.\na.dkvlmlw\nr'r'('r'\nbcefewfgfs\nawswflswstsosqa\n.a.a.\n",
"abe\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`a`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\na,.\na.dkvlmlw\nr'r'('r'('\nbcefewfgfs\nawswflswstsosqa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`a`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\na,.\na.dkvlmlw\nr'r'('r'('\nbcefewfgfs\naqsostswslfwswa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`a`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.dkvlmlw\nr'r'('r'('\nbcefewfgfs\naqsostswslfwswa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`a`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.dkvlmlw\nr'r'('r'('\nbcefewfgfs\naqsostswslfefwswa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`a`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.dkvlmlw\n'('r'('r'r\nbcefewfgfs\naqsostswslfefwswa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\na`ab`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.dkvlmlw\n'('r'('r'r\nbcefewfgfs\naqsostswslfefwswa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.dkvlmlw\n'('r'('r'r\nbcefewfgfs\naqsostswslfefwswa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.dkvuvlmlw\n'('r'('r'r\nbcefewfgfs\naqsostswslfefwswa\n.a.a.\n",
"abea\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.dkvuvlmlw\n'('r'('r'r\nbcesefewfgfses\naqsostswslfefwswa\n.a.a.\n",
"eba\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.-.dkvuvlmlw\n'('r'('r'r\nbcesefewfgfses\naqsostswslfefwswa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.-.dkvuvlmlw\n'('r'('r'r\nbcesefewfsfgfsfes\naqsostswslfefwswa\n.a.a.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`aba\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.-.dkvuvlmlw\n'('r'('r'r\nbcesefewfsfgfsfes\naqsostswslfefwswa\n.a.aba.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na.-.dkvuvlmlw\n'('r'('r'r\nbcesefewfsfgfsfes\naqsostswslfefwswa\n.a.aba.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nbcesefewfsfgfsfes\naqsostswslfefwswa\n.a.aba.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nbcesefewfsfgfsfes\nasaqsostswsaslfefwswa\n.a.aba.\n",
"abcdkefghijkelmnopqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nbcesefewfsfgfsfes\nawswfeflsaswstsosqasa\n.a.aba.\n",
"ababe\n",
"abcdkefgfhijkelmnopqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nbcesefewfsfgfsfes\nawswfeflsaswstsosqasa\n.a.aba.\n",
"abcdkefgfhijkelmnopqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsefsfgfsfwefesecb\nawswfeflsaswstsosqasa\n.a.aba.\n",
"abae\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsefsfgfsfwefesecb\nawswfeflsaswstsosqasa\n.a.aba.\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\naba.\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsefsfgfsfwefesecb\nawswfeflsaswstsosqasa\n.a.aba.\n",
"aeab\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\naba.\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsdfsfgfsfwefesecb\nawswfeflsaswstsosqasa\n.a.aba.\n",
"baea\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsdfsfgfsfwefesecb\nawswfeflsaswstsosqasa\n.a.aba.\n",
"baea`\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsdfsfgfsfwefesecb\nawswfeflsaswstsosqasa\n.a.aba/\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsdfsfgfsfwefesecb\nawswfeflsaswstsosqara\n.a.aba/\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswa\n.a.aba/\n",
"ba`ea`\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a.-.dkvuvlmlw\n'('r'('r'r\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"`ae`ab\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a./.-.dkvuvlmlw\n'('r'('r'r\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"ca`ea`\n",
"abcdkefgfhijkelmnoqpqprstuvuvwxyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a./.-.dkvuvlmlw\nr'r'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"ca`e`\n",
"abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\naba,.\na`a./.-.dkvuvlmlw\nr'r'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\n.,aba\na`a./.-.dkvuvlmlw\nr'r'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\n.,aba\nwlmlvuvkd.-./.a`a\nr'r'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"c`e`\n",
"abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.aba\n,.,.,aba\nwlmlvuvkd.-./.a`a\nr'r'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.ababa\n,.,.,aba\nwlmlvuvkd.-./.a`a\nr'r'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"b`e`\n",
"abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.ababa\n,.,.,aba\nwlmlvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"b`e`_\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.ababa\n,.,.,aba\nwlmlvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.ababa\n,.,.,aba\nwlmklvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"b`ea_\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\nababa.\n,.,.,aba\nwlmklvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\naraqsostswsaslfefwswxwa\n.a.aba/\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\nababa.\n,.,.,aba\nwlmklvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfeflsaswstsosqara\n.a.aba/\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\nababa.\n,.,.,aba\nwlmklvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstsosqara\n.a.aba/\n",
"b`e_a\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\nababa`a.\n,.,.,aba\nwlmklvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstsosqara\n.a.aba/\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\nababa`a.\n,.,+,.,aba\nwlmklvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstsosqara\n.a.aba/\n",
"a_e`b\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\nababa`a.\n,.,+,.,aba\nwlmklvwvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstsosqara\n.a.aba/\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\nababa`a.\n,.,+,.,aba\nwlmklvwvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqara\n.a.aba/\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.a`ababa\n,.,+,.,aba\nwlmklvwvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqara\n.a.aba/\n",
"a_e_`b\n",
"`abcdkefgxhijkelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.a`ababa\n,.,+,.,ababa\nwlmklvwvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqara\n.a.aba/\n",
"`abcdkefgxhijdelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.a`ababa\n,.,+,.,ababa\nwlmklvwvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqara\n.a.aba/\n",
"a^e_`b\n",
"`abcdkefgxhijdelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.a`ababa\n,.,+,.,ababa\nwlmklvwvuvuvkd.-./.a`a\nr'r'&'('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqara\n.a.aba/\n",
"`abcdkefgxhijdelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.a`ababa\n,.,+,.,ababa\nwlmklvwvuvuvkd.-./.a`a\nr'r'&'('('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqara\n.a.aba/\n",
"`abcdkefgxhijdelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n.a`ababa\n,.,+,.,ababa\nwlmklvwvuvuvkd.-./.a`a\nr'sr'&'('('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqara\n.a.aba/\n",
"b`_e^a\n",
"`abcdkefgxhijdelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n-.a`ababa\n,.,+,.,ababa\nwlmklvwvuvuvkd.-./.a`a\nr'sr'&'('('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqara\n.a.aba/\n",
"c`_e^a\n",
"`abcdkefgxhijdelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n-.a`ababa\n,.,+,.,ababa\nwlmklvwvuvuvkd.-./.a`a\nr'sr'&'('('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqaraba\n.a.aba/\n",
"`abcdkefgxhijdelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n-.a`ababa\n,.,+,.,ababa\nwlmklvwvuvuvkd.-./.a`a\nr'sr'&'('('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqaraba\n.a.ababa/\n",
"`abcdkefgxhijdelmnoqpqprstuvuvwxfyz\naba`ab`ababa\nabcdefghijrlmnopqkstuvwxyz\n-.a`ababa\n,.a.,+,.,ab.aba\nwlmklvwvuvuvkd.-./.a`a\nr'sr'&'('('r'('\nsdfsfgfsfwefesecb\nawxwswfegflsaswstspsqaraba\n.a.ababa/\n"
]
}
|
After the Tatvik Hiring Challenge, Karan's NLP professor has given him another homework. Since Manhattan Associates Hiring Challenge is round the corner and Karan is busy preparing for it, he turns to you for help.
Given a string, replace all the consecutively occurring characters by a single, same character.
Input:
The first line contains the number of test cases T. Each test case contains the string, on a separate line.
Output:
Print the modified string, each on a new line.
Constraints:
1 ≤ T ≤ 100
1 ≤ length(string) < 10^6
SAMPLE INPUT
1
aabbcc
SAMPLE OUTPUT
abc
|
{
"inputs": [
"6\nICPC.@bmail.com\np+con+test@BMAIL.COM\nP@bmail.com\na@bmail.com.ru\nI.cpc@Bmail.Com\na+b@bmail.com.ru",
"8\ntest@bbmail.com\ntes.t@bbmail.com\ntest@bmail.com\ntes.t@bmail.com\ntest+bmail.com@bbmail.com\ntes.t+bmail.com@bbmail.com\ntest+bmail.com@bmail.com\ntes.t+bmail.com@bmail.com",
"2\new+@bmail.comm\new+@bmail.com",
"5\na+@bmail.com\naa+@bmail.com\naaa+@bmail.com\naaaa+@bmail.com\naaaaa+@bmail.com",
"5\na+@bmail.com\na.++@bmail.com\na.+++@bmail.com\na.++++@bmail.com\na++++++@bmail.com",
"2\na+@bmai.lcom\na@bmai.lcom",
"3\na@a.a\nb@bmail.com\nb+.+.@bmail.com",
"2\nasbmail.com+asdasdasd@bmails.com\nasdasdasd+ASDASDASD@bmails.com",
"2\nq+q+q+asdasdasdbmail.com@bmail.com\nq+asdasdawefgrjgwasldkfmaslkdfjsakldfj@bmaiL.COM",
"2\nabcd@rt.com.com\nabcd+a@rt.com.com",
"16\na@bmail.com\na@bmail.bmail.com\na@bmail\na@bmailc.om\na@bmailcom\na+b@mailcom\na@b.mailcom\nbmail.com@a\naa@bmail.com\naa@bmail.bmail.com\naa@bmail\naa@bmailc.om\naa@bmailcom\naa+b@mailcom\naa@b.mailcom\nbmail.com@aa",
"15\nIiT@Yxva.WfK\nj@BmAil.CoM\niIT@YXVa.wFk\nVkaVrN@YRK.m\ndM@BMaiL.com\no@A.oenMU\nyZ@bMaiL.coM\ndm@bmAIl.COM\nC@BMaIL.com\nQc@Jgzb.OqhJ\nc@bmAiL.cOm\nDT@BMaiL.com\nO@A.OENMU\nAX@bMAIL.cOm\ns@BMaIL.Com",
"5\na@bmail.com\naa@bmail.com\naaa@bmail.com\naaaa@bmail.com\naaaaa@bmail.com",
"2\na+a@gmail.com\na@gmail.com",
"2\nasdasdasd+asdasdasd@bmail.com\nasdasdasd+ASDASDASD@bmail.com",
"5\na@qwe.qwe\naa@qwe.qwe\naaa@qwe.qwe\naaaa@qwe.qwe\naaaaa@qwe.qwe",
"6\nICPC.@bmail.com\np+con+test@BMAIL.COM\nP@bmail.com\na@bmail.com.ru\nI.cpc@Bmail.Com\na+b@bmail.com.ru",
"2\na+a@bmail.com\na@bmail.com",
"2\nq@mail.com\nq+qedasdwqerdasdbmail.com@bmail.com",
"2\nqqq@b.m.a.i.l.com\nqqq@bmail.com",
"2\nqqq@b.m.a.i.l.com\nqqq+@b.m.a.i.l.com",
"5\na+@bmail.com\na.++@bmail.coom\na.+++@bma.il.com\na.++++@bMail.com\na.b++++++@bmail.com",
"15\nXd@oW.I\nd@zb.oqHJ\nS@kA.RnWn.Kf\nMU@bMAil.COM\nc@bMaIL.CoM\nkt+.i@X.xV\nC@BMaIL.com\ngf@bMaIL.coM\nN+.oP@Uu.V\nN+.Op@UU.V\nA@JjWsp.CFce\nMU@BMAIL.COM\nPu@bMAil.CoM\nGf@BMaIl.COm\nkt+.O@x.xv",
"8\ntest@bbmail.com\ntes.t@bbmail.com\ntest@bmail.com\ntes.t@bmail.com\ntest+bmail.com@bbmail.com\nmoc.liambb@moc.liamb+t.set\ntest+bmail.com@bmail.com\ntes.t+bmail.com@bmail.com",
"2\new+@bmail.comn\new+@bmail.com",
"5\na+@bmail.com\naa+@bmail.com\naaa+@bmail.com\naaaa+@bmail.com\naaaaa+@bmajl.com",
"5\na+@bmail.com\na.*+@bmail.com\na.+++@bmail.com\na.++++@bmail.com\na++++++@bmail.com",
"2\na+@bmai.lcom\na@bmai/lcom",
"3\na@a.a\nc@bmail.com\nb+.+.@bmail.com",
"2\nasbmail.com+asdasdasd@bmails.com\nasdasdasd+ASDASDASD@bmbils.com",
"2\nq+q+q+asdasdasdbmail.com@bmail.com\nq+asdasdawefgrjgwasldkfmaslkdfj@akldfjsbmaiL.COM",
"2\nmoc.moc.tr@dcba\nabcd+a@rt.com.com",
"16\na@bmahl.com\na@bmail.bmail.com\na@bmail\na@bmailc.om\na@bmailcom\na+b@mailcom\na@b.mailcom\nbmail.com@a\naa@bmail.com\naa@bmail.bmail.com\naa@bmail\naa@bmailc.om\naa@bmailcom\naa+b@mailcom\naa@b.mailcom\nbmail.com@aa",
"15\nIiT@fxva.WYK\nj@BmAil.CoM\niIT@YXVa.wFk\nVkaVrN@YRK.m\ndM@BMaiL.com\no@A.oenMU\nyZ@bMaiL.coM\ndm@bmAIl.COM\nC@BMaIL.com\nQc@Jgzb.OqhJ\nc@bmAiL.cOm\nDT@BMaiL.com\nO@A.OENMU\nAX@bMAIL.cOm\ns@BMaIL.Com",
"5\na@bmail.com\naa@bmail.com\naaa@bnail.com\naaaa@bmail.com\naaaaa@bmail.com",
"2\na+a@gmail.com\na@gmail.col",
"2\nbsdasdasd+asdasdasd@bmail.com\nasdasdasd+ASDASDASD@bmail.com",
"5\na@qwd.qwe\naa@qwe.qwe\naaa@qwe.qwe\naaaa@qwe.qwe\naaaaa@qwe.qwe",
"6\nICPC.@bmail.com\np+con+test@BMAIL.COM\nP@bmail.com\na@bmail.com.ru\nI.cpc@Bmajl.Com\na+b@bmail.com.ru",
"2\na+a@amail.com\na@bmail.com",
"2\nq@mail.com\nmoc.liamb@moc.liambdsadreqwdsadeq+q",
"2\nqqr@b.m.a.i.l.com\nqqq@bmail.com",
"2\nqqq@b.m.a.i.l.com\nqqq+@c.m.a.i.l.com",
"5\na+@bmail.com\na.+,@bmail.coom\na.+++@bma.il.com\na.++++@bMail.com\na.b++++++@bmail.com",
"15\nXd@oW.I\nd@zb.oqHJ\nS@kA.RnWn.Kf\nMU@bMAil.COM\nc@bMaIL.CoM\nkt+.i@X.xV\nC@BMaIL.com\ngo@bMaIL.cfM\nN+.oP@Uu.V\nN+.Op@UU.V\nA@JjWsp.CFce\nMU@BMAIL.COM\nPu@bMAil.CoM\nGf@BMaIl.COm\nkt+.O@x.xv",
"6\nICPC.@bmail.com\np+con+test@BMAIL.COM\nP@bmail.com\na@bmail.com.ru\nI.cpc@Bmail.Con\na+b@bmail.com.ru",
"8\ntest@bbmail.com\ntes.t@bbmail.com\ntest@bmail.com\ntes.t@bmail.com\ntest+bmail.com@bbmail.com\nmoc.liambb@moc.liamb+t.set\ntest,bmail.com@bmail.com\ntes.t+bmail.com@bmail.com",
"2\nnmoc.liamb@+we\new+@bmail.com",
"5\na+@bmail.com\naa+@bmail.com\naaa*@bmail.com\naaaa+@bmail.com\naaaaa+@bmajl.com",
"5\na+@bmail.com\na.*+@bmail.cpm\na.+++@bmail.com\na.++++@bmail.com\na++++++@bmail.com",
"2\nmocl.iamb@+a\na@bmai/lcom",
"3\na@a.a\nc@bmail.com\nmoc.liamb@.+.+b",
"2\nmoc.sliamb@dsadsadsa+moc.liambsa\nasdasdasd+ASDASDASD@bmbils.com",
"2\nmoc.liamb@moc.liambdsadsadsa+q+q+q\nq+asdasdawefgrjgwasldkfmaslkdfj@akldfjsbmaiL.COM",
"2\nmoc.mob.tr@dcba\nabcd+a@rt.com.com",
"16\na@bmahl.com\na@bmail.bmail.com\na@bmail\na@bmailc.om\na@bmailcom\na+b@mailcom\na@b.mailcom\na@moc.liamb\naa@bmail.com\naa@bmail.bmail.com\naa@bmail\naa@bmailc.om\naa@bmailcom\naa+b@mailcom\naa@b.mailcom\nbmail.com@aa",
"15\nIiT@fxva.WYK\nj@BmAil.CoM\niIT@YXVa.wFk\nVkaVrN@YRK.m\nmoc.LiaMB@Md\no@A.oenMU\nyZ@bMaiL.coM\ndm@bmAIl.COM\nC@BMaIL.com\nQc@Jgzb.OqhJ\nc@bmAiL.cOm\nDT@BMaiL.com\nO@A.OENMU\nAX@bMAIL.cOm\ns@BMaIL.Com",
"5\na@bmail.com\naa@bmail.com\naaa@bnbil.com\naaaa@bmail.com\naaaaa@bmail.com",
"2\na+a@gmail.com\nloc.liamg@a",
"2\nbsdasdasd+asdasdasd@bmail.com\nasdasDasd+ASDASDASd@bmail.com",
"5\newq.dwq@a\naa@qwe.qwe\naaa@qwe.qwe\naaaa@qwe.qwe\naaaaa@qwe.qwe",
"6\nmoc.liamb@.CPCI\np+con+test@BMAIL.COM\nP@bmail.com\na@bmail.com.ru\nI.cpc@Bmajl.Com\na+b@bmail.com.ru",
"2\nmoc.liama@a+a\na@bmail.com",
"2\nq@mail.com\nmoc.liamb@mnc.liambdsadreqwdsadeq+q",
"2\nqqr@b.m.a.i.l.com\nqqqcbmail.@om",
"2\nmoc.l.i.a.m.b@qqq\nqqq+@c.m.a.i.l.com",
"5\nmoc.liamb@+a\na.+,@bmail.coom\na.+++@bma.il.com\na.++++@bMail.com\na.b++++++@bmail.com",
"15\nXd@oW.I\nJHqo.bz@d\nS@kA.RnWn.Kf\nMU@bMAil.COM\nc@bMaIL.CoM\nkt+.i@X.xV\nC@BMaIL.com\ngo@bMaIL.cfM\nN+.oP@Uu.V\nN+.Op@UU.V\nA@JjWsp.CFce\nMU@BMAIL.COM\nPu@bMAil.CoM\nGf@BMaIl.COm\nkt+.O@x.xv",
"6\nICPC.@bmail.com\np+con+test@BMAIL.COM\nP@bmail.com\na@bmail.com.ru\nI.cpc@Bmail.Con\na+c@bmail.com.ru",
"8\ntest@bbmail.com\ntes.t@bbmail.com\ntest@bmail.com\ntes.t@bmail.com\ntest+bmaim.com@bbmail.com\nmoc.liambb@moc.liamb+t.set\ntest,bmail.com@bmail.com\ntes.t+bmail.com@bmail.com",
"2\nnmoc.liamb@+we\nmoc.liamb@+we",
"5\na+@bmail.com\naa+@bmail.com\naaa*@bmail.com\naaaa+@amail.com\naaaaa+@bmajl.com",
"2\nmocl.hamb@+a\na@bmai/lcom",
"3\na@a.a\nc@bmail.com\nmoc.libmb@.+.+b",
"2\nmoc.liamb@moc.liambdsadsadsa+q+q+q\nMOC.Liambsjfdlka@jfdklsamfkdlsawgjrgfewadsadsa+q",
"2\nnoc.mob.tr@dcba\nabcd+a@rt.com.com",
"16\na@bmahl.com\na@bmail.bmail.com\na@bmail\na@bmailc.om\na@bmailcom\na+b@mailcom\nmocliam.b@a\na@moc.liamb\naa@bmail.com\naa@bmail.bmail.com\naa@bmail\naa@bmailc.om\naa@bmailcom\naa+b@mailcom\naa@b.mailcom\nbmail.com@aa",
"15\nIiT@fxva.WYK\nj@BmAil.CoM\niIT@YXVa.wFk\nVkaVrN@YRK.m\nmoc.LiaMB@Md\no@A.oenMU\nyZ@bMaiL.coM\ndm@bmBIl.COM\nC@BMaIL.com\nQc@Jgzb.OqhJ\nc@bmAiL.cOm\nDT@BMaiL.com\nO@A.OENMU\nAX@bMAIL.cOm\ns@BMaIL.Com",
"5\na@bmajl.com\naa@bmail.com\naaa@bnbil.com\naaaa@bmail.com\naaaaa@bmail.com",
"2\na+b@gmail.com\nloc.liamg@a",
"2\nbsdasdasd+asdasdasd@bmail.com\nasdasDasd+ASDBSDASd@bmail.com",
"5\newq.dwq@a\naa@qwe.qwe\naaa@qwe.qwe\naaaa@qwe.qwe\newq.ewq@aaaaa",
"6\nmoc.liamb@.CPCI\np+con+test@BMAIL.COM\nO@bmail.com\na@bmail.com.ru\nI.cpc@Bmajl.Com\na+b@bmail.com.ru",
"2\nmoc.liama@a+a\na@bmail/com",
"2\nq@maik.com\nmoc.liamb@mnc.liambdsadreqwdsadeq+q",
"2\nqqr@blm.a.i...com\nqqqcbmail.@om",
"2\nmoc.l.i.a.m.b@qqq\nqqq+@c.m.i.a.l.com",
"5\nmoc.liamb@+a\na.+,@bmajl.coom\na.+++@bma.il.com\na.++++@bMail.com\na.b++++++@bmail.com",
"15\nXd@oW.I\nJHqo.bz@d\nS@kA.RnWn.Kf\nMU@bMAil.COM\nc@bMaIL.CoM\nkt+.i@X.xV\nC@BMaIL.com\ngo@bMaIL.cfM\nV.uU@Po.+N\nN+.Op@UU.V\nA@JjWsp.CFce\nMU@BMAIL.COM\nPu@bMAil.CoM\nGf@BMaIl.COm\nkt+.O@x.xv",
"6\nICPC.@bmail.com\np+con+test@BMAIL.COM\nP@bmail.com\na@bmail.com.ru\nI.cpc@Amail.Con\na+c@bmail.com.ru",
"8\ntest@bbmail.com\ntes.t@bbmail.com\nmoc.liamb@tset\ntes.t@bmail.com\ntest+bmaim.com@bbmail.com\nmoc.liambb@moc.liamb+t.set\ntest,bmail.com@bmail.com\ntes.t+bmail.com@bmail.com",
"2\new+@bmail.comn\nmoc.liamb@+we",
"5\na+@bmailmco.\naa+@bmail.com\naaa*@bmail.com\naaaa+@amail.com\naaaaa+@bmajl.com",
"2\nmocl.hamb@+a\na@bmai/lcmo",
"3\na@a.a\nmoc.liamb@c\nmoc.libmb@.+.+b",
"2\nmoc.liamb@moc.liambdsadsads`+q+q+q\nMOC.Liambsjfdlka@jfdklsamfkdlsawgjrgfewadsadsa+q",
"2\nnoc.mob.tr@dcba\nmoc.moc.tr@a+dcba",
"16\na@.mahlbcom\na@bmail.bmail.com\na@bmail\na@bmailc.om\na@bmailcom\na+b@mailcom\nmocliam.b@a\na@moc.liamb\naa@bmail.com\naa@bmail.bmail.com\naa@bmail\naa@bmailc.om\naa@bmailcom\naa+b@mailcom\naa@b.mailcom\nbmail.com@aa",
"15\nIiT@fxva.WYK\nj@BmAil.CoM\niIT@YXVa.wFk\nVkaVrN@YRK.m\nmoc.LiaMB@Md\no@A.odnMU\nyZ@bMaiL.coM\ndm@bmBIl.COM\nC@BMaIL.com\nQc@Jgzb.OqhJ\nc@bmAiL.cOm\nDT@BMaiL.com\nO@A.OENMU\nAX@bMAIL.cOm\ns@BMaIL.Com",
"5\na@bmajl.com\naa@bmail.bom\naaa@bnbil.com\naaaa@bmail.com\naaaaa@bmail.com",
"2\na+b@gmail.com\na@gmail.col",
"2\nbsdasdasd+asdasdasd@bmail.com\nmoc.liamb@dSADSBDSA+dsaDsadsa",
"5\newq.dwq@a\naa@qwe.qwe\naaa@qwe.qwd\naaaa@qwe.qwe\newq.ewq@aaaaa",
"6\nmoc.liamb@.CPCI\np+con+test@BMAIL.COM\nO@bmail.com\na@bmail.com.su\nI.cpc@Bmajl.Com\na+b@bmail.com.ru",
"2\nmoc.liama@a+a\nmoc/liamb@a",
"2\nq@maik/com\nmoc.liamb@mnc.liambdsadreqwdsadeq+q",
"2\nqqr@blm.a.i...com\nqpqcbmail.@om",
"2\nmoc.l.i.a.m.b@qqq\nmoc.l.a.i.m.c@+qqq",
"5\nmoc.liamb@+a\na.+,@bmajl.coom\na.+++@bma.il.com\na.,+++@bMail.com\na.b++++++@bmail.com",
"6\nICPC.@bmail.com\np+con+test@BMAIL.COM\nP@bmail.com\na@bmajl.com.ru\nI.cpc@Amail.Con\na+c@bmail.com.ru",
"8\ntest@bbmail.com\nses.t@bbmail.com\nmoc.liamb@tset\ntes.t@bmail.com\ntest+bmaim.com@bbmail.com\nmoc.liambb@moc.liamb+t.set\ntest,bmail.com@bmail.com\ntes.t+bmail.com@bmail.com",
"2\new+@bmail.comn\nmoc.libmb@+we",
"5\na+@bmailmco.\naa+@bmail.com\naaa*@bmaik.com\naaaa+@amail.com\naaaaa+@bmajl.com",
"2\nmocl.hamb@+a\na@bmai/lmco",
"3\na.a@a\nmoc.liamb@c\nmoc.libmb@.+.+b",
"2\nmoc.liamb@moc.liambdsadsads`+q+q+q\nMOC.Li`mbsjfdlka@jfdklsamfkdlsawgjrgfewadsadsa+q",
"2\nnoc-mob.tr@dcba\nmoc.moc.tr@a+dcba",
"16\na@.mahlbcom\na@bmail.bmail.com\na@bmail\na@bmailc.om\na@bmailcom\na+b@mailcom\nmocliam.b@a\na@moc.liamb\naa@bmail.com\naa@bmail.bmail.com\nliamb@aa\naa@bmailc.om\naa@bmailcom\naa+b@mailcom\naa@b.mailcom\nbmail.com@aa",
"15\nIiT@fxva.WYK\nj@BmAil.CoM\niIT@YXVa.wFk\nVkaVrN@YRK.m\nmoc.LiaMB@Md\no@A.odnMU\nyZ@bMaiL.coM\ndm@bmBIl.COM\nC@BMaIL.com\nQc@Jgzb.OqhJ\nc@bmAiL.cOm\nDT@BMaiL.com\nO@A.OENMU\nmOc.LIAMb@XA\ns@BMaIL.Com",
"5\na@bmajl.com\nmob.liamb@aa\naaa@bnbil.com\naaaa@bmail.com\naaaaa@bmail.com",
"2\na+b@gmail.com\na@gmaic.lol",
"2\nbsdasdasd+asdasdasd@bmail.com\nmoc.liamb@dSADSBDSA+csaDsadsa",
"5\newq.dwq@a\newq.ewq@aa\naaa@qwe.qwd\naaaa@qwe.qwe\newq.ewq@aaaaa"
],
"outputs": [
"4\n2 ICPC.@bmail.com I.cpc@Bmail.Com\n2 p+con+test@BMAIL.COM P@bmail.com\n1 a@bmail.com.ru\n1 a+b@bmail.com.ru\n",
"5\n1 test@bbmail.com \n1 tes.t@bbmail.com \n4 test@bmail.com tes.t@bmail.com test+bmail.com@bmail.com tes.t+bmail.com@bmail.com \n1 test+bmail.com@bbmail.com \n1 tes.t+bmail.com@bbmail.com",
"2\n1 ew+@bmail.comm\n1 ew+@bmail.com\n",
"5\n1 a+@bmail.com\n1 aa+@bmail.com\n1 aaa+@bmail.com\n1 aaaa+@bmail.com\n1 aaaaa+@bmail.com\n",
"1\n5 a+@bmail.com a.++@bmail.com a.+++@bmail.com a.++++@bmail.com a++++++@bmail.com\n",
"2\n1 a+@bmai.lcom\n1 a@bmai.lcom\n",
"2\n1 a@a.a\n2 b@bmail.com b+.+.@bmail.com\n",
"2\n1 asbmail.com+asdasdasd@bmails.com\n1 asdasdasd+ASDASDASD@bmails.com\n",
"1\n2 q+q+q+asdasdasdbmail.com@bmail.com q+asdasdawefgrjgwasldkfmaslkdfjsakldfj@bmaiL.COM\n",
"2\n1 abcd@rt.com.com\n1 abcd+a@rt.com.com\n",
"16\n1 a@bmail.com \n1 a@bmail.bmail.com \n1 a@bmail \n1 a@bmailc.om \n1 a@bmailcom \n1 a+b@mailcom \n1 a@b.mailcom \n1 bmail.com@a \n1 aa@bmail.com \n1 aa@bmail.bmail.com \n1 aa@bmail \n1 aa@bmailc.om \n1 aa@bmailcom \n1 aa+b@mailcom \n1 aa@b.mailcom \n1 bmail.com@aa",
"11\n2 IiT@Yxva.WfK iIT@YXVa.wFk \n1 j@BmAil.CoM \n1 VkaVrN@YRK.m \n2 dM@BMaiL.com dm@bmAIl.COM \n2 o@A.oenMU O@A.OENMU \n1 yZ@bMaiL.coM \n2 C@BMaIL.com c@bmAiL.cOm \n1 Qc@Jgzb.OqhJ \n1 DT@BMaiL.com \n1 AX@bMAIL.cOm \n1 s@BMaIL.Com",
"5\n1 a@bmail.com\n1 aa@bmail.com\n1 aaa@bmail.com\n1 aaaa@bmail.com\n1 aaaaa@bmail.com\n",
"2\n1 a+a@gmail.com \n1 a@gmail.com \n",
"1\n2 asdasdasd+asdasdasd@bmail.com asdasdasd+ASDASDASD@bmail.com\n",
"5\n1 a@qwe.qwe\n1 aa@qwe.qwe\n1 aaa@qwe.qwe\n1 aaaa@qwe.qwe\n1 aaaaa@qwe.qwe\n",
"4\n2 ICPC.@bmail.com I.cpc@Bmail.Com\n2 p+con+test@BMAIL.COM P@bmail.com\n1 a@bmail.com.ru\n1 a+b@bmail.com.ru\n",
"1\n2 a+a@bmail.com a@bmail.com\n",
"2\n1 q+qedasdwqerdasdbmail.com@bmail.com\n1 q@mail.com\n",
"2\n1 qqq@b.m.a.i.l.com \n1 qqq@bmail.com \n",
"2\n1 qqq@b.m.a.i.l.com\n1 qqq+@b.m.a.i.l.com\n",
"4\n1 a.+++@bma.il.com\n1 a.++@bmail.coom\n2 a+@bmail.com a.++++@bMail.com\n1 a.b++++++@bmail.com\n",
"11\n1 Xd@oW.I \n1 d@zb.oqHJ \n1 S@kA.RnWn.Kf \n2 MU@bMAil.COM MU@BMAIL.COM \n2 c@bMaIL.CoM C@BMaIL.com \n1 kt+.i@X.xV \n2 gf@bMaIL.coM Gf@BMaIl.COm \n2 N+.oP@Uu.V N+.Op@UU.V \n1 A@JjWsp.CFce \n1 Pu@bMAil.CoM \n1 kt+.O@x.xv",
"5\n1 test@bbmail.com\n1 tes.t@bbmail.com\n4 test@bmail.com tes.t@bmail.com test+bmail.com@bmail.com tes.t+bmail.com@bmail.com\n1 test+bmail.com@bbmail.com\n1 moc.liambb@moc.liamb+t.set\n",
"2\n1 ew+@bmail.comn\n1 ew+@bmail.com\n",
"5\n1 a+@bmail.com\n1 aa+@bmail.com\n1 aaa+@bmail.com\n1 aaaa+@bmail.com\n1 aaaaa+@bmajl.com\n",
"2\n4 a+@bmail.com a.+++@bmail.com a.++++@bmail.com a++++++@bmail.com\n1 a.*+@bmail.com\n",
"2\n1 a+@bmai.lcom\n1 a@bmai/lcom\n",
"3\n1 a@a.a\n1 c@bmail.com\n1 b+.+.@bmail.com\n",
"2\n1 asbmail.com+asdasdasd@bmails.com\n1 asdasdasd+ASDASDASD@bmbils.com\n",
"2\n1 q+q+q+asdasdasdbmail.com@bmail.com\n1 q+asdasdawefgrjgwasldkfmaslkdfj@akldfjsbmaiL.COM\n",
"2\n1 moc.moc.tr@dcba\n1 abcd+a@rt.com.com\n",
"16\n1 a@bmahl.com\n1 a@bmail.bmail.com\n1 a@bmail\n1 a@bmailc.om\n1 a@bmailcom\n1 a+b@mailcom\n1 a@b.mailcom\n1 bmail.com@a\n1 aa@bmail.com\n1 aa@bmail.bmail.com\n1 aa@bmail\n1 aa@bmailc.om\n1 aa@bmailcom\n1 aa+b@mailcom\n1 aa@b.mailcom\n1 bmail.com@aa\n",
"12\n1 IiT@fxva.WYK\n1 j@BmAil.CoM\n1 iIT@YXVa.wFk\n1 VkaVrN@YRK.m\n2 dM@BMaiL.com dm@bmAIl.COM\n2 o@A.oenMU O@A.OENMU\n1 yZ@bMaiL.coM\n2 C@BMaIL.com c@bmAiL.cOm\n1 Qc@Jgzb.OqhJ\n1 DT@BMaiL.com\n1 AX@bMAIL.cOm\n1 s@BMaIL.Com\n",
"5\n1 a@bmail.com\n1 aa@bmail.com\n1 aaa@bnail.com\n1 aaaa@bmail.com\n1 aaaaa@bmail.com\n",
"2\n1 a+a@gmail.com\n1 a@gmail.col\n",
"2\n1 bsdasdasd+asdasdasd@bmail.com\n1 asdasdasd+ASDASDASD@bmail.com\n",
"5\n1 a@qwd.qwe\n1 aa@qwe.qwe\n1 aaa@qwe.qwe\n1 aaaa@qwe.qwe\n1 aaaaa@qwe.qwe\n",
"5\n1 ICPC.@bmail.com\n2 p+con+test@BMAIL.COM P@bmail.com\n1 a@bmail.com.ru\n1 I.cpc@Bmajl.Com\n1 a+b@bmail.com.ru\n",
"2\n1 a+a@amail.com\n1 a@bmail.com\n",
"2\n1 q@mail.com\n1 moc.liamb@moc.liambdsadreqwdsadeq+q\n",
"2\n1 qqr@b.m.a.i.l.com\n1 qqq@bmail.com\n",
"2\n1 qqq@b.m.a.i.l.com\n1 qqq+@c.m.a.i.l.com\n",
"4\n2 a+@bmail.com a.++++@bMail.com\n1 a.+,@bmail.coom\n1 a.+++@bma.il.com\n1 a.b++++++@bmail.com\n",
"12\n1 Xd@oW.I\n1 d@zb.oqHJ\n1 S@kA.RnWn.Kf\n2 MU@bMAil.COM MU@BMAIL.COM\n2 c@bMaIL.CoM C@BMaIL.com\n1 kt+.i@X.xV\n1 go@bMaIL.cfM\n2 N+.oP@Uu.V N+.Op@UU.V\n1 A@JjWsp.CFce\n1 Pu@bMAil.CoM\n1 Gf@BMaIl.COm\n1 kt+.O@x.xv\n",
"5\n1 ICPC.@bmail.com\n2 p+con+test@BMAIL.COM P@bmail.com\n1 a@bmail.com.ru\n1 I.cpc@Bmail.Con\n1 a+b@bmail.com.ru\n",
"6\n1 test@bbmail.com\n1 tes.t@bbmail.com\n3 test@bmail.com tes.t@bmail.com tes.t+bmail.com@bmail.com\n1 test+bmail.com@bbmail.com\n1 moc.liambb@moc.liamb+t.set\n1 test,bmail.com@bmail.com\n",
"2\n1 nmoc.liamb@+we\n1 ew+@bmail.com\n",
"5\n1 a+@bmail.com\n1 aa+@bmail.com\n1 aaa*@bmail.com\n1 aaaa+@bmail.com\n1 aaaaa+@bmajl.com\n",
"2\n4 a+@bmail.com a.+++@bmail.com a.++++@bmail.com a++++++@bmail.com\n1 a.*+@bmail.cpm\n",
"2\n1 mocl.iamb@+a\n1 a@bmai/lcom\n",
"3\n1 a@a.a\n1 c@bmail.com\n1 moc.liamb@.+.+b\n",
"2\n1 moc.sliamb@dsadsadsa+moc.liambsa\n1 asdasdasd+ASDASDASD@bmbils.com\n",
"2\n1 moc.liamb@moc.liambdsadsadsa+q+q+q\n1 q+asdasdawefgrjgwasldkfmaslkdfj@akldfjsbmaiL.COM\n",
"2\n1 moc.mob.tr@dcba\n1 abcd+a@rt.com.com\n",
"16\n1 a@bmahl.com\n1 a@bmail.bmail.com\n1 a@bmail\n1 a@bmailc.om\n1 a@bmailcom\n1 a+b@mailcom\n1 a@b.mailcom\n1 a@moc.liamb\n1 aa@bmail.com\n1 aa@bmail.bmail.com\n1 aa@bmail\n1 aa@bmailc.om\n1 aa@bmailcom\n1 aa+b@mailcom\n1 aa@b.mailcom\n1 bmail.com@aa\n",
"13\n1 IiT@fxva.WYK\n1 j@BmAil.CoM\n1 iIT@YXVa.wFk\n1 VkaVrN@YRK.m\n1 moc.LiaMB@Md\n2 o@A.oenMU O@A.OENMU\n1 yZ@bMaiL.coM\n1 dm@bmAIl.COM\n2 C@BMaIL.com c@bmAiL.cOm\n1 Qc@Jgzb.OqhJ\n1 DT@BMaiL.com\n1 AX@bMAIL.cOm\n1 s@BMaIL.Com\n",
"5\n1 a@bmail.com\n1 aa@bmail.com\n1 aaa@bnbil.com\n1 aaaa@bmail.com\n1 aaaaa@bmail.com\n",
"2\n1 a+a@gmail.com\n1 loc.liamg@a\n",
"2\n1 bsdasdasd+asdasdasd@bmail.com\n1 asdasDasd+ASDASDASd@bmail.com\n",
"5\n1 ewq.dwq@a\n1 aa@qwe.qwe\n1 aaa@qwe.qwe\n1 aaaa@qwe.qwe\n1 aaaaa@qwe.qwe\n",
"5\n1 moc.liamb@.CPCI\n2 p+con+test@BMAIL.COM P@bmail.com\n1 a@bmail.com.ru\n1 I.cpc@Bmajl.Com\n1 a+b@bmail.com.ru\n",
"2\n1 moc.liama@a+a\n1 a@bmail.com\n",
"2\n1 q@mail.com\n1 moc.liamb@mnc.liambdsadreqwdsadeq+q\n",
"2\n1 qqr@b.m.a.i.l.com\n1 qqqcbmail.@om\n",
"2\n1 moc.l.i.a.m.b@qqq\n1 qqq+@c.m.a.i.l.com\n",
"5\n1 moc.liamb@+a\n1 a.+,@bmail.coom\n1 a.+++@bma.il.com\n1 a.++++@bMail.com\n1 a.b++++++@bmail.com\n",
"12\n1 Xd@oW.I\n1 JHqo.bz@d\n1 S@kA.RnWn.Kf\n2 MU@bMAil.COM MU@BMAIL.COM\n2 c@bMaIL.CoM C@BMaIL.com\n1 kt+.i@X.xV\n1 go@bMaIL.cfM\n2 N+.oP@Uu.V N+.Op@UU.V\n1 A@JjWsp.CFce\n1 Pu@bMAil.CoM\n1 Gf@BMaIl.COm\n1 kt+.O@x.xv\n",
"5\n1 ICPC.@bmail.com\n2 p+con+test@BMAIL.COM P@bmail.com\n1 a@bmail.com.ru\n1 I.cpc@Bmail.Con\n1 a+c@bmail.com.ru\n",
"6\n1 test@bbmail.com\n1 tes.t@bbmail.com\n3 test@bmail.com tes.t@bmail.com tes.t+bmail.com@bmail.com\n1 test+bmaim.com@bbmail.com\n1 moc.liambb@moc.liamb+t.set\n1 test,bmail.com@bmail.com\n",
"2\n1 nmoc.liamb@+we\n1 moc.liamb@+we\n",
"5\n1 a+@bmail.com\n1 aa+@bmail.com\n1 aaa*@bmail.com\n1 aaaa+@amail.com\n1 aaaaa+@bmajl.com\n",
"2\n1 mocl.hamb@+a\n1 a@bmai/lcom\n",
"3\n1 a@a.a\n1 c@bmail.com\n1 moc.libmb@.+.+b\n",
"2\n1 moc.liamb@moc.liambdsadsadsa+q+q+q\n1 MOC.Liambsjfdlka@jfdklsamfkdlsawgjrgfewadsadsa+q\n",
"2\n1 noc.mob.tr@dcba\n1 abcd+a@rt.com.com\n",
"16\n1 a@bmahl.com\n1 a@bmail.bmail.com\n1 a@bmail\n1 a@bmailc.om\n1 a@bmailcom\n1 a+b@mailcom\n1 mocliam.b@a\n1 a@moc.liamb\n1 aa@bmail.com\n1 aa@bmail.bmail.com\n1 aa@bmail\n1 aa@bmailc.om\n1 aa@bmailcom\n1 aa+b@mailcom\n1 aa@b.mailcom\n1 bmail.com@aa\n",
"13\n1 IiT@fxva.WYK\n1 j@BmAil.CoM\n1 iIT@YXVa.wFk\n1 VkaVrN@YRK.m\n1 moc.LiaMB@Md\n2 o@A.oenMU O@A.OENMU\n1 yZ@bMaiL.coM\n1 dm@bmBIl.COM\n2 C@BMaIL.com c@bmAiL.cOm\n1 Qc@Jgzb.OqhJ\n1 DT@BMaiL.com\n1 AX@bMAIL.cOm\n1 s@BMaIL.Com\n",
"5\n1 a@bmajl.com\n1 aa@bmail.com\n1 aaa@bnbil.com\n1 aaaa@bmail.com\n1 aaaaa@bmail.com\n",
"2\n1 a+b@gmail.com\n1 loc.liamg@a\n",
"2\n1 bsdasdasd+asdasdasd@bmail.com\n1 asdasDasd+ASDBSDASd@bmail.com\n",
"5\n1 ewq.dwq@a\n1 aa@qwe.qwe\n1 aaa@qwe.qwe\n1 aaaa@qwe.qwe\n1 ewq.ewq@aaaaa\n",
"6\n1 moc.liamb@.CPCI\n1 p+con+test@BMAIL.COM\n1 O@bmail.com\n1 a@bmail.com.ru\n1 I.cpc@Bmajl.Com\n1 a+b@bmail.com.ru\n",
"2\n1 moc.liama@a+a\n1 a@bmail/com\n",
"2\n1 q@maik.com\n1 moc.liamb@mnc.liambdsadreqwdsadeq+q\n",
"2\n1 qqr@blm.a.i...com\n1 qqqcbmail.@om\n",
"2\n1 moc.l.i.a.m.b@qqq\n1 qqq+@c.m.i.a.l.com\n",
"5\n1 moc.liamb@+a\n1 a.+,@bmajl.coom\n1 a.+++@bma.il.com\n1 a.++++@bMail.com\n1 a.b++++++@bmail.com\n",
"13\n1 Xd@oW.I\n1 JHqo.bz@d\n1 S@kA.RnWn.Kf\n2 MU@bMAil.COM MU@BMAIL.COM\n2 c@bMaIL.CoM C@BMaIL.com\n1 kt+.i@X.xV\n1 go@bMaIL.cfM\n1 V.uU@Po.+N\n1 N+.Op@UU.V\n1 A@JjWsp.CFce\n1 Pu@bMAil.CoM\n1 Gf@BMaIl.COm\n1 kt+.O@x.xv\n",
"5\n1 ICPC.@bmail.com\n2 p+con+test@BMAIL.COM P@bmail.com\n1 a@bmail.com.ru\n1 I.cpc@Amail.Con\n1 a+c@bmail.com.ru\n",
"7\n1 test@bbmail.com\n1 tes.t@bbmail.com\n1 moc.liamb@tset\n2 tes.t@bmail.com tes.t+bmail.com@bmail.com\n1 test+bmaim.com@bbmail.com\n1 moc.liambb@moc.liamb+t.set\n1 test,bmail.com@bmail.com\n",
"2\n1 ew+@bmail.comn\n1 moc.liamb@+we\n",
"5\n1 a+@bmailmco.\n1 aa+@bmail.com\n1 aaa*@bmail.com\n1 aaaa+@amail.com\n1 aaaaa+@bmajl.com\n",
"2\n1 mocl.hamb@+a\n1 a@bmai/lcmo\n",
"3\n1 a@a.a\n1 moc.liamb@c\n1 moc.libmb@.+.+b\n",
"2\n1 moc.liamb@moc.liambdsadsads`+q+q+q\n1 MOC.Liambsjfdlka@jfdklsamfkdlsawgjrgfewadsadsa+q\n",
"2\n1 noc.mob.tr@dcba\n1 moc.moc.tr@a+dcba\n",
"16\n1 a@.mahlbcom\n1 a@bmail.bmail.com\n1 a@bmail\n1 a@bmailc.om\n1 a@bmailcom\n1 a+b@mailcom\n1 mocliam.b@a\n1 a@moc.liamb\n1 aa@bmail.com\n1 aa@bmail.bmail.com\n1 aa@bmail\n1 aa@bmailc.om\n1 aa@bmailcom\n1 aa+b@mailcom\n1 aa@b.mailcom\n1 bmail.com@aa\n",
"14\n1 IiT@fxva.WYK\n1 j@BmAil.CoM\n1 iIT@YXVa.wFk\n1 VkaVrN@YRK.m\n1 moc.LiaMB@Md\n1 o@A.odnMU\n1 yZ@bMaiL.coM\n1 dm@bmBIl.COM\n2 C@BMaIL.com c@bmAiL.cOm\n1 Qc@Jgzb.OqhJ\n1 DT@BMaiL.com\n1 O@A.OENMU\n1 AX@bMAIL.cOm\n1 s@BMaIL.Com\n",
"5\n1 a@bmajl.com\n1 aa@bmail.bom\n1 aaa@bnbil.com\n1 aaaa@bmail.com\n1 aaaaa@bmail.com\n",
"2\n1 a+b@gmail.com\n1 a@gmail.col\n",
"2\n1 bsdasdasd+asdasdasd@bmail.com\n1 moc.liamb@dSADSBDSA+dsaDsadsa\n",
"5\n1 ewq.dwq@a\n1 aa@qwe.qwe\n1 aaa@qwe.qwd\n1 aaaa@qwe.qwe\n1 ewq.ewq@aaaaa\n",
"6\n1 moc.liamb@.CPCI\n1 p+con+test@BMAIL.COM\n1 O@bmail.com\n1 a@bmail.com.su\n1 I.cpc@Bmajl.Com\n1 a+b@bmail.com.ru\n",
"2\n1 moc.liama@a+a\n1 moc/liamb@a\n",
"2\n1 q@maik/com\n1 moc.liamb@mnc.liambdsadreqwdsadeq+q\n",
"2\n1 qqr@blm.a.i...com\n1 qpqcbmail.@om\n",
"2\n1 moc.l.i.a.m.b@qqq\n1 moc.l.a.i.m.c@+qqq\n",
"5\n1 moc.liamb@+a\n1 a.+,@bmajl.coom\n1 a.+++@bma.il.com\n1 a.,+++@bMail.com\n1 a.b++++++@bmail.com\n",
"5\n1 ICPC.@bmail.com\n2 p+con+test@BMAIL.COM P@bmail.com\n1 a@bmajl.com.ru\n1 I.cpc@Amail.Con\n1 a+c@bmail.com.ru\n",
"7\n1 test@bbmail.com\n1 ses.t@bbmail.com\n1 moc.liamb@tset\n2 tes.t@bmail.com tes.t+bmail.com@bmail.com\n1 test+bmaim.com@bbmail.com\n1 moc.liambb@moc.liamb+t.set\n1 test,bmail.com@bmail.com\n",
"2\n1 ew+@bmail.comn\n1 moc.libmb@+we\n",
"5\n1 a+@bmailmco.\n1 aa+@bmail.com\n1 aaa*@bmaik.com\n1 aaaa+@amail.com\n1 aaaaa+@bmajl.com\n",
"2\n1 mocl.hamb@+a\n1 a@bmai/lmco\n",
"3\n1 a.a@a\n1 moc.liamb@c\n1 moc.libmb@.+.+b\n",
"2\n1 moc.liamb@moc.liambdsadsads`+q+q+q\n1 MOC.Li`mbsjfdlka@jfdklsamfkdlsawgjrgfewadsadsa+q\n",
"2\n1 noc-mob.tr@dcba\n1 moc.moc.tr@a+dcba\n",
"16\n1 a@.mahlbcom\n1 a@bmail.bmail.com\n1 a@bmail\n1 a@bmailc.om\n1 a@bmailcom\n1 a+b@mailcom\n1 mocliam.b@a\n1 a@moc.liamb\n1 aa@bmail.com\n1 aa@bmail.bmail.com\n1 liamb@aa\n1 aa@bmailc.om\n1 aa@bmailcom\n1 aa+b@mailcom\n1 aa@b.mailcom\n1 bmail.com@aa\n",
"14\n1 IiT@fxva.WYK\n1 j@BmAil.CoM\n1 iIT@YXVa.wFk\n1 VkaVrN@YRK.m\n1 moc.LiaMB@Md\n1 o@A.odnMU\n1 yZ@bMaiL.coM\n1 dm@bmBIl.COM\n2 C@BMaIL.com c@bmAiL.cOm\n1 Qc@Jgzb.OqhJ\n1 DT@BMaiL.com\n1 O@A.OENMU\n1 mOc.LIAMb@XA\n1 s@BMaIL.Com\n",
"5\n1 a@bmajl.com\n1 mob.liamb@aa\n1 aaa@bnbil.com\n1 aaaa@bmail.com\n1 aaaaa@bmail.com\n",
"2\n1 a+b@gmail.com\n1 a@gmaic.lol\n",
"2\n1 bsdasdasd+asdasdasd@bmail.com\n1 moc.liamb@dSADSBDSA+csaDsadsa\n",
"5\n1 ewq.dwq@a\n1 ewq.ewq@aa\n1 aaa@qwe.qwd\n1 aaaa@qwe.qwe\n1 ewq.ewq@aaaaa\n"
]
}
|
Polycarp has quite recently learned about email aliases. Of course, he used to suspect that the case of the letters doesn't matter in email addresses. He also learned that a popular mail server in Berland bmail.com ignores dots (characters '.') and all the part of an address from the first character "plus" ('+') to character "at" ('@') in a login part of email addresses.
Formally, any email address in this problem will look like "login@domain", where:
a "login" is a non-empty sequence of lowercase and uppercase letters, dots ('.') and pluses ('+'), which starts from a letter; a "domain" is a non-empty sequence of lowercase and uppercase letters and dots, at that the dots split the sequences into non-empty words, consisting only from letters (that is, the "domain" starts from a letter, ends with a letter and doesn't contain two or more consecutive dots). When you compare the addresses, the case of the characters isn't taken into consideration. Besides, when comparing the bmail.com addresses, servers ignore the dots in the login and all characters from the first character "plus" ('+') to character "at" ('@') in login part of an email address.
For example, addresses saratov@example.com and SaratoV@Example.Com correspond to the same account. Similarly, addresses ACM.ICPC.@bmail.com and A.cmIcpc@Bmail.Com also correspond to the same account (the important thing here is that the domains of these addresses are bmail.com). The next example illustrates the use of character '+' in email address aliases: addresses polycarp+contest@BMAIL.COM, Polycarp@bmail.com and polycarp++acm+icpc@Bmail.Com also correspond to the same account on the server bmail.com. However, addresses a@bmail.com.ru and a+b@bmail.com.ru are not equivalent, because '+' is a special character only for bmail.com addresses.
Polycarp has thousands of records in his address book. Until today, he sincerely thought that that's exactly the number of people around the world that he is communicating to. Now he understands that not always distinct records in the address book represent distinct people.
Help Polycarp bring his notes in order by merging equivalent addresses into groups.
Input
The first line of the input contains a positive integer n (1 ≤ n ≤ 2·10^4) — the number of email addresses in Polycarp's address book.
The following n lines contain the email addresses, one per line. It is guaranteed that all of them are correct. All the given lines are distinct. The lengths of the addresses are from 3 to 100, inclusive.
Output
Print the number of groups k and then in k lines print the description of every group.
In the i-th line print the number of addresses in the group and all addresses that belong to the i-th group, separated by a space. It is allowed to print the groups and addresses in each group in any order.
Print the email addresses exactly as they were given in the input. Each address should go to exactly one group.
Examples
Input
6
ICPC.@bmail.com
p+con+test@BMAIL.COM
P@bmail.com
a@bmail.com.ru
I.cpc@Bmail.Com
a+b@bmail.com.ru
Output
4
2 ICPC.@bmail.com I.cpc@Bmail.Com
2 p+con+test@BMAIL.COM P@bmail.com
1 a@bmail.com.ru
1 a+b@bmail.com.ru
|
{
"inputs": [
"5 4\n1 2 1\n2 3 1\n1 3 6\n4 5 8\n",
"3 2\n2 1 4\n1 3 2\n",
"5 5\n1 2 1\n2 3 1\n3 4 1\n1 5 1\n5 4 10\n",
"18 27\n3 16 55467\n17 11 829\n5 12 15831\n14 6 24056\n5 2 63216\n15 6 38762\n2 6 10654\n12 6 51472\n11 9 79384\n1 6 67109\n5 13 86794\n7 6 74116\n10 3 44030\n5 7 71499\n16 17 33019\n5 14 54625\n9 6 10151\n5 10 3514\n5 1 92436\n13 6 27160\n5 8 88344\n4 6 500\n5 18 89693\n8 6 92670\n5 4 70972\n5 15 3523\n18 6 96483\n",
"18 28\n6 9 19885\n16 18 61121\n9 18 75119\n12 18 92157\n4 18 5478\n6 1 22729\n6 13 83924\n2 18 57057\n7 18 65538\n6 4 46391\n6 12 4853\n6 5 66670\n6 11 82272\n1 18 58153\n6 17 97593\n6 3 31390\n13 18 83855\n11 18 19183\n3 18 16411\n10 2 76826\n8 18 90900\n6 16 57839\n5 18 42056\n14 15 49059\n17 14 33352\n6 7 60836\n15 10 50020\n6 8 63341\n",
"17 25\n1 2 1\n2 3 1\n3 4 1\n4 5 1\n5 6 1\n6 7 1\n7 9 1\n1 10 45\n10 9 77\n1 11 46\n11 9 33\n1 12 38\n12 9 78\n1 13 100\n13 9 55\n1 14 900\n14 9 555\n1 15 10\n15 9 17\n1 16 20\n16 9 1000\n1 17 1\n17 9 1\n1 8 43\n8 9 56\n",
"18 24\n9 17 48683\n3 12 41915\n18 6 17241\n5 10 39778\n14 7 95632\n17 11 30074\n8 6 51160\n13 6 90222\n1 6 21198\n14 8 37096\n14 1 62635\n14 18 49880\n2 6 55652\n16 6 37748\n11 16 81043\n4 5 36735\n12 9 55991\n14 4 78702\n14 13 6392\n7 6 37255\n15 6 53614\n14 15 26699\n14 2 94627\n10 3 56470\n",
"18 24\n10 18 60743\n3 10 94138\n3 9 9732\n3 14 65395\n13 7 81775\n12 15 44058\n3 8 56939\n16 18 98065\n7 16 63782\n3 17 61418\n11 18 43408\n3 1 63802\n6 13 46065\n4 5 94316\n5 6 22038\n3 11 42135\n3 12 21261\n14 18 24435\n15 2 19154\n1 18 79848\n8 18 4809\n2 4 41288\n17 18 28846\n9 18 22015\n",
"18 0\n",
"18 27\n18 14 92378\n9 14 33194\n13 1 75439\n13 10 20082\n13 9 92211\n11 3 41140\n13 17 52606\n12 14 1429\n5 14 31908\n17 14 92037\n10 14 15241\n6 14 18999\n13 7 83220\n13 6 66611\n13 18 77570\n13 5 60426\n16 2 69053\n3 14 73770\n13 12 51246\n13 16 45428\n7 14 50863\n2 15 66826\n8 11 57508\n13 4 21005\n4 14 94154\n15 8 98855\n1 14 40817\n",
"5 4\n4 3 72116\n3 5 4357\n3 2 95445\n5 2 49272\n",
"18 29\n14 2 75847\n13 14 42853\n7 11 51081\n7 12 97571\n10 15 85399\n7 9 81891\n7 1 37335\n7 5 28694\n7 18 76478\n8 15 84377\n11 15 23029\n7 10 64179\n5 15 87104\n2 16 34658\n3 15 56316\n7 3 61206\n1 15 45991\n7 6 48219\n7 4 27301\n7 17 12381\n16 15 6305\n7 13 74920\n9 15 81329\n7 8 81902\n4 15 43229\n17 15 29806\n18 15 73826\n12 15 68369\n6 15 20978\n",
"18 5\n13 10 80858\n5 1 93908\n12 16 70953\n5 4 47640\n18 12 57551\n",
"5 10\n5 2 94151\n1 4 66407\n4 2 25654\n5 3 89853\n1 3 17662\n4 3 92953\n3 2 691\n1 2 66925\n5 1 95636\n5 4 44074\n",
"18 25\n13 14 91152\n17 18 59026\n3 11 87504\n13 12 17097\n12 11 57866\n13 15 2552\n16 17 70259\n13 2 12426\n10 8 35580\n2 11 59186\n9 11 73242\n7 11 28527\n13 16 3113\n4 10 76945\n13 6 69805\n6 11 65820\n13 3 86138\n5 4 84139\n8 11 95317\n15 11 14103\n14 11 24091\n18 1 75096\n13 9 63681\n13 7 58603\n1 5 12315\n",
"18 5\n6 18 49855\n16 13 32806\n18 17 54509\n12 16 23750\n3 2 7347\n",
"18 40\n2 11 61030\n1 11 66614\n2 15 63814\n2 16 69232\n13 6 6809\n12 16 7790\n14 7 36259\n1 13 13510\n17 1 8744\n6 8 48695\n2 12 16003\n13 8 27719\n16 8 77344\n10 4 5203\n1 14 10696\n5 9 84015\n13 3 69029\n11 15 82352\n13 7 17710\n3 8 10226\n2 13 2996\n5 10 28778\n1 15 34091\n10 8 90848\n5 14 82262\n17 3 67682\n12 11 46439\n4 7 8305\n10 16 31711\n10 3 95484\n16 7 53686\n18 7 79411\n17 13 99934\n13 4 29779\n17 14 43257\n11 8 77224\n5 3 70058\n12 9 87998\n12 7 65184\n17 4 42826\n",
"18 40\n3 6 98845\n9 17 21520\n3 2 81023\n5 1 84308\n1 8 24241\n10 16 58674\n18 10 54734\n14 13 64951\n11 16 79607\n13 6 84584\n3 12 40873\n3 16 91181\n6 8 92940\n5 2 51627\n17 15 86662\n3 8 86835\n13 15 41723\n10 15 43250\n3 4 33679\n14 3 63674\n10 6 81229\n18 8 38827\n5 12 64349\n6 2 69110\n6 15 71350\n3 11 57293\n13 16 26640\n9 12 77060\n4 6 8240\n2 17 89489\n9 6 88581\n17 12 70896\n13 11 78806\n18 9 86834\n1 16 82190\n18 16 51980\n9 11 12274\n18 6 96542\n18 3 60877\n18 1 21978\n",
"5 4\n5 1 21370\n3 2 28216\n4 5 28239\n5 3 97189\n",
"17 0\n",
"18 26\n17 8 84158\n2 11 29808\n17 16 66593\n17 18 5309\n15 5 34960\n17 15 23410\n17 10 89495\n7 11 84008\n17 13 77935\n12 11 40595\n17 6 78148\n16 11 50976\n10 11 74680\n9 1 75358\n13 11 49350\n17 7 1023\n5 4 43081\n17 12 87710\n1 14 59999\n6 11 96643\n4 9 27305\n3 11 83110\n8 11 89077\n17 3 5745\n18 11 26526\n14 2 31050\n",
"3 0\n",
"18 23\n8 11 94636\n15 11 48502\n9 7 69838\n13 5 71202\n6 11 42098\n5 9 90769\n14 12 94704\n2 11 74498\n4 17 74907\n16 18 52660\n18 13 79706\n10 11 1560\n14 15 60470\n14 16 34695\n7 1 41973\n3 11 39701\n14 10 90728\n12 11 64679\n1 4 8224\n14 3 72578\n14 6 78982\n17 2 93668\n14 8 9547\n",
"18 1\n16 15 44371\n",
"5 4\n3 2 22863\n4 5 60240\n5 2 24603\n1 2 55306\n",
"5 0\n",
"5 10\n3 2 85016\n2 5 18371\n4 2 74512\n4 1 12095\n3 1 40528\n3 5 29309\n4 5 35481\n1 5 68464\n1 2 57303\n4 3 77551\n",
"18 28\n2 16 12376\n5 11 86738\n4 11 28558\n10 11 81949\n13 11 11257\n2 4 65164\n8 11 69612\n7 11 57186\n2 14 46312\n17 11 60313\n18 5 95266\n2 17 55942\n6 11 80163\n1 12 20449\n2 1 30159\n14 11 1315\n9 18 63913\n15 11 29072\n2 10 33014\n2 15 91416\n2 3 57823\n3 11 23385\n16 11 83867\n2 13 55272\n2 8 86541\n2 6 36592\n2 7 16298\n12 9 77978\n",
"5 5\n1 4 2167\n1 3 16525\n5 4 12243\n5 3 2207\n1 2 27131\n",
"5 2\n2 4 59153\n2 5 7094\n",
"18 26\n1 14 31936\n1 13 37317\n15 7 40976\n1 4 19166\n7 2 45168\n1 16 84927\n1 18 14356\n18 10 98321\n2 10 77806\n1 11 59821\n3 10 21123\n16 10 60563\n5 17 18112\n4 10 34362\n13 10 43950\n6 10 92648\n1 9 97348\n17 8 42244\n1 3 50109\n14 10 36936\n11 10 45419\n1 5 48891\n12 15 23531\n9 10 39742\n1 6 11801\n8 12 10566\n",
"18 17\n1 2 1\n1 3 2\n1 4 3\n1 5 4\n1 6 5\n1 7 6\n1 8 7\n1 9 8\n1 10 9\n1 11 10\n1 12 11\n1 13 12\n1 14 13\n1 15 14\n1 16 15\n1 17 16\n1 18 17\n",
"18 28\n8 2 4867\n1 12 20866\n16 12 14701\n2 12 39036\n3 12 17035\n8 7 40303\n13 12 79491\n17 12 57316\n15 18 35598\n8 6 17339\n6 12 52975\n8 9 79806\n8 4 45350\n8 11 93144\n18 5 62726\n11 12 71240\n10 12 9380\n7 12 71665\n5 17 60017\n8 3 97493\n8 14 59338\n9 15 88931\n14 12 49871\n8 13 94188\n8 16 63921\n8 1 12348\n8 10 25680\n4 12 82216\n",
"5 2\n3 5 42110\n2 4 44037\n",
"18 29\n11 16 1859\n18 17 94877\n18 10 11008\n18 13 48268\n12 9 46676\n1 16 48312\n7 16 48789\n2 16 22717\n6 16 89971\n5 16 5390\n18 15 55140\n3 16 73548\n18 3 96797\n18 4 37012\n18 6 79652\n9 1 36345\n18 2 84642\n4 16 58483\n18 7 53916\n18 8 46678\n18 5 90500\n18 11 74118\n14 16 31116\n17 16 95977\n10 16 27580\n15 16 34623\n18 14 22981\n13 12 94702\n8 16 58805\n",
"6 5\n1 2 100\n2 3 100\n4 3 100\n4 5 100\n5 6 100\n",
"5 5\n2 1 52913\n4 3 67731\n4 1 39287\n5 1 54290\n5 2 45181\n",
"18 24\n2 16 12432\n3 16 22397\n14 15 559\n8 11 81457\n6 10 42193\n18 16 72986\n13 16 12677\n9 3 39275\n6 2 35510\n6 17 36967\n11 1 6053\n6 4 27446\n12 16 97943\n6 5 13884\n10 16 15856\n6 12 7143\n4 16 90720\n7 9 8777\n1 7 26333\n5 16 70469\n17 14 93907\n6 18 20621\n15 8 68919\n6 13 15116\n",
"2 0\n",
"18 23\n11 18 22966\n8 2 95219\n11 3 74045\n13 2 3566\n14 5 1707\n6 2 86795\n11 8 90994\n11 13 76876\n17 14 16859\n12 6 35320\n9 4 97638\n3 2 2295\n11 15 56214\n11 16 22682\n10 17 38059\n11 10 2109\n4 7 35279\n15 2 37776\n18 2 91318\n5 9 85938\n16 2 70496\n1 12 3424\n7 1 72066\n",
"18 26\n1 2 1\n2 3 1\n3 4 1\n4 5 1\n5 6 1\n6 7 1\n7 18 1\n18 9 1\n1 10 45\n10 9 77\n1 11 46\n11 9 33\n1 12 38\n12 9 78\n1 13 100\n13 9 55\n1 14 900\n14 9 555\n1 15 10\n15 9 17\n1 16 20\n16 9 1000\n1 17 1\n17 9 1\n1 8 43\n8 9 56\n",
"5 10\n4 1 35762\n2 3 34383\n4 2 99133\n2 1 65490\n1 3 69912\n5 2 7380\n5 1 28188\n4 3 62455\n5 4 32502\n5 3 63357\n",
"18 23\n1 7 70746\n18 1 17002\n11 8 4574\n18 17 45190\n16 7 14267\n15 7 30842\n13 6 44006\n18 15 56326\n4 3 84294\n5 13 17013\n18 16 85683\n8 4 96578\n18 12 30945\n18 2 78392\n17 7 99900\n14 7 54200\n2 7 64181\n12 7 41343\n10 14 33085\n9 5 77031\n18 9 34127\n3 10 23949\n6 11 75251\n",
"18 40\n8 17 59330\n15 10 60419\n4 16 88771\n12 16 60418\n7 12 65525\n11 12 41507\n1 7 73944\n11 6 22879\n9 3 32080\n16 18 39165\n12 17 47460\n11 18 65104\n11 2 41561\n14 12 86249\n15 17 76820\n9 1 96053\n5 15 4766\n14 11 41176\n11 10 48894\n14 6 26791\n5 2 36114\n13 12 11051\n11 1 51023\n9 11 86192\n13 17 95923\n3 12 45381\n9 10 66287\n7 15 94895\n11 3 29175\n14 4 64720\n1 13 5345\n11 13 46282\n2 6 69067\n11 17 53222\n17 4 78658\n11 15 9783\n15 6 34932\n15 18 972\n13 3 18779\n16 6 66777\n",
"18 5\n9 6 36233\n5 10 21004\n15 7 37300\n13 15 75970\n4 8 22619\n",
"5 10\n3 1 38315\n2 4 46788\n5 2 9674\n3 2 53417\n3 5 87408\n5 1 46883\n3 4 62487\n2 1 60285\n5 4 94121\n1 4 3697\n",
"6 0\n",
"18 5\n8 3 75748\n15 16 38540\n8 4 48631\n13 4 10920\n8 12 95912\n",
"18 28\n18 6 43416\n4 3 77183\n4 8 27025\n15 6 21085\n3 1 61216\n1 10 96643\n10 2 55653\n4 5 56797\n4 14 28183\n4 9 10036\n4 11 32539\n12 6 86239\n4 18 43385\n4 12 23161\n2 15 91245\n4 7 83028\n14 6 58330\n13 6 9804\n4 17 5508\n11 6 21567\n5 6 63678\n4 16 59452\n8 6 99649\n16 6 3931\n7 6 26975\n4 13 43916\n17 6 31256\n9 6 44466\n",
"18 25\n9 2 21447\n15 2 89555\n4 7 4936\n3 2 53849\n4 11 1913\n13 14 88268\n4 9 82412\n10 8 79861\n12 2 82681\n16 6 47231\n4 17 67525\n4 12 11771\n4 3 58823\n17 2 95683\n6 5 89192\n11 2 62017\n1 2 57001\n4 13 58610\n4 1 29514\n7 2 45029\n8 18 20424\n5 10 43689\n4 15 88967\n14 16 24295\n18 2 44594\n",
"18 1\n4 11 51182\n",
"18 29\n10 5 17131\n1 11 58125\n1 15 34257\n1 7 71065\n9 5 34522\n1 3 80877\n2 5 1688\n1 14 1968\n18 5 28392\n12 16 54851\n6 5 99430\n7 5 54811\n1 4 1603\n1 13 8111\n4 5 76084\n1 6 61874\n1 10 50445\n3 5 94852\n15 5 66095\n1 17 10789\n1 2 65214\n17 5 8426\n1 18 98838\n8 5 531\n1 9 50367\n16 8 92285\n13 12 91967\n11 5 98932\n14 5 26256\n",
"18 26\n9 15 70596\n15 3 95440\n5 18 89743\n7 14 79584\n7 1 74097\n7 2 73369\n3 10 88270\n7 17 2753\n7 4 20650\n7 8 22466\n6 10 17471\n7 16 88249\n7 13 37681\n12 9 38580\n17 10 84766\n4 5 62108\n11 10 24794\n13 10 25231\n8 10 40731\n18 12 93330\n7 6 24752\n7 11 13157\n16 10 25144\n1 10 31928\n14 10 33969\n2 10 4189\n",
"18 27\n3 8 22907\n16 13 42113\n4 8 87999\n6 18 39937\n11 8 36711\n10 16 53293\n6 1 20041\n6 15 48530\n17 8 52657\n6 17 86320\n5 8 33077\n1 8 74709\n12 8 34662\n13 2 61806\n6 11 6472\n6 14 31289\n9 8 10820\n6 10 32159\n6 4 14876\n7 5 33249\n2 7 54048\n15 8 16305\n6 9 90495\n14 8 10179\n6 3 89600\n6 12 43364\n18 8 58963\n",
"18 25\n16 5 92356\n16 9 17954\n16 10 61492\n18 11 56561\n13 4 97939\n6 2 76046\n14 3 84790\n2 14 54517\n16 8 99933\n5 4 32460\n16 13 92453\n7 4 74810\n16 12 3706\n16 18 67577\n9 4 60112\n8 4 63465\n12 4 62802\n17 4 17512\n1 4 67067\n3 15 60735\n15 17 30180\n10 4 73503\n11 6 55293\n16 7 24813\n16 1 29824\n",
"5 4\n1 2 1\n2 3 1\n1 3 6\n4 5 8\n",
"18 26\n5 10 22818\n5 18 44826\n5 6 82655\n5 16 33023\n11 12 55377\n5 11 79148\n10 12 6513\n3 1 55737\n2 12 20780\n14 12 3239\n5 2 7201\n7 4 45958\n16 12 94248\n17 12 3767\n5 13 81654\n6 12 27378\n5 17 27423\n8 7 5289\n9 12 83324\n1 8 53037\n5 9 6638\n13 12 14672\n18 15 57986\n4 12 97931\n5 14 5589\n15 3 24673\n",
"5 5\n1 3 3660\n4 1 51039\n2 5 79358\n2 4 6373\n4 3 47163\n",
"18 1\n6 12 39261\n",
"5 4\n3 5 46432\n2 5 12204\n5 1 10639\n2 4 35820\n",
"18 27\n12 9 20732\n17 3 59545\n12 13 67854\n14 3 83984\n12 5 89722\n8 16 38\n6 3 11668\n9 3 30223\n1 11 49214\n12 6 4795\n12 14 40512\n16 7 30419\n12 1 29207\n12 18 81192\n4 3 59565\n15 3 34857\n12 4 52587\n13 3 99060\n12 15 45803\n2 3 21071\n10 3 22641\n12 10 41592\n5 3 56187\n11 8 75162\n7 17 19639\n12 2 20577\n18 3 34004\n",
"18 50\n10 3 14\n5 16 64931\n12 1 34517\n6 7 18587\n8 4 9\n5 1 29\n8 1 4538\n13 11 16087\n3 16 101\n12 15 49\n5 4 5\n12 4 1\n8 11 24\n12 3 1\n9 8 51757\n9 11 81\n18 6 8141\n16 6 8\n17 14 15\n5 11 2337\n13 17 1553\n5 18 15\n15 7 14\n10 11 2798\n8 15 9\n9 3 1\n4 18 36637\n18 14 1\n9 18 286\n3 13 2\n13 15 50069\n15 14 1067\n9 5 6\n16 15 40590\n12 5 254\n18 1 3633\n3 2 12258\n10 16 14\n15 11 5\n5 13 78491\n10 18 421\n10 2 22\n4 17 5\n9 10 10\n8 14 55\n7 2 11983\n17 1 518\n3 15 62931\n12 14 32311\n1 11 53088\n",
"18 1\n4 18 46072\n",
"17 24\n1 2 1\n2 3 1\n3 4 1\n4 5 1\n5 6 1\n6 7 1\n7 8 1\n8 9 1\n1 10 45\n10 9 77\n1 11 46\n11 9 33\n1 12 38\n12 9 78\n1 13 100\n13 9 55\n1 14 900\n14 9 555\n1 15 10\n15 9 17\n1 16 20\n16 9 1000\n1 17 1\n17 9 1\n",
"18 29\n3 13 19291\n6 2 7436\n14 2 55055\n8 18 1280\n1 2 83021\n11 16 39939\n11 3 95890\n11 14 10762\n15 2 84254\n10 2 55930\n11 17 10850\n18 2 24990\n11 15 48888\n11 12 65914\n11 9 74707\n11 5 2304\n17 2 75735\n7 2 89409\n13 8 17546\n11 6 82567\n11 7 39979\n9 2 39810\n16 2 28802\n11 4 58719\n4 2 4793\n12 2 85472\n11 1 86699\n11 10 57769\n5 2 15546\n",
"18 29\n2 16 27871\n3 14 55413\n3 9 70936\n5 18 74774\n3 15 64848\n4 16 6222\n3 5 84436\n3 10 84035\n17 16 70761\n3 1 59108\n3 2 54547\n15 16 15621\n13 16 6491\n8 16 63559\n3 7 27179\n10 16 2972\n6 16 12892\n18 11 36042\n14 16 47827\n3 6 80974\n12 16 31591\n11 17 73316\n3 4 13607\n3 13 77348\n1 16 20443\n7 16 47951\n3 8 4840\n3 12 64140\n9 16 20824\n",
"18 40\n18 11 5656\n9 3 15325\n9 17 73275\n16 3 40902\n4 10 82957\n6 1 52476\n6 11 96515\n4 11 48457\n4 6 77082\n18 13 83877\n14 12 5451\n18 7 83386\n9 10 4616\n18 15 81143\n7 12 50878\n8 11 65816\n16 10 94916\n2 11 41950\n3 13 82721\n18 14 32463\n13 1 534\n8 14 95180\n2 15 13782\n9 15 78449\n8 15 66242\n7 15 36206\n16 5 38627\n4 7 7313\n15 5 9630\n2 7 35363\n9 5 40055\n2 17 23488\n4 18 92099\n14 7 33479\n7 11 27549\n11 13 50444\n2 9 88428\n12 1 28375\n6 13 56246\n4 13 60048\n",
"18 17\n1 2 1\n1 3 1\n1 4 1\n1 5 1\n1 6 1\n1 7 1\n1 8 1\n1 9 1\n1 10 1\n1 11 1\n1 12 1\n1 13 1\n1 14 1\n1 15 1\n1 16 1\n1 17 1\n1 18 1\n",
"18 24\n17 12 542\n8 13 22774\n17 16 18905\n16 6 49332\n2 6 21357\n17 1 90937\n15 7 1201\n10 8 91447\n17 2 26645\n4 6 94382\n17 4 13468\n1 6 43261\n14 10 85675\n18 5 74747\n5 11 17821\n17 15 9831\n7 14 19097\n9 6 64285\n17 9 44679\n3 6 56523\n12 6 81119\n17 3 61955\n13 18 64580\n11 6 20402\n",
"18 28\n15 12 3203\n4 14 2800\n15 17 88976\n5 14 35069\n15 13 66995\n15 6 39078\n15 8 74044\n15 18 56927\n17 14 84764\n15 16 23958\n15 5 14440\n15 2 42807\n15 4 84381\n12 14 52753\n13 14 23811\n9 3 61465\n15 11 71093\n6 14 19693\n2 14 56703\n15 1 3453\n1 9 89385\n10 14 24998\n8 14 32949\n7 10 10143\n16 14 80164\n11 14 19672\n3 7 40638\n18 14 59104\n",
"18 25\n1 14 22651\n11 9 24291\n5 15 46220\n1 5 69121\n16 3 17794\n1 6 61762\n7 15 21135\n1 10 46144\n14 15 71226\n3 17 53209\n12 15 86736\n2 15 58053\n9 4 59416\n4 15 86314\n17 18 79498\n18 11 92367\n1 8 33666\n1 12 59278\n13 16 90864\n1 2 91662\n1 13 50705\n6 15 9392\n8 15 4772\n1 7 57801\n10 15 94806\n",
"18 26\n11 6 36381\n11 13 22299\n12 3 722\n11 7 58748\n10 16 16240\n11 18 29188\n13 16 7738\n8 16 26592\n11 9 78065\n18 16 54073\n14 12 24774\n3 2 75981\n15 16 98543\n2 17 40545\n11 1 46238\n11 5 98997\n7 16 13007\n9 16 67769\n1 16 2592\n17 8 80543\n11 10 66086\n5 16 8817\n11 4 21918\n11 15 47557\n4 16 32738\n6 14 16943\n",
"18 25\n11 1 77138\n2 17 22115\n11 6 30948\n15 17 81680\n13 7 94544\n8 17 38966\n16 9 67880\n5 17 37770\n1 17 85623\n11 15 49765\n9 12 5211\n11 2 80\n11 18 15126\n18 17 5052\n11 8 98885\n12 10 88564\n11 13 4529\n10 14 25237\n3 17 25060\n6 17 55293\n11 5 14335\n4 17 45281\n14 3 62763\n7 16 23493\n11 4 59789\n",
"18 24\n2 8 96994\n14 10 70552\n17 10 2223\n2 1 23715\n2 9 67918\n12 10 33849\n4 7 62718\n2 5 40500\n9 4 16765\n2 12 94252\n13 16 56886\n16 18 20827\n2 14 71070\n2 6 18179\n8 10 52634\n2 17 71727\n15 3 53827\n18 10 94360\n3 13 64621\n11 15 22441\n6 10 64516\n7 11 23174\n1 10 30361\n5 10 54857\n",
"18 27\n7 15 57642\n10 3 91909\n2 15 3271\n11 15 47305\n12 15 42909\n1 15 2417\n9 12 19027\n5 15 12883\n14 15 58635\n9 14 72826\n16 10 36255\n9 13 42598\n9 18 25293\n6 15 84816\n18 15 4117\n9 4 83762\n9 17 68385\n9 5 69317\n9 7 61509\n3 8 6634\n9 11 85159\n13 16 75214\n4 15 91297\n9 2 60392\n17 15 75525\n8 1 59013\n9 6 78338\n",
"5 5\n1 4 94282\n2 3 3978\n5 4 46564\n3 4 41014\n2 1 42019\n",
"18 23\n3 5 46856\n15 5 94015\n16 17 39309\n16 9 19178\n13 6 62243\n12 1 70914\n6 8 17500\n16 18 38153\n2 13 83280\n16 7 14071\n11 10 58957\n7 5 83085\n10 15 9931\n4 5 78985\n16 4 23236\n17 5 44507\n16 2 61826\n1 14 93815\n18 5 66457\n8 12 81485\n9 5 48056\n16 3 30038\n14 11 40954\n",
"18 23\n11 4 31780\n16 7 63720\n3 11 8780\n18 7 77554\n17 15 16979\n14 7 94163\n9 7 64489\n5 6 58704\n15 9 26245\n13 3 99674\n5 18 27808\n5 14 88802\n4 12 59392\n8 7 23275\n5 13 28690\n12 1 25120\n6 7 32925\n1 2 90248\n5 10 24691\n5 8 90392\n2 17 17129\n5 16 42217\n10 7 37769\n",
"5 2\n1 4 66320\n5 4 15102\n",
"18 25\n1 2 1\n2 3 1\n3 4 1\n4 5 1\n5 6 1\n6 7 1\n7 8 1\n8 18 1\n18 9 1\n1 10 45\n10 9 77\n1 11 46\n11 9 33\n1 12 38\n12 9 78\n1 13 100\n13 9 55\n1 14 900\n14 9 555\n1 15 10\n15 9 17\n1 16 20\n16 9 1000\n1 17 1\n17 9 1\n",
"5 2\n2 3 35584\n4 5 55130\n",
"17 26\n1 3 1\n3 4 1\n4 5 1\n5 6 1\n6 7 1\n7 9 1\n1 10 45\n10 9 77\n1 11 46\n11 9 33\n1 12 38\n12 9 78\n1 13 100\n13 9 55\n1 14 900\n14 9 555\n1 15 10\n15 9 17\n1 16 20\n16 9 1000\n1 17 1\n17 9 1\n1 8 43\n8 9 56\n1 2 99\n2 9 155\n",
"18 24\n10 18 60743\n3 10 94138\n2 9 9732\n3 14 65395\n13 7 81775\n12 15 44058\n3 8 56939\n16 18 98065\n7 16 63782\n3 17 61418\n11 18 43408\n3 1 63802\n6 13 46065\n4 5 94316\n5 6 22038\n3 11 42135\n3 12 21261\n14 18 24435\n15 2 19154\n1 18 79848\n8 18 4809\n2 4 41288\n17 18 28846\n9 18 22015\n",
"13 0\n",
"18 5\n13 10 80858\n5 1 93908\n12 16 70953\n1 4 47640\n18 12 57551\n",
"18 40\n3 6 98845\n9 17 21520\n3 2 81023\n5 1 84308\n1 8 24241\n10 16 58674\n18 10 54734\n14 13 64951\n11 16 79607\n13 6 84584\n3 12 40873\n3 16 91181\n6 8 92940\n5 2 51627\n17 15 86662\n3 8 86835\n13 15 41723\n10 15 43250\n3 4 33679\n14 3 63674\n10 6 81229\n18 8 38827\n5 10 64349\n6 2 69110\n6 15 71350\n3 11 57293\n13 16 26640\n9 12 77060\n4 6 8240\n2 17 89489\n9 6 88581\n17 12 70896\n13 11 78806\n18 9 86834\n1 16 82190\n18 16 51980\n9 11 12274\n18 6 96542\n18 3 60877\n18 1 21978\n",
"5 4\n5 1 21370\n3 2 28216\n4 5 28239\n5 3 166715\n",
"8 0\n",
"18 23\n8 11 94636\n15 11 48502\n9 7 69838\n13 5 71202\n6 11 42098\n5 9 90769\n14 12 94704\n2 11 74498\n5 17 74907\n16 18 52660\n18 13 79706\n10 11 1560\n14 15 60470\n14 16 34695\n7 1 41973\n3 11 39701\n14 10 90728\n12 11 64679\n1 4 8224\n14 3 72578\n14 6 78982\n17 2 93668\n14 8 9547\n",
"18 1\n16 15 3461\n",
"5 4\n3 4 22863\n4 5 60240\n5 2 24603\n1 2 55306\n",
"5 0\n3 2 85016\n2 5 18371\n4 2 74512\n4 1 12095\n3 1 40528\n3 5 29309\n4 5 35481\n1 5 68464\n1 2 57303\n4 3 77551\n",
"18 28\n2 16 12376\n5 11 86738\n4 11 28558\n10 11 81949\n13 11 11257\n2 4 65164\n8 11 69612\n7 11 57186\n2 14 46312\n17 11 60313\n18 5 95266\n2 17 55942\n6 11 80163\n1 12 20449\n2 1 30159\n14 11 1315\n9 18 63913\n15 11 29072\n2 10 33014\n2 15 91416\n2 3 57823\n3 11 23385\n16 11 83867\n2 13 55272\n2 8 133215\n2 6 36592\n2 7 16298\n12 9 77978\n",
"5 5\n1 4 2167\n1 5 16525\n5 4 12243\n5 3 2207\n1 2 27131\n",
"18 28\n8 2 4867\n1 12 20866\n16 12 14701\n2 12 39036\n3 12 17035\n8 7 40303\n13 12 177\n17 12 57316\n15 18 35598\n8 6 17339\n6 12 52975\n8 9 79806\n8 4 45350\n8 11 93144\n18 5 62726\n11 12 71240\n10 12 9380\n7 12 71665\n5 17 60017\n8 3 97493\n8 14 59338\n9 15 88931\n14 12 49871\n8 13 94188\n8 16 63921\n8 1 12348\n8 10 25680\n4 12 82216\n",
"18 29\n11 16 1859\n18 17 94877\n18 10 11008\n18 13 48268\n12 9 46676\n1 16 48312\n7 16 48789\n2 16 22717\n6 16 89971\n5 16 5390\n18 15 55140\n3 16 73548\n18 3 96797\n18 4 37012\n18 6 79652\n9 1 36345\n18 2 84642\n4 16 58483\n18 7 53916\n18 8 46678\n18 5 90500\n5 11 74118\n14 16 31116\n17 16 95977\n10 16 27580\n15 16 34623\n18 14 22981\n13 12 94702\n8 16 58805\n",
"5 3\n2 1 52913\n4 3 67731\n4 1 39287\n5 1 54290\n5 2 45181\n",
"4 0\n",
"18 23\n11 18 22966\n8 2 95219\n11 3 74045\n13 2 3566\n14 5 1707\n6 2 86795\n11 8 90994\n11 13 76876\n17 14 16859\n12 6 35320\n9 4 97638\n3 2 2295\n11 15 56214\n17 16 22682\n10 17 38059\n11 10 2109\n4 7 35279\n15 2 37776\n18 2 91318\n5 9 85938\n16 2 70496\n1 12 3424\n7 1 72066\n",
"18 40\n8 17 59330\n15 10 60419\n4 16 88771\n12 16 60418\n7 12 65525\n11 12 41507\n1 7 73944\n11 6 22879\n9 3 32080\n16 18 39165\n12 17 47460\n11 18 65104\n11 2 41561\n14 12 86249\n15 17 76820\n8 1 96053\n5 15 4766\n14 11 41176\n11 10 48894\n14 6 26791\n5 2 36114\n13 12 11051\n11 1 51023\n9 11 86192\n13 17 95923\n3 12 45381\n9 10 66287\n7 15 94895\n11 3 29175\n14 4 64720\n1 13 5345\n11 13 46282\n2 6 69067\n11 17 53222\n17 4 78658\n11 15 9783\n15 6 34932\n15 18 972\n13 3 18779\n16 6 66777\n",
"18 5\n5 6 36233\n5 10 21004\n15 7 37300\n13 15 75970\n4 8 22619\n",
"18 5\n5 3 75748\n15 16 38540\n8 4 48631\n13 4 10920\n8 12 95912\n",
"18 28\n18 6 43416\n4 3 77183\n4 8 10267\n15 6 21085\n3 1 61216\n1 10 96643\n10 2 55653\n4 5 56797\n4 14 28183\n4 9 10036\n4 11 32539\n12 6 86239\n4 18 43385\n4 12 23161\n2 15 91245\n4 7 83028\n14 6 58330\n13 6 9804\n4 17 5508\n11 6 21567\n5 6 63678\n4 16 59452\n8 6 99649\n16 6 3931\n7 6 26975\n4 13 43916\n17 6 31256\n9 6 44466\n",
"18 25\n9 2 21447\n15 2 89555\n4 7 4936\n3 2 53849\n4 11 2994\n13 14 88268\n4 9 82412\n10 8 79861\n12 2 82681\n16 6 47231\n4 17 67525\n4 12 11771\n4 3 58823\n17 2 95683\n6 5 89192\n11 2 62017\n1 2 57001\n4 13 58610\n4 1 29514\n7 2 45029\n8 18 20424\n5 10 43689\n4 15 88967\n14 16 24295\n18 2 44594\n",
"18 1\n8 11 51182\n",
"18 26\n9 15 70596\n15 3 95440\n5 18 89743\n7 14 79584\n7 1 74097\n7 2 73369\n3 10 47963\n7 17 2753\n7 4 20650\n7 8 22466\n6 10 17471\n7 16 88249\n7 13 37681\n12 9 38580\n17 10 84766\n4 5 62108\n11 10 24794\n13 10 25231\n8 10 40731\n18 12 93330\n7 6 24752\n7 11 13157\n16 10 25144\n1 10 31928\n14 10 33969\n2 10 4189\n",
"18 27\n3 8 22907\n16 13 42113\n4 8 87999\n6 18 39937\n11 8 36711\n10 16 53293\n6 1 20041\n6 15 48530\n17 8 52657\n6 17 86320\n5 8 33077\n1 8 74709\n12 8 34662\n13 2 61806\n6 11 10185\n6 14 31289\n9 8 10820\n6 10 32159\n6 4 14876\n7 5 33249\n2 7 54048\n15 8 16305\n6 9 90495\n14 8 10179\n6 3 89600\n6 12 43364\n18 8 58963\n",
"18 25\n16 5 92356\n16 9 17954\n16 10 61492\n18 11 56561\n13 4 97939\n6 2 76046\n14 3 84790\n2 14 54517\n16 8 99933\n5 4 32460\n16 2 92453\n7 4 74810\n16 12 3706\n16 18 67577\n9 4 60112\n8 4 63465\n12 4 62802\n17 4 17512\n1 4 67067\n3 15 60735\n15 17 30180\n10 4 73503\n11 6 55293\n16 7 24813\n16 1 29824\n",
"5 4\n1 2 1\n2 3 1\n1 3 6\n4 5 13\n",
"5 5\n1 3 3660\n4 1 51039\n2 5 79358\n2 4 6373\n5 3 47163\n",
"18 1\n6 12 65293\n",
"18 27\n12 9 20732\n17 3 59545\n12 13 67854\n14 3 83984\n12 5 89722\n8 16 38\n6 3 11668\n9 3 30223\n1 11 49214\n12 6 4795\n12 14 40512\n16 7 30419\n12 1 29207\n12 18 131504\n4 3 59565\n15 3 34857\n12 4 52587\n13 3 99060\n12 15 45803\n2 3 21071\n10 3 22641\n12 10 41592\n5 3 56187\n11 8 75162\n7 17 19639\n12 2 20577\n18 3 34004\n",
"17 24\n1 2 1\n2 3 1\n3 4 1\n4 5 1\n5 6 1\n6 7 1\n7 8 1\n8 9 1\n1 10 71\n10 9 77\n1 11 46\n11 9 33\n1 12 38\n12 9 78\n1 13 100\n13 9 55\n1 14 900\n14 9 555\n1 15 10\n15 9 17\n1 16 20\n16 9 1000\n1 17 1\n17 9 1\n",
"18 29\n3 13 19291\n6 2 7436\n14 2 55055\n8 18 1280\n1 2 83021\n11 16 39939\n11 3 95890\n11 14 10762\n15 2 84254\n10 2 55930\n11 17 10850\n18 2 24990\n11 15 48888\n11 12 65914\n11 9 74707\n11 5 2304\n17 2 75735\n7 2 89409\n13 8 17546\n11 6 82567\n11 7 54169\n9 2 39810\n16 2 28802\n11 4 58719\n4 2 4793\n12 2 85472\n11 1 86699\n11 10 57769\n5 2 15546\n",
"18 29\n2 16 27871\n3 14 55413\n3 9 70936\n5 18 74774\n3 15 64848\n4 16 6222\n3 5 102563\n3 10 84035\n17 16 70761\n3 1 59108\n3 2 54547\n15 16 15621\n13 16 6491\n8 16 63559\n3 7 27179\n10 16 2972\n6 16 12892\n18 11 36042\n14 16 47827\n3 6 80974\n12 16 31591\n11 17 73316\n3 4 13607\n3 13 77348\n1 16 20443\n7 16 47951\n3 8 4840\n3 12 64140\n9 16 20824\n",
"18 40\n18 11 5656\n9 3 15325\n9 17 73275\n16 3 40902\n4 10 82957\n6 1 52476\n6 11 96515\n4 11 48457\n4 6 77082\n18 13 83877\n14 12 5451\n18 7 83386\n9 10 4616\n18 15 81143\n7 12 50878\n8 11 65816\n16 10 94916\n2 11 41950\n3 13 82721\n18 14 32463\n13 1 534\n8 14 95180\n2 15 13782\n9 15 78449\n8 15 66242\n7 15 36206\n16 5 38627\n4 7 7313\n15 3 9630\n2 7 35363\n9 5 40055\n2 17 23488\n4 18 92099\n14 7 33479\n7 11 27549\n11 13 50444\n2 9 88428\n12 1 28375\n6 13 56246\n4 13 60048\n",
"18 24\n17 12 542\n15 13 22774\n17 16 18905\n16 6 49332\n2 6 21357\n17 1 90937\n15 7 1201\n10 8 91447\n17 2 26645\n4 6 94382\n17 4 13468\n1 6 43261\n14 10 85675\n18 5 74747\n5 11 17821\n17 15 9831\n7 14 19097\n9 6 64285\n17 9 44679\n3 6 56523\n12 6 81119\n17 3 61955\n13 18 64580\n11 6 20402\n",
"18 28\n15 12 3203\n4 14 2800\n15 17 88976\n5 14 35069\n15 13 66995\n15 6 39078\n15 8 74044\n15 18 56927\n17 14 84764\n15 16 23958\n15 5 14440\n15 2 42807\n15 4 84381\n12 14 52753\n13 14 23811\n9 3 61465\n15 11 71093\n6 14 19693\n2 14 56703\n15 1 3453\n1 9 89385\n10 14 24998\n8 14 32949\n7 10 10143\n16 14 143316\n11 14 19672\n3 7 40638\n18 14 59104\n",
"18 25\n1 14 22651\n11 9 24291\n5 15 46220\n1 5 69121\n16 3 17794\n1 6 61762\n7 15 21135\n1 10 46144\n14 15 71226\n3 17 53209\n12 15 86736\n2 15 58053\n9 4 59416\n4 15 86314\n17 18 79498\n18 11 92367\n1 8 33666\n1 12 59278\n13 16 90864\n1 2 91662\n1 13 50705\n6 15 9392\n8 15 3346\n1 7 57801\n10 15 94806\n",
"18 26\n11 6 36381\n11 13 22299\n12 3 722\n11 7 58748\n10 16 16240\n11 18 29188\n13 16 7738\n8 16 26592\n11 9 78065\n18 16 54073\n14 12 24774\n3 2 75981\n15 16 98543\n2 17 40545\n11 1 46238\n11 5 98997\n7 16 13007\n9 16 67769\n1 16 2592\n17 8 80543\n11 10 66086\n5 16 8817\n11 4 21918\n11 15 47557\n4 16 32738\n7 14 16943\n",
"18 27\n7 15 57642\n10 3 91909\n2 15 3271\n11 15 47305\n12 15 42909\n1 15 2417\n9 12 19027\n5 15 12883\n14 15 58635\n9 14 72826\n16 10 36255\n9 13 42598\n9 18 25293\n6 15 84816\n18 15 4117\n9 4 83762\n9 17 68385\n9 5 69317\n9 7 61509\n3 8 6634\n9 11 85159\n9 16 75214\n4 15 91297\n9 2 60392\n17 15 75525\n8 1 59013\n9 6 78338\n",
"5 5\n2 4 94282\n2 3 3978\n5 4 46564\n3 4 41014\n2 1 42019\n",
"18 25\n1 2 1\n2 3 1\n3 4 1\n4 5 1\n5 6 1\n6 7 1\n7 8 1\n8 18 1\n18 9 1\n1 10 45\n10 9 77\n1 11 46\n11 9 33\n1 12 38\n12 9 78\n1 13 100\n13 9 55\n1 14 900\n14 9 708\n1 15 10\n15 9 17\n1 16 20\n16 9 1000\n1 17 1\n17 9 1\n",
"5 2\n2 3 35584\n2 5 55130\n",
"5 4\n1 4 1\n2 3 1\n1 3 6\n4 5 8\n",
"18 24\n10 18 60743\n3 10 94138\n2 9 1073\n3 14 65395\n13 7 81775\n12 15 44058\n3 8 56939\n16 18 98065\n7 16 63782\n3 17 61418\n11 18 43408\n3 1 63802\n6 13 46065\n4 5 94316\n5 6 22038\n3 11 42135\n3 12 21261\n14 18 24435\n15 2 19154\n1 18 79848\n8 18 4809\n2 4 41288\n17 18 28846\n9 18 22015\n"
],
"outputs": [
"2 1 0 1 0 \n",
"1 2 0 \n",
"3 2 1 0 1 \n",
"6 6 5 6 7 0 1 1 1 6 2 1 6 6 1 4 3 1 \n",
"1 1 5 5 5 6 1 1 1 2 5 1 5 4 3 1 5 0 \n",
"7 6 5 4 3 2 1 1 0 1 6 1 6 6 1 1 1 \n",
"9 9 6 9 8 0 9 1 4 7 2 5 1 10 1 1 3 9 \n",
"1 7 10 6 5 4 2 9 1 9 1 9 3 9 8 1 9 0 \n",
"0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \n",
"6 5 1 1 6 6 6 3 6 6 2 6 7 0 4 6 1 1 \n",
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"3 0 1 2 4 \n",
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"3 3 1 1 3 1 0 0 1 2 1 2 2 2 0 1 4 1 \n",
"3 2 5 4 4 3 0 2 4 4 3 0 4 6 0 2 1 6 \n",
"1 0 1 3 2 \n",
"0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \n",
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"0 1 1 0 0 \n",
"1 4 4 1 4 1 4 1 2 1 4 3 4 1 4 0 1 5 \n",
"3 2 1 2 1 0 \n",
"0 1 0 1 2 \n",
"4 9 1 1 1 10 3 6 2 9 5 1 9 8 7 0 9 1 \n",
"0 0 \n",
"3 0 10 5 7 1 4 1 6 10 11 2 10 8 10 1 9 1 \n",
"8 7 6 5 4 3 2 1 0 1 7 1 7 7 1 1 1 1 \n",
"1 2 0 3 4 \n",
"1 10 3 4 9 7 0 5 10 2 6 1 8 1 10 10 1 11 \n",
"7 4 5 2 5 0 5 4 9 3 8 4 6 9 4 1 3 0 \n",
"0 0 0 1 1 0 0 0 1 0 0 0 2 0 1 0 0 0 \n",
"1 2 4 0 3 \n",
"0 0 0 0 0 0 \n",
"0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 \n",
"4 2 5 6 1 0 5 1 1 3 5 1 5 1 1 5 1 1 \n",
"1 0 8 9 4 5 1 2 8 3 1 1 8 7 1 6 1 1 \n",
"0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \n",
"5 4 1 1 0 1 4 1 4 4 1 3 4 1 1 2 4 4 \n",
"7 7 1 7 6 7 8 1 3 0 1 4 7 7 2 7 1 5 \n",
"1 3 6 1 1 7 2 0 6 6 1 6 4 6 6 5 6 1 \n",
"1 5 3 0 8 6 1 8 1 1 7 1 1 4 2 9 1 8 \n",
"2 1 0 1 0 \n",
"4 1 5 1 8 7 2 3 1 7 7 0 7 7 6 1 7 7 \n",
"1 3 0 2 2 \n",
"0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 \n",
"0 2 2 1 1 \n",
"6 1 0 1 6 1 2 4 1 6 5 7 1 1 6 3 1 6 \n",
"2 0 5 4 5 2 1 6 7 6 1 6 4 2 3 4 3 3 \n",
"0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \n",
"8 7 6 5 4 3 2 1 0 1 7 1 7 7 1 1 1 ",
"4 0 4 4 1 4 1 2 4 4 5 1 3 1 1 4 1 1 \n",
"4 4 5 4 4 4 1 1 4 4 2 4 4 4 4 0 1 3 \n",
"0 4 2 6 1 3 3 5 3 2 2 2 1 4 2 3 2 5 \n",
"1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \n",
"9 9 9 1 2 0 8 5 1 6 1 1 4 7 9 1 10 3 \n",
"5 1 3 5 1 5 2 5 4 1 5 1 5 0 6 1 5 1 \n",
"9 8 6 1 8 8 8 8 2 1 3 1 8 1 0 7 5 4 \n",
"7 3 4 1 7 7 7 1 7 7 8 5 7 6 1 0 2 1 \n",
"1 1 1 8 1 1 7 8 5 3 9 4 8 2 1 6 0 8 \n",
"1 10 4 8 1 1 7 9 9 0 6 9 3 9 5 2 9 1 \n",
"1 6 3 1 6 1 6 2 7 4 6 1 6 6 0 5 1 6 \n",
"1 2 1 0 1 \n",
"5 10 1 1 0 8 1 7 1 2 3 6 9 4 1 11 1 1 \n",
"5 4 9 7 11 10 0 10 1 1 8 6 10 1 2 1 3 1 \n",
"1 0 0 0 1 \n",
"9 8 7 6 5 4 3 2 0 1 8 1 8 8 1 1 1 1 ",
"0 1 0 1 0 \n",
"6 1 5 4 3 2 1 1 0 1 5 1 5 5 1 1 1 ",
"1 7 10 6 5 4 2 9 1 9 1 9 3 9 8 1 9 0 \n",
"0 0 0 0 0 0 0 0 0 0 0 0 0 \n",
"1 0 0 0 2 0 0 0 0 0 0 1 1 0 0 0 0 2 \n",
"4 2 5 4 5 3 0 2 5 4 4 0 5 6 0 3 1 6 \n",
"1 0 1 3 2 \n",
"0 0 0 0 0 0 0 0 \n",
"1 2 7 0 4 7 2 2 3 7 1 7 5 8 7 7 3 6 \n",
"0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 \n",
"1 0 3 2 1 \n",
"0 0 0 0 0 \n",
"5 6 5 5 1 1 1 5 3 1 0 4 5 5 5 1 1 2 \n",
"2 1 0 0 1 \n",
"1 1 5 1 2 1 1 6 5 5 5 0 5 5 4 5 1 3 \n",
"1 4 4 1 4 1 4 1 2 1 3 3 4 1 4 0 1 5 \n",
"0 1 0 1 0 \n",
"0 0 0 0 \n",
"3 0 10 5 7 1 4 1 6 10 11 2 10 8 10 1 9 1 \n",
"7 4 5 2 5 0 5 8 9 3 8 4 6 9 4 1 3 0 \n",
"0 0 0 1 1 0 0 0 0 0 0 0 2 0 1 0 0 0 \n",
"0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 \n",
"4 2 5 6 1 0 5 1 1 3 5 1 5 1 1 5 1 1 \n",
"1 0 8 9 4 5 1 2 8 3 1 1 8 7 1 6 1 1 \n",
"0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 \n",
"7 7 1 7 6 7 8 1 3 0 1 4 7 7 2 7 1 5 \n",
"1 3 6 1 1 7 2 0 6 6 1 6 4 6 6 5 6 1 \n",
"1 5 3 0 8 6 1 8 1 1 7 1 1 4 2 9 1 8 \n",
"2 1 0 1 0 \n",
"1 3 0 2 2 \n",
"0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 \n",
"6 1 0 1 6 1 2 4 1 6 5 7 1 1 6 3 1 6 \n",
"8 7 6 5 4 3 2 1 0 1 7 1 7 7 1 1 1 \n",
"4 0 4 4 1 4 1 2 4 4 5 1 3 1 1 4 1 1 \n",
"4 4 5 4 4 4 1 1 4 4 2 4 4 4 4 0 1 3 \n",
"0 5 2 7 3 4 4 6 4 3 3 3 1 5 3 4 3 6 \n",
"5 5 5 1 2 0 4 1 1 2 1 1 4 3 5 1 6 3 \n",
"5 1 3 5 1 5 2 5 4 1 5 1 5 0 6 1 5 1 \n",
"9 8 6 1 8 8 8 8 2 1 3 1 8 1 0 7 5 4 \n",
"7 3 4 1 7 7 7 1 7 7 8 5 7 6 1 0 2 1 \n",
"1 5 3 1 5 1 5 2 6 4 5 1 5 5 0 5 1 5 \n",
"1 2 1 0 1 \n",
"9 8 7 6 5 4 3 2 0 1 8 1 8 8 1 1 1 1 \n",
"0 1 0 0 0 \n",
"2 2 1 1 0 \n",
"1 7 10 6 5 4 2 9 1 9 1 9 3 9 8 1 9 0 \n"
]
}
|
You are given a directed acyclic graph (a directed graph that does not contain cycles) of n vertices and m arcs. The i-th arc leads from the vertex x_i to the vertex y_i and has the weight w_i.
Your task is to select an integer a_v for each vertex v, and then write a number b_i on each arcs i such that b_i = a_{x_i} - a_{y_i}. You must select the numbers so that:
* all b_i are positive;
* the value of the expression ∑ _{i = 1}^{m} w_i b_i is the lowest possible.
It can be shown that for any directed acyclic graph with non-negative w_i, such a way to choose numbers exists.
Input
The first line contains two integers n and m (2 ≤ n ≤ 18; 0 ≤ m ≤ (n(n - 1))/(2)).
Then m lines follow, the i-th of them contains three integers x_i, y_i and w_i (1 ≤ x_i, y_i ≤ n, 1 ≤ w_i ≤ 10^5, x_i ≠ y_i) — the description of the i-th arc.
It is guaranteed that the lines describe m arcs of a directed acyclic graph without multiple arcs between the same pair of vertices.
Output
Print n integers a_1, a_2, ..., a_n (0 ≤ a_v ≤ 10^9), which must be written on the vertices so that all b_i are positive, and the value of the expression ∑ _{i = 1}^{m} w_i b_i is the lowest possible. If there are several answers, print any of them. It can be shown that the answer always exists, and at least one of the optimal answers satisfies the constraints 0 ≤ a_v ≤ 10^9.
Examples
Input
3 2
2 1 4
1 3 2
Output
1 2 0
Input
5 4
1 2 1
2 3 1
1 3 6
4 5 8
Output
43 42 41 1337 1336
Input
5 5
1 2 1
2 3 1
3 4 1
1 5 1
5 4 10
Output
4 3 2 1 2
|
{
"inputs": [
"237 7\n",
"15 2\n",
"117 3\n",
"1000 1\n",
"1 8\n",
"1000 2\n",
"1 5\n",
"998 9\n",
"1 4\n",
"1000 4\n",
"8 2\n",
"23 4\n",
"666 5\n",
"2 1\n",
"25 5\n",
"1000 5\n",
"15 5\n",
"999 8\n",
"8 9\n",
"1 7\n",
"2 3\n",
"12 4\n",
"1 9\n",
"6 7\n",
"1 6\n",
"1000 6\n",
"2 5\n",
"3 6\n",
"999 9\n",
"1000 3\n",
"1 2\n",
"1000 9\n",
"1 3\n",
"9 3\n",
"105 6\n",
"109 1\n",
"1000 7\n",
"546 4\n",
"997 6\n",
"1000 8\n",
"261 1\n",
"4 2\n",
"100 3\n",
"437 9\n",
"228 9\n",
"4 7\n",
"2 7\n",
"2 9\n",
"5 5\n",
"33 1\n",
"403 9\n",
"57 2\n",
"33 2\n",
"1 1\n",
"1001 1\n",
"21 4\n",
"9 5\n",
"2 6\n",
"105 1\n",
"109 2\n",
"3 1\n",
"237 3\n",
"117 2\n",
"2 2\n",
"1010 5\n",
"4 9\n",
"1000 12\n",
"1100 2\n",
"3 2\n",
"1000 18\n",
"2 8\n",
"4 3\n",
"473 6\n",
"1001 8\n",
"6 2\n",
"100 6\n",
"168 9\n",
"3 5\n",
"42 1\n",
"224 9\n",
"33 3\n",
"29 2\n",
"25 4\n",
"1001 7\n",
"8 5\n",
"1000 19\n",
"1100 1\n",
"2 4\n",
"17 1\n",
"1001 9\n",
"5 2\n",
"100 12\n",
"168 1\n",
"73 1\n",
"16 9\n",
"33 5\n",
"6 1\n",
"387 3\n",
"29 1\n",
"25 2\n",
"1010 9\n",
"3 9\n",
"1100 19\n",
"0100 1\n",
"4 4\n",
"16 1\n",
"1001 5\n",
"5 4\n",
"186 1\n",
"73 2\n",
"28 9\n",
"33 4\n",
"4 1\n",
"387 4\n",
"35 1\n",
"25 1\n",
"1010 13\n",
"3 3\n",
"1100 22\n",
"4 8\n",
"5 6\n",
"106 1\n",
"50 9\n",
"11 4\n",
"6 3\n",
"157 4\n",
"41 1\n",
"49 1\n",
"0010 13\n",
"8 3\n",
"4 13\n",
"9 6\n",
"50 1\n",
"11 2\n",
"10 3\n",
"94 4\n",
"19 1\n",
"60 1\n",
"13 3\n",
"8 13\n",
"9 9\n",
"20 2\n",
"10 1\n",
"19 2\n",
"59 1\n",
"13 4\n",
"12 13\n",
"20 1\n",
"59 2\n",
"13 6\n"
],
"outputs": [
"1\n",
"2\n",
"9\n",
"1\n",
"8\n",
"1\n",
"5\n",
"5\n",
"4\n",
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"1\n",
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"5\n",
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"1\n",
"5\n",
"2\n",
"1\n",
"1\n",
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"1\n",
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"7\n",
"2\n",
"9\n",
"1\n",
"4\n",
"8\n",
"1\n",
"1\n",
"3\n",
"1\n",
"7\n",
"5\n",
"5\n",
"5\n",
"5\n",
"1\n",
"7\n",
"3\n",
"6\n",
"4\n",
"1\n",
"1\n",
"4\n",
"5\n",
"3\n",
"2\n",
"8\n",
"7\n",
"9\n",
"6\n",
"1\n",
"1\n",
"5\n",
"1\n",
"1\n",
"4\n",
"1\n",
"4\n",
"5\n",
"2\n",
"8\n",
"2\n",
"1\n",
"5\n",
"5\n",
"5\n",
"5\n",
"1\n",
"8\n",
"2\n",
"7\n",
"5\n",
"1\n",
"1\n",
"2\n",
"3\n",
"9\n",
"2\n",
"1\n",
"5\n",
"7\n",
"5\n",
"5\n",
"5\n",
"9\n",
"9\n",
"2\n",
"1\n",
"3\n",
"1\n",
"1\n",
"1\n",
"5\n",
"5\n",
"2\n",
"5\n",
"4\n",
"5\n",
"8\n",
"5\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
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"5\n",
"1\n",
"4\n",
"5\n",
"2\n",
"1\n",
"9\n",
"1\n",
"5\n",
"5\n",
"4\n",
"1\n",
"2\n",
"1\n",
"1\n",
"9\n",
"1\n",
"1\n",
"5\n",
"1\n",
"1\n",
"1\n",
"8\n",
"9\n",
"8\n",
"5\n",
"1\n",
"8\n",
"2\n"
]
}
|
Polycarp urgently needs a shovel! He comes to the shop and chooses an appropriate one. The shovel that Policarp chooses is sold for k burles. Assume that there is an unlimited number of such shovels in the shop.
In his pocket Polycarp has an unlimited number of "10-burle coins" and exactly one coin of r burles (1 ≤ r ≤ 9).
What is the minimum number of shovels Polycarp has to buy so that he can pay for the purchase without any change? It is obvious that he can pay for 10 shovels without any change (by paying the requied amount of 10-burle coins and not using the coin of r burles). But perhaps he can buy fewer shovels and pay without any change. Note that Polycarp should buy at least one shovel.
Input
The single line of input contains two integers k and r (1 ≤ k ≤ 1000, 1 ≤ r ≤ 9) — the price of one shovel and the denomination of the coin in Polycarp's pocket that is different from "10-burle coins".
Remember that he has an unlimited number of coins in the denomination of 10, that is, Polycarp has enough money to buy any number of shovels.
Output
Print the required minimum number of shovels Polycarp has to buy so that he can pay for them without any change.
Examples
Input
117 3
Output
9
Input
237 7
Output
1
Input
15 2
Output
2
Note
In the first example Polycarp can buy 9 shovels and pay 9·117 = 1053 burles. Indeed, he can pay this sum by using 10-burle coins and one 3-burle coin. He can't buy fewer shovels without any change.
In the second example it is enough for Polycarp to buy one shovel.
In the third example Polycarp should buy two shovels and pay 2·15 = 30 burles. It is obvious that he can pay this sum without any change.
|
{
"inputs": [
"5\n1 3 5 7 9\n",
"5\n2 3 5 7 11\n",
"5\n4 6 9 3 6\n",
"1\n5\n",
"1\n1000000\n",
"5\n3 3 6 2 2\n",
"1\n1\n",
"2\n1 1000000\n",
"2\n999999 1000000\n",
"1\n1343\n",
"1\n4\n",
"5\n3 2 6 2 2\n",
"5\n1 3 5 11 9\n",
"5\n2 3 5 10 11\n",
"5\n3 2 6 2 3\n",
"5\n2 3 5 9 17\n",
"5\n3 2 3 2 6\n",
"5\n3 3 3 4 6\n",
"5\n3 3 2 4 6\n",
"1\n2\n",
"1\n1113\n",
"5\n4 1 9 3 6\n",
"1\n2191\n",
"5\n1 3 10 11 9\n",
"5\n2 3 5 10 17\n",
"5\n3 2 2 2 3\n",
"1\n3724\n",
"5\n1 3 10 11 1\n",
"5\n3 2 2 2 6\n",
"1\n4314\n",
"5\n1 3 16 11 1\n",
"1\n8066\n",
"5\n1 3 16 20 1\n",
"5\n3 2 3 4 6\n",
"1\n7224\n",
"5\n2 3 16 20 1\n",
"1\n13916\n",
"5\n2 3 2 20 1\n",
"1\n19583\n",
"5\n4 3 2 20 1\n",
"5\n3 3 2 4 2\n",
"1\n12306\n",
"5\n4 3 2 35 1\n",
"1\n2816\n",
"5\n4 3 1 35 1\n",
"1\n414\n",
"1\n392\n",
"1\n360\n",
"1\n335\n",
"1\n536\n",
"1\n167\n",
"1\n136\n",
"1\n233\n",
"1\n188\n",
"1\n280\n",
"1\n79\n",
"1\n46\n",
"1\n6\n",
"5\n5 3 6 2 2\n",
"1\n248\n",
"5\n1 3 5 1 9\n"
],
"outputs": [
"1 4\n1 ",
"5 0\n1 2 3 4 5 ",
"1 3\n2 ",
"1 0\n1 ",
"1 0\n1 ",
"2 2\n1 3 ",
"1 0\n1 ",
"1 1\n1 ",
"2 0\n1 2 ",
"1 0\n1 ",
"1 0\n1\n",
"1 3\n2\n",
"1 4\n1\n",
"1 1\n3\n",
"1 2\n2\n",
"5 0\n1 2 3 4 5\n",
"1 1\n4\n",
"1 2\n1\n",
"1 2\n3\n",
"1 0\n1\n",
"1 0\n1\n",
"1 4\n1\n",
"1 0\n1\n",
"1 4\n1\n",
"1 1\n3\n",
"1 2\n2\n",
"1 0\n1\n",
"1 4\n1\n",
"1 3\n2\n",
"1 0\n1\n",
"1 4\n1\n",
"1 0\n1\n",
"1 4\n1\n",
"5 0\n1 2 3 4 5\n",
"1 0\n1\n",
"1 4\n1\n",
"1 0\n1\n",
"1 4\n1\n",
"1 0\n1\n",
"1 4\n1\n",
"1 2\n3\n",
"1 0\n1\n",
"1 4\n1\n",
"1 0\n1\n",
"1 4\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 0\n1\n",
"1 2\n3\n",
"1 0\n1\n",
"1 4\n1\n"
]
}
|
Simon has an array a1, a2, ..., an, consisting of n positive integers. Today Simon asked you to find a pair of integers l, r (1 ≤ l ≤ r ≤ n), such that the following conditions hold:
1. there is integer j (l ≤ j ≤ r), such that all integers al, al + 1, ..., ar are divisible by aj;
2. value r - l takes the maximum value among all pairs for which condition 1 is true;
Help Simon, find the required pair of numbers (l, r). If there are multiple required pairs find all of them.
Input
The first line contains integer n (1 ≤ n ≤ 3·105).
The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 106).
Output
Print two integers in the first line — the number of required pairs and the maximum value of r - l. On the following line print all l values from optimal pairs in increasing order.
Examples
Input
5
4 6 9 3 6
Output
1 3
2
Input
5
1 3 5 7 9
Output
1 4
1
Input
5
2 3 5 7 11
Output
5 0
1 2 3 4 5
Note
In the first sample the pair of numbers is right, as numbers 6, 9, 3 are divisible by 3.
In the second sample all numbers are divisible by number 1.
In the third sample all numbers are prime, so conditions 1 and 2 are true only for pairs of numbers (1, 1), (2, 2), (3, 3), (4, 4), (5, 5).
|
{
"inputs": [
"3 4\n1 3\n1 1\n1 2\n2 3\n",
"4 6\n1 2\n1 4\n1 2\n3 3\n1 3\n1 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"300000 1\n1 300000\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 7\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"300000 1\n1 86053\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"4 4\n1 3\n1 1\n1 2\n2 3\n",
"4 6\n1 2\n1 4\n1 2\n3 3\n2 3\n1 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"4 6\n1 2\n1 4\n1 2\n3 3\n2 3\n2 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 2\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 1\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 1\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n2 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"4 4\n1 3\n2 1\n1 2\n2 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 5\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 5\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 8\n1 5\n2 2\n2 2\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n2 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 1\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n2 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 8\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 3\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n2 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n2 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"4 4\n1 1\n2 1\n1 2\n2 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 3\n2 4\n1 7\n1 1\n2 5\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 5\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n2 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n2 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 8\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 3\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n2 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 3\n2 4\n1 7\n1 1\n2 5\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 3\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 5\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n2 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n2 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 7\n2 1\n2 1\n3 1\n1 9\n1 8\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 1\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 1\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n2 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 8\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 3\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n2 10\n1 7\n1 8\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n2 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 2\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n3 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 7\n2 1\n2 1\n3 1\n1 9\n1 8\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 1\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 1\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n2 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 7\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 2\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n3 2\n2 8\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n2 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 7\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 2\n2 10\n1 10\n1 1\n2 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n3 2\n2 8\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n2 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"300000 1\n2 86053\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 4\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 8\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 5\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n2 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 1\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 6\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 14\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 3\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n2 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 2\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"4 4\n1 3\n2 1\n1 2\n1 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 5\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 4\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 2\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 5\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 7\n2 1\n2 1\n3 1\n1 9\n1 8\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n3 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 3\n1 3\n1 9\n1 6\n1 3\n1 8\n2 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n2 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 2\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 3\n2 4\n1 7\n1 1\n2 5\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n1 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 3\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 5\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 8\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n2 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n2 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 7\n2 1\n2 1\n3 1\n1 9\n1 8\n1 8\n1 10\n3 8\n2 8\n1 6\n1 2\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n2 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 1\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 1\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n2 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 7\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 2\n2 10\n1 10\n1 1\n1 10\n1 6\n1 3\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n3 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n2 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 7\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 2\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n2 10\n1 6\n3 32\n2 3\n1 5\n2 10\n3 2\n2 8\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"4 6\n1 3\n1 4\n1 2\n3 3\n2 3\n2 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 8\n1 5\n2 2\n2 2\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 3\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"4 6\n1 2\n1 4\n1 2\n3 3\n3 3\n1 3\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 7\n2 1\n2 1\n3 1\n1 9\n1 8\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 7\n2 1\n2 1\n3 1\n1 9\n1 8\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 1\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 3\n1 3\n1 9\n1 6\n1 3\n1 8\n2 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n2 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n2 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n3 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 1\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 3\n2 4\n1 7\n1 1\n2 5\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 3\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 9\n1 1\n2 6\n1 2\n2 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 7\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 2\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n3 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"5 4\n1 3\n1 1\n1 2\n2 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 1\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 2\n3 3\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 6\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 9\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"4 6\n1 2\n1 4\n1 2\n3 3\n3 3\n2 3\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n1 9\n1 6\n2 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 2\n1 7\n1 1\n2 4\n2 9\n1 2\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n2 1\n3 1\n1 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 1\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"6 6\n1 3\n1 4\n1 2\n3 3\n2 3\n2 3\n",
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"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n2 6\n2 1\n2 1\n3 1\n1 9\n1 8\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 10\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n1 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n2 4\n1 1\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 4\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n2 3\n1 6\n1 10\n2 1\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n1 10\n1 7\n1 8\n",
"10 85\n2 2\n1 10\n1 1\n2 6\n1 2\n1 4\n1 7\n2 1\n1 1\n3 3\n2 9\n1 6\n1 8\n1 10\n3 8\n2 8\n1 6\n1 3\n1 9\n1 6\n1 3\n1 8\n1 1\n1 6\n1 8\n2 1\n2 10\n1 10\n1 1\n1 10\n1 6\n2 2\n1 8\n1 3\n1 4\n1 9\n1 5\n1 5\n2 2\n2 4\n1 7\n1 1\n3 4\n2 9\n1 1\n1 7\n1 8\n3 33\n1 10\n2 2\n1 3\n1 10\n1 6\n3 32\n2 3\n1 5\n2 10\n2 2\n2 3\n2 3\n3 16\n1 3\n2 2\n1 1\n3 18\n2 2\n2 5\n1 5\n1 9\n2 4\n1 3\n1 4\n1 3\n1 6\n1 10\n2 2\n1 7\n1 7\n2 8\n1 1\n3 1\n1 8\n2 10\n1 7\n1 8\n"
],
"outputs": [
"1\n2\n3\n2\n\n",
"1\n2\n3\n0\n1\n2\n\n",
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"1\n2\n3\n0\n0\n1\n",
"0\n1\n2\n2\n3\n4\n5\n4\n4\n3\n4\n5\n6\n7\n1\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n17\n16\n17\n18\n18\n19\n20\n21\n22\n2\n3\n3\n4\n5\n6\n6\n5\n6\n4\n4\n4\n4\n4\n5\n5\n6\n6\n6\n5\n6\n7\n7\n8\n9\n7\n8\n9\n9\n10\n11\n10\n11\n11\n12\n13\n14\n15\n",
"0\n1\n2\n2\n3\n4\n4\n3\n3\n2\n3\n4\n5\n6\n0\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n8\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n17\n16\n17\n18\n18\n19\n20\n21\n22\n1\n2\n2\n3\n4\n5\n5\n4\n5\n3\n3\n3\n3\n3\n4\n4\n5\n5\n5\n4\n5\n6\n6\n7\n8\n6\n7\n8\n8\n9\n10\n9\n10\n10\n11\n12\n13\n14\n",
"0\n1\n2\n2\n3\n4\n4\n3\n3\n2\n3\n4\n5\n6\n0\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n8\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n17\n16\n17\n18\n18\n19\n20\n21\n22\n1\n2\n2\n3\n4\n5\n5\n4\n5\n3\n3\n3\n3\n3\n4\n4\n5\n5\n5\n4\n5\n6\n6\n7\n8\n6\n7\n8\n8\n9\n10\n9\n10\n10\n11\n12\n13\n14\n",
"0\n1\n2\n2\n3\n4\n5\n4\n5\n3\n4\n5\n6\n7\n2\n1\n2\n3\n4\n5\n6\n7\n7\n8\n9\n9\n7\n8\n9\n10\n11\n12\n13\n14\n15\n14\n15\n16\n15\n14\n15\n16\n16\n17\n18\n19\n20\n1\n2\n2\n3\n4\n5\n5\n4\n5\n3\n3\n3\n3\n3\n4\n4\n5\n5\n5\n4\n5\n6\n6\n7\n8\n6\n7\n8\n8\n9\n10\n9\n10\n10\n11\n12\n13\n14\n",
"0\n1\n2\n2\n3\n3\n4\n3\n3\n2\n3\n4\n5\n6\n0\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n8\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n17\n16\n17\n18\n18\n19\n20\n21\n22\n1\n2\n2\n3\n4\n5\n5\n4\n5\n3\n3\n3\n3\n3\n4\n4\n5\n5\n5\n4\n5\n6\n6\n7\n8\n6\n7\n8\n8\n9\n10\n9\n10\n10\n11\n12\n13\n14\n",
"0\n1\n2\n2\n3\n4\n5\n4\n5\n3\n4\n5\n5\n6\n1\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n7\n8\n9\n10\n11\n11\n12\n13\n14\n15\n16\n17\n14\n13\n14\n15\n13\n11\n12\n13\n14\n0\n1\n1\n2\n3\n4\n4\n3\n4\n2\n2\n2\n2\n2\n3\n3\n4\n4\n4\n3\n4\n5\n4\n5\n6\n7\n8\n9\n9\n10\n11\n11\n12\n12\n13\n14\n15\n16\n",
"0\n1\n2\n2\n3\n3\n4\n3\n3\n2\n3\n4\n5\n6\n0\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n9\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n19\n18\n17\n18\n19\n19\n20\n21\n22\n23\n1\n2\n2\n3\n4\n5\n5\n4\n5\n3\n3\n3\n3\n3\n4\n4\n5\n5\n5\n4\n5\n6\n6\n7\n8\n6\n7\n8\n8\n9\n10\n9\n10\n10\n11\n12\n13\n14\n",
"1\n2\n3\n2\n",
"0\n1\n2\n2\n3\n4\n5\n4\n5\n3\n4\n5\n6\n7\n2\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n7\n8\n9\n10\n11\n11\n12\n13\n14\n15\n16\n17\n17\n16\n17\n18\n18\n16\n17\n18\n19\n1\n2\n2\n3\n4\n5\n5\n4\n5\n3\n3\n3\n3\n3\n4\n4\n5\n5\n5\n4\n5\n6\n6\n7\n8\n9\n10\n11\n11\n12\n13\n12\n13\n13\n14\n15\n16\n17\n",
"0\n1\n2\n2\n3\n4\n5\n4\n5\n3\n4\n5\n6\n7\n2\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n7\n8\n9\n10\n11\n11\n12\n13\n14\n15\n16\n17\n17\n16\n17\n18\n18\n19\n20\n21\n22\n2\n3\n3\n4\n5\n6\n6\n5\n6\n4\n4\n4\n4\n4\n5\n5\n6\n6\n6\n5\n6\n7\n7\n8\n9\n10\n11\n12\n12\n13\n14\n13\n14\n14\n15\n16\n17\n18\n",
"0\n1\n2\n2\n3\n4\n5\n4\n5\n3\n4\n5\n5\n6\n1\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n7\n8\n9\n10\n11\n11\n12\n13\n14\n15\n16\n17\n17\n16\n17\n18\n18\n16\n17\n18\n19\n0\n1\n1\n2\n3\n4\n4\n3\n4\n2\n2\n2\n2\n2\n3\n3\n4\n4\n4\n3\n4\n5\n5\n6\n7\n8\n9\n10\n10\n11\n12\n12\n13\n13\n14\n15\n16\n17\n",
"1\n2\n3\n0\n0\n0\n",
"0\n1\n2\n2\n3\n4\n5\n4\n5\n3\n4\n5\n5\n6\n1\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n7\n8\n9\n10\n11\n11\n12\n13\n14\n15\n16\n17\n17\n17\n18\n19\n18\n16\n17\n18\n19\n0\n1\n1\n2\n3\n4\n4\n3\n4\n2\n2\n2\n2\n2\n3\n3\n4\n4\n4\n3\n4\n5\n5\n6\n7\n8\n9\n10\n10\n11\n12\n12\n13\n13\n14\n15\n16\n17\n",
"0\n1\n2\n2\n3\n4\n5\n4\n4\n3\n4\n5\n6\n7\n1\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n17\n16\n17\n18\n18\n19\n20\n21\n22\n2\n3\n3\n4\n5\n6\n6\n5\n6\n4\n4\n4\n4\n4\n5\n5\n6\n6\n6\n5\n6\n7\n7\n8\n9\n7\n8\n9\n9\n10\n11\n10\n11\n11\n12\n13\n14\n15\n",
"1\n2\n3\n0\n0\n0\n",
"0\n1\n2\n2\n3\n4\n5\n4\n5\n3\n4\n5\n6\n7\n2\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n8\n9\n10\n11\n12\n12\n13\n11\n12\n13\n14\n15\n15\n14\n15\n16\n16\n17\n18\n19\n20\n1\n2\n2\n2\n3\n4\n4\n4\n5\n3\n3\n3\n3\n3\n4\n4\n5\n5\n5\n4\n5\n6\n6\n7\n8\n9\n10\n11\n11\n12\n13\n12\n13\n13\n14\n15\n16\n17\n",
"0\n1\n2\n2\n3\n4\n4\n3\n3\n2\n3\n4\n5\n6\n0\n0\n1\n2\n3\n4\n5\n6\n7\n8\n9\n8\n7\n8\n9\n10\n11\n12\n13\n14\n15\n16\n17\n18\n17\n16\n17\n18\n18\n19\n20\n21\n22\n1\n2\n2\n3\n4\n5\n5\n4\n5\n3\n3\n3\n3\n3\n4\n4\n5\n5\n5\n4\n5\n6\n6\n7\n8\n6\n7\n8\n7\n8\n9\n8\n9\n9\n10\n11\n12\n13\n",
"0\n1\n2\n2\n3\n4\n5\n4\n5\n3\n3\n4\n5\n6\n1\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n9\n8\n9\n10\n11\n12\n12\n13\n14\n15\n16\n17\n18\n18\n17\n18\n19\n19\n17\n18\n19\n20\n0\n1\n1\n2\n3\n4\n4\n3\n4\n2\n2\n2\n2\n2\n3\n3\n4\n4\n4\n3\n4\n5\n5\n6\n7\n8\n9\n10\n10\n11\n12\n12\n13\n13\n14\n13\n14\n15\n"
]
}
|
Thor is getting used to the Earth. As a gift Loki gave him a smartphone. There are n applications on this phone. Thor is fascinated by this phone. He has only one minor issue: he can't count the number of unread notifications generated by those applications (maybe Loki put a curse on it so he can't).
q events are about to happen (in chronological order). They are of three types:
1. Application x generates a notification (this new notification is unread).
2. Thor reads all notifications generated so far by application x (he may re-read some notifications).
3. Thor reads the first t notifications generated by phone applications (notifications generated in first t events of the first type). It's guaranteed that there were at least t events of the first type before this event. Please note that he doesn't read first t unread notifications, he just reads the very first t notifications generated on his phone and he may re-read some of them in this operation.
Please help Thor and tell him the number of unread notifications after each event. You may assume that initially there are no notifications in the phone.
Input
The first line of input contains two integers n and q (1 ≤ n, q ≤ 300 000) — the number of applications and the number of events to happen.
The next q lines contain the events. The i-th of these lines starts with an integer typei — type of the i-th event. If typei = 1 or typei = 2 then it is followed by an integer xi. Otherwise it is followed by an integer ti (1 ≤ typei ≤ 3, 1 ≤ xi ≤ n, 1 ≤ ti ≤ q).
Output
Print the number of unread notifications after each event.
Examples
Input
3 4
1 3
1 1
1 2
2 3
Output
1
2
3
2
Input
4 6
1 2
1 4
1 2
3 3
1 3
1 3
Output
1
2
3
0
1
2
Note
In the first sample:
1. Application 3 generates a notification (there is 1 unread notification).
2. Application 1 generates a notification (there are 2 unread notifications).
3. Application 2 generates a notification (there are 3 unread notifications).
4. Thor reads the notification generated by application 3, there are 2 unread notifications left.
In the second sample test:
1. Application 2 generates a notification (there is 1 unread notification).
2. Application 4 generates a notification (there are 2 unread notifications).
3. Application 2 generates a notification (there are 3 unread notifications).
4. Thor reads first three notifications and since there are only three of them so far, there will be no unread notification left.
5. Application 3 generates a notification (there is 1 unread notification).
6. Application 3 generates a notification (there are 2 unread notifications).
|
{
"inputs": [
"3 3 4\n111\n111\n111\n111\n111\n111",
"3 3 4\n111\n111\n111\n111\n111\n011",
"3 3 4\n111\n111\n011\n111\n011\n111",
"3 1 4\n111\n111\n011\n111\n011\n111",
"5 0 4\n011\n111\n011\n011\n010\n111",
"5 4 2\n101\n110\n011\n111\n100\n101",
"3 3 4\n111\n111\n011\n111\n111\n111",
"3 1 4\n111\n111\n011\n111\n010\n111",
"5 1 4\n111\n111\n011\n111\n010\n111",
"5 1 4\n011\n111\n011\n111\n010\n111",
"5 1 4\n011\n111\n011\n011\n010\n111",
"8 1 4\n011\n111\n011\n011\n010\n111",
"8 1 4\n011\n101\n011\n011\n010\n111",
"8 1 4\n011\n101\n011\n011\n000\n111",
"8 2 4\n011\n101\n011\n011\n000\n111",
"8 2 0\n011\n101\n011\n011\n000\n111",
"8 2 0\n011\n001\n011\n011\n000\n111",
"8 2 0\n011\n001\n011\n111\n000\n111",
"8 2 0\n011\n000\n011\n111\n000\n111",
"8 2 0\n010\n000\n011\n111\n000\n111",
"8 2 0\n010\n001\n011\n111\n000\n111",
"8 2 0\n010\n001\n011\n111\n001\n111",
"8 2 0\n010\n001\n111\n111\n001\n111",
"8 2 0\n010\n001\n111\n111\n000\n111",
"8 1 0\n010\n001\n111\n111\n001\n111",
"8 1 0\n110\n001\n111\n111\n001\n111",
"8 1 0\n110\n011\n111\n111\n001\n111",
"3 3 4\n111\n111\n111\n111\n111\n110",
"3 3 4\n111\n111\n111\n101\n111\n011",
"3 2 4\n111\n111\n011\n111\n111\n111",
"3 3 4\n111\n111\n010\n111\n011\n111",
"3 1 4\n111\n011\n011\n111\n011\n111",
"3 1 4\n101\n111\n011\n111\n010\n111",
"5 1 4\n111\n111\n011\n111\n010\n110",
"5 1 4\n001\n111\n011\n111\n010\n111",
"8 1 4\n011\n111\n011\n111\n010\n111",
"1 1 4\n011\n101\n011\n011\n010\n111",
"8 0 4\n011\n101\n011\n011\n000\n111",
"8 2 4\n011\n101\n001\n011\n000\n111",
"8 2 0\n011\n101\n011\n111\n000\n111",
"8 2 0\n010\n001\n011\n011\n000\n111",
"8 2 0\n011\n001\n011\n111\n000\n101",
"8 2 0\n011\n000\n011\n111\n001\n111",
"8 2 0\n010\n000\n011\n111\n000\n011",
"8 2 0\n010\n001\n011\n011\n001\n111",
"8 2 0\n010\n001\n011\n111\n001\n011",
"8 2 0\n010\n011\n111\n111\n000\n111",
"11 1 0\n010\n001\n111\n111\n001\n111",
"6 1 0\n110\n001\n111\n111\n001\n111",
"8 1 0\n110\n011\n111\n111\n001\n110",
"3 3 4\n111\n111\n111\n111\n110\n110",
"3 3 4\n111\n111\n111\n101\n111\n001",
"3 2 4\n111\n111\n011\n110\n111\n111",
"3 3 4\n111\n111\n010\n011\n011\n111",
"1 1 4\n111\n011\n011\n111\n011\n111",
"3 1 4\n101\n111\n011\n101\n010\n111",
"5 1 4\n111\n111\n011\n111\n010\n100",
"0 1 4\n001\n111\n011\n111\n010\n111",
"5 0 4\n011\n111\n010\n011\n010\n111",
"8 1 5\n011\n111\n011\n111\n010\n111",
"1 1 4\n111\n101\n011\n011\n010\n111",
"8 0 1\n011\n101\n011\n011\n000\n111",
"8 2 4\n010\n101\n001\n011\n000\n111",
"8 2 1\n011\n101\n011\n111\n000\n111",
"8 2 0\n011\n000\n011\n111\n000\n101",
"8 2 0\n011\n000\n011\n111\n011\n111",
"0 2 0\n010\n000\n011\n111\n000\n011",
"8 2 0\n010\n101\n011\n011\n001\n111",
"8 2 0\n010\n011\n011\n111\n001\n011",
"8 2 0\n010\n011\n111\n011\n000\n111",
"11 1 0\n000\n001\n111\n111\n001\n111",
"6 1 1\n110\n001\n111\n111\n001\n111",
"8 1 0\n110\n011\n110\n111\n001\n110",
"3 3 4\n111\n111\n111\n111\n110\n010",
"3 3 4\n111\n111\n111\n101\n111\n000",
"3 2 4\n111\n111\n111\n110\n111\n111",
"6 3 4\n111\n111\n010\n011\n011\n111",
"1 1 4\n111\n011\n011\n111\n011\n011",
"3 0 4\n101\n111\n011\n101\n010\n111",
"5 1 4\n111\n111\n010\n111\n010\n110",
"0 1 4\n011\n111\n011\n111\n010\n111",
"5 0 4\n011\n111\n010\n111\n010\n111",
"8 1 5\n011\n110\n011\n111\n010\n111",
"1 1 4\n111\n100\n011\n011\n010\n111",
"8 0 1\n011\n101\n011\n111\n000\n111",
"2 2 4\n010\n101\n001\n011\n000\n111",
"8 2 1\n011\n101\n011\n111\n010\n111",
"8 3 0\n011\n000\n011\n111\n000\n101",
"8 2 0\n001\n000\n011\n111\n011\n111",
"0 2 0\n010\n000\n011\n011\n000\n011",
"8 2 1\n010\n011\n111\n011\n000\n111",
"11 1 0\n000\n001\n011\n111\n001\n111",
"6 1 1\n110\n001\n111\n110\n001\n111",
"8 1 0\n110\n011\n100\n111\n001\n110",
"3 0 4\n111\n111\n111\n111\n110\n010",
"3 3 4\n110\n111\n111\n101\n111\n000",
"3 2 4\n111\n111\n110\n110\n111\n111",
"6 1 4\n111\n111\n010\n011\n011\n111",
"1 1 4\n110\n011\n011\n111\n011\n011",
"3 0 4\n101\n111\n011\n101\n010\n101",
"5 1 8\n111\n111\n010\n111\n010\n110"
],
"outputs": [
"2",
"2\n",
"3\n",
"1\n",
"0\n",
"4\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"3\n",
"2\n",
"3\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"0\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"3\n",
"2\n",
"3\n",
"1\n",
"1\n",
"1\n",
"0\n",
"0\n",
"1\n",
"1\n",
"0\n",
"2\n",
"2\n",
"2\n",
"2\n",
"0\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"3\n",
"3\n",
"2\n",
"3\n",
"1\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"1\n",
"0\n",
"2\n",
"2\n",
"3\n",
"2\n",
"0\n",
"2\n",
"1\n",
"1\n",
"1\n",
"0\n",
"3\n",
"2\n",
"1\n",
"1\n",
"0\n",
"1\n"
]
}
|
E: Arai's --Arai's-
problem
Arai's is a female idol group that has been popular since the school idol era. Nowadays, it is active at the world level as a large group to which many "Arai" belong. And today, it was decided to start a new project. They decided to try to further increase sales by forming several small units.
"Arai" has A people and "Arai" has B people in Arai's, and it consists of A + B people "Arai" in total. The new unit will consist of a pair of "Arai" and one "Arai". (Here, the same "Arai" must not belong to multiple units.) However, one "Arai" does not think well about some "Arai", and there is also "Arai". "Arai" doesn't really think about some "Arai". When "Arai" and others form a unit, they do not accept "Arai" who they do not like as a pair, and on the other hand, they cannot form a unit unless they accept it.
As Arai's manager, you want to make as many units as you can, but the friendships of the members made you feel the limits. So you thought about meeting with "Arai" individually and telling good rumors about "Arai" who wants to form a unit. "Arai" who had an interview will review "Arai" who heard the rumor and will accept it as a pair of units.
But you can't take that much time, so you can only hear rumors up to K times. You have tried to maximize the number of units you can form in a limited amount of time. Find the maximum number of units you can form.
Input format
A B K
a_1_1
...
a_A
b_1_1
...
b_B
On the first line, the number of "Arai" A and the number B of "Arai" (1 \ ≤ A, B \ ≤ 200, where A and B are integers), and the number of people who can hear rumors K ( 0 \ ≤ K \ ≤ 200, where K is an integer) is given, separated by blanks.
The following line A is given a string consisting of only 0s and 1s of length B, respectively. When the j-th character of the character string a_i on the i-th line is 1, the i-th "Arai" does not think well about the j-th "Arai".
The following line B is given a string consisting of only 0s and 1s of length A, respectively. When the j-th character of the character string b_i on the i-th line is 1, the i-th "Arai" does not think well about the j-th "Arai".
Output format
Output the maximum number of units you can form on one line.
Input example 1
3 3 4
111
111
111
111
111
111
Output example 1
2
Input example 2
3 3 2
101
100
010
001
011
111
Output example 2
3
Input example 3
5 6 3
101101
110110
010111
110110
110111
01010
10101
11101
01011
11011
11011
Output example 3
Four
Example
Input
3 3 4
111
111
111
111
111
111
Output
2
|
{
"inputs": [
"7\n1 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 2 2\n4 4 4\n",
"2\n2 2 8\n3 2 2\n",
"2\n2 2 8\n3 3 2\n",
"7\n1 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 2 2\n0 4 4\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 3\n2 3 2\n3 2 2\n0 4 4\n",
"2\n2 2 7\n3 3 0\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 2\n2 3 2\n3 2 2\n0 4 4\n",
"2\n1 2 7\n3 3 0\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 2\n3 2 2\n0 4 1\n",
"2\n1 3 7\n5 0 0\n",
"2\n1 3 7\n5 0 1\n",
"7\n0 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 3\n4 2 2\n0 6 1\n",
"7\n0 1 2\n0 0 0\n9 1 1\n2 0 4\n2 2 3\n4 2 2\n0 6 1\n",
"7\n0 2 2\n0 0 0\n9 1 1\n2 0 4\n2 2 3\n4 2 2\n0 6 1\n",
"2\n2 2 8\n2 2 2\n",
"7\n1 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 2 2\n7 4 4\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 3\n2 3 2\n3 2 2\n1 4 4\n",
"2\n2 0 7\n3 3 0\n",
"2\n1 3 7\n5 3 1\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 1 4\n2 3 2\n3 2 2\n0 4 1\n",
"2\n0 3 7\n5 0 1\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 3\n4 2 1\n0 4 1\n",
"2\n0 2 8\n2 2 2\n",
"7\n0 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 2 2\n7 4 4\n",
"2\n2 1 8\n3 4 2\n",
"7\n1 2 1\n0 0 0\n9 1 7\n2 0 3\n2 3 2\n3 2 2\n0 4 7\n",
"2\n3 0 7\n3 3 2\n",
"2\n1 0 7\n4 3 0\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 1 4\n2 3 2\n3 2 0\n0 4 1\n",
"7\n0 1 2\n0 0 0\n9 1 1\n2 2 4\n1 2 3\n6 2 2\n0 6 1\n",
"7\n0 2 2\n0 0 0\n9 2 1\n3 0 4\n2 2 3\n4 2 2\n0 6 1\n",
"7\n0 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 2 2\n7 4 0\n",
"7\n1 4 1\n0 0 0\n16 0 1\n2 2 2\n2 3 2\n3 2 2\n0 4 4\n",
"7\n1 2 0\n0 0 0\n9 0 1\n2 2 4\n2 3 2\n4 2 2\n0 4 1\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 4\n2 1 3\n5 2 2\n0 6 1\n",
"7\n0 2 1\n0 0 0\n6 1 1\n2 2 4\n2 3 3\n4 2 2\n0 6 0\n",
"7\n0 1 1\n0 0 0\n11 1 1\n2 2 4\n3 3 3\n4 2 3\n0 6 1\n",
"7\n0 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 1 2\n7 4 0\n",
"2\n0 1 7\n3 3 1\n",
"2\n2 2 7\n3 3 2\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 2 2\n2 3 2\n3 2 2\n0 4 4\n",
"2\n1 2 7\n5 3 0\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 2\n3 2 2\n0 4 4\n",
"2\n1 3 7\n5 3 0\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 2\n4 2 2\n0 4 1\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 3\n4 2 2\n0 4 1\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 3\n4 2 2\n0 6 1\n",
"7\n0 1 1\n0 0 0\n9 1 1\n2 2 4\n2 2 3\n4 2 2\n0 6 1\n",
"7\n0 1 2\n0 0 0\n9 1 1\n2 2 4\n2 2 3\n4 2 2\n0 6 1\n",
"2\n2 2 8\n3 4 2\n",
"7\n1 2 1\n0 0 0\n9 1 7\n2 2 3\n2 3 2\n3 2 2\n0 4 7\n",
"2\n3 2 7\n3 3 2\n",
"2\n2 2 2\n3 3 0\n",
"7\n1 2 1\n0 0 0\n16 1 1\n2 2 2\n2 3 2\n3 2 2\n0 4 4\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 4 2\n2 3 2\n3 2 2\n0 4 4\n",
"2\n1 2 7\n4 3 0\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 4\n2 3 2\n4 2 2\n0 4 1\n",
"7\n1 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 3\n5 2 2\n0 6 1\n",
"7\n0 1 1\n0 0 0\n6 1 1\n2 2 4\n2 3 3\n4 2 2\n0 6 1\n",
"7\n0 1 1\n0 0 0\n9 1 1\n2 2 4\n2 3 3\n4 2 3\n0 6 1\n",
"7\n0 1 2\n0 0 0\n9 1 1\n2 2 4\n2 2 3\n6 2 2\n0 6 1\n",
"7\n0 2 2\n0 0 0\n9 1 1\n3 0 4\n2 2 3\n4 2 2\n0 6 1\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 3\n3 3 2\n3 2 2\n1 4 4\n",
"7\n1 4 1\n0 0 0\n16 1 1\n2 2 2\n2 3 2\n3 2 2\n0 4 4\n",
"2\n2 1 7\n3 3 0\n",
"7\n1 1 1\n0 0 0\n9 2 1\n2 4 2\n2 3 2\n3 2 2\n0 4 4\n",
"2\n2 3 7\n5 3 1\n",
"7\n1 2 0\n0 0 0\n9 1 1\n2 2 4\n2 3 2\n4 2 2\n0 4 1\n",
"2\n0 3 7\n5 1 1\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 4\n2 3 3\n4 2 1\n0 4 1\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 4\n2 3 3\n5 2 2\n0 6 1\n",
"7\n0 2 1\n0 0 0\n6 1 1\n2 2 4\n2 3 3\n4 2 2\n0 6 1\n",
"7\n0 1 1\n0 0 0\n11 1 1\n2 2 4\n2 3 3\n4 2 3\n0 6 1\n",
"2\n0 2 8\n2 2 3\n",
"2\n2 1 8\n5 4 2\n",
"7\n1 2 1\n0 0 0\n9 1 7\n2 0 3\n2 3 2\n3 4 2\n0 4 7\n",
"2\n3 0 7\n3 6 2\n",
"2\n0 1 7\n3 3 0\n",
"7\n1 1 1\n0 0 0\n9 2 1\n2 4 2\n2 3 2\n5 2 2\n0 4 4\n",
"2\n1 1 7\n4 3 0\n",
"2\n2 3 7\n4 3 1\n",
"2\n0 3 7\n5 1 0\n",
"7\n1 2 1\n0 0 0\n9 1 1\n2 2 8\n2 3 3\n4 2 1\n0 4 1\n",
"7\n0 1 2\n0 0 0\n9 1 1\n2 2 4\n1 2 3\n3 2 2\n0 6 1\n",
"7\n0 2 2\n0 0 0\n9 2 1\n3 0 4\n2 2 3\n4 2 2\n0 6 2\n",
"2\n0 2 8\n4 2 3\n",
"2\n2 1 8\n5 2 2\n",
"7\n1 2 1\n0 0 0\n6 1 7\n2 0 3\n2 3 2\n3 4 2\n0 4 7\n",
"2\n3 0 7\n3 0 2\n",
"7\n1 4 1\n0 0 0\n16 0 1\n2 2 1\n2 3 2\n3 2 2\n0 4 4\n"
],
"outputs": [
"3\n0\n4\n5\n5\n5\n7\n",
"5\n5\n",
"5\n5\n",
"3\n0\n4\n5\n5\n5\n3\n",
"3\n0\n3\n5\n5\n5\n3\n",
"5\n3\n",
"3\n0\n3\n4\n5\n5\n3\n",
"4\n3\n",
"3\n0\n3\n5\n5\n5\n2\n",
"4\n1\n",
"4\n2\n",
"2\n0\n3\n5\n5\n5\n2\n",
"2\n0\n3\n3\n5\n5\n2\n",
"3\n0\n3\n3\n5\n5\n2\n",
"5\n4\n",
"3\n0\n4\n5\n5\n5\n7\n",
"3\n0\n3\n5\n5\n5\n4\n",
"3\n3\n",
"4\n4\n",
"3\n0\n3\n4\n5\n5\n2\n",
"3\n2\n",
"3\n0\n3\n5\n5\n4\n2\n",
"3\n4\n",
"2\n0\n4\n5\n5\n5\n7\n",
"4\n5\n",
"3\n0\n4\n3\n5\n5\n3\n",
"3\n5\n",
"2\n3\n",
"3\n0\n3\n4\n5\n3\n2\n",
"2\n0\n3\n5\n4\n5\n2\n",
"3\n0\n4\n3\n5\n5\n2\n",
"2\n0\n4\n5\n5\n5\n3\n",
"3\n0\n2\n4\n5\n5\n3\n",
"2\n0\n2\n5\n5\n5\n2\n",
"3\n0\n3\n5\n4\n5\n2\n",
"2\n0\n3\n5\n5\n5\n1\n",
"2\n0\n3\n5\n6\n5\n2\n",
"2\n0\n4\n5\n5\n4\n3\n",
"2\n4\n",
"5\n5\n",
"3\n0\n3\n4\n5\n5\n3\n",
"4\n3\n",
"3\n0\n3\n5\n5\n5\n3\n",
"4\n3\n",
"3\n0\n3\n5\n5\n5\n2\n",
"3\n0\n3\n5\n5\n5\n2\n",
"3\n0\n3\n5\n5\n5\n2\n",
"2\n0\n3\n5\n5\n5\n2\n",
"2\n0\n3\n5\n5\n5\n2\n",
"5\n5\n",
"3\n0\n4\n5\n5\n5\n3\n",
"5\n5\n",
"4\n3\n",
"3\n0\n3\n4\n5\n5\n3\n",
"3\n0\n3\n5\n5\n5\n3\n",
"4\n3\n",
"3\n0\n3\n5\n5\n5\n2\n",
"3\n0\n3\n5\n5\n5\n2\n",
"2\n0\n3\n5\n5\n5\n2\n",
"2\n0\n3\n5\n5\n5\n2\n",
"2\n0\n3\n5\n5\n5\n2\n",
"3\n0\n3\n3\n5\n5\n2\n",
"3\n0\n3\n5\n5\n5\n4\n",
"3\n0\n3\n4\n5\n5\n3\n",
"4\n3\n",
"3\n0\n4\n5\n5\n5\n3\n",
"5\n4\n",
"2\n0\n3\n5\n5\n5\n2\n",
"3\n3\n",
"3\n0\n3\n5\n5\n4\n2\n",
"3\n0\n3\n5\n5\n5\n2\n",
"2\n0\n3\n5\n5\n5\n2\n",
"2\n0\n3\n5\n5\n5\n2\n",
"3\n5\n",
"4\n5\n",
"3\n0\n4\n3\n5\n5\n3\n",
"3\n5\n",
"2\n3\n",
"3\n0\n4\n5\n5\n5\n3\n",
"3\n3\n",
"5\n4\n",
"3\n2\n",
"3\n0\n3\n5\n5\n4\n2\n",
"2\n0\n3\n5\n4\n5\n2\n",
"3\n0\n4\n3\n5\n5\n3\n",
"3\n5\n",
"4\n5\n",
"3\n0\n4\n3\n5\n5\n3\n",
"3\n3\n",
"3\n0\n2\n4\n5\n5\n3\n"
]
}
|
Tired of boring office work, Denis decided to open a fast food restaurant.
On the first day he made a portions of dumplings, b portions of cranberry juice and c pancakes with condensed milk.
The peculiarity of Denis's restaurant is the procedure of ordering food. For each visitor Denis himself chooses a set of dishes that this visitor will receive. When doing so, Denis is guided by the following rules:
* every visitor should receive at least one dish (dumplings, cranberry juice, pancakes with condensed milk are all considered to be dishes);
* each visitor should receive no more than one portion of dumplings, no more than one portion of cranberry juice and no more than one pancake with condensed milk;
* all visitors should receive different sets of dishes.
What is the maximum number of visitors Denis can feed?
Input
The first line contains an integer t (1 ≤ t ≤ 500) — the number of test cases to solve.
Each of the remaining t lines contains integers a, b and c (0 ≤ a, b, c ≤ 10) — the number of portions of dumplings, the number of portions of cranberry juice and the number of condensed milk pancakes Denis made.
Output
For each test case print a single integer — the maximum number of visitors Denis can feed.
Example
Input
7
1 2 1
0 0 0
9 1 7
2 2 3
2 3 2
3 2 2
4 4 4
Output
3
0
4
5
5
5
7
Note
In the first test case of the example, Denis can feed the first visitor with dumplings, give the second a portion of cranberry juice, and give the third visitor a portion of cranberry juice and a pancake with a condensed milk.
In the second test case of the example, the restaurant Denis is not very promising: he can serve no customers.
In the third test case of the example, Denise can serve four visitors. The first guest will receive a full lunch of dumplings, a portion of cranberry juice and a pancake with condensed milk. The second visitor will get only dumplings. The third guest will receive a pancake with condensed milk, and the fourth guest will receive a pancake and a portion of dumplings. Please note that Denis hasn't used all of the prepared products, but is unable to serve more visitors.
|
{
"inputs": [
"6\n5 0\n10 0\n12 -4\n10 -8\n5 -8\n3 -4\n",
"4\n0 0\n0 1\n1 1\n1 0\n",
"4\n-100000 -100000\n-99999 -99999\n100000 99999\n0 -100\n",
"4\n0 0\n1 100\n100 0\n1 -100\n",
"4\n-1000000000 1000000000\n1000000000 500000000\n1000000000 -1000000000\n-500000000 -1000000000\n",
"4\n-10000 -10000\n-9999 -9999\n10000 9999\n0 -1000\n",
"4\n-1000000000 -1000000000\n-999999999 -999999999\n1000000000 999999999\n0 -1\n",
"5\n0 0\n0 10\n10 10\n20 0\n10 -1\n",
"4\n1000000000 1000000000\n1000000000 -1000000000\n-1000000000 -1000000000\n-1000000000 1000000000\n",
"4\n2 0\n0 0\n0 14\n8 14\n",
"5\n10 -1\n0 0\n0 10\n10 10\n20 0\n",
"4\n-1000000000 -1000000000\n-1000000000 1000000000\n1000000000 1000000000\n1000000000 -1000000000\n",
"4\n0 0\n0 10\n10 10\n6 4\n",
"19\n449447997 711296339\n530233434 692216537\n535464528 613140435\n535533467 100893188\n530498867 -265063956\n519107979 -271820709\n482156929 -287792333\n-303730271 -287970295\n-416935204 -263348201\n-443613873 -249980523\n-453444829 -173903413\n-462102798 -80789280\n-462064673 -13220755\n-461368561 482595837\n-457749751 687048095\n-448625206 709399396\n-145117181 710688825\n159099640 711650577\n400454061 711503381\n",
"4\n0 0\n1 100\n100 1\n1 -100\n",
"4\n-1000000000 1000000000\n1000000000 500000000\n0000000000 -1000000000\n-500000000 -1000000000\n",
"4\n1000000000 1000000000\n1000000000 -1000000000\n-1000000000 -1000000000\n-1000000000 1000001000\n",
"4\n3 0\n0 0\n0 14\n8 14\n",
"4\n0 0\n0 10\n5 10\n6 4\n",
"6\n5 0\n9 0\n12 -4\n10 -8\n5 -8\n3 -4\n",
"4\n0 0\n1 1\n1 1\n1 0\n",
"4\n-1000000000 1000000000\n1000100000 500000000\n0000000000 -1000000000\n-500000000 -1000000000\n",
"4\n1100000000 1000000000\n1000000000 -1000000000\n-1000000000 -1000000000\n-1000000000 1000001000\n",
"4\n3 0\n1 0\n0 14\n8 14\n",
"5\n6 -1\n0 0\n0 10\n10 10\n20 1\n",
"4\n0 0\n0 10\n1 10\n6 4\n",
"4\n-1000000000 1000000000\n1000100001 500000000\n0000000000 -1000000000\n-500000000 -1000000000\n",
"4\n1100000000 1000000000\n1001000000 -1000000000\n-1000000000 -1000000000\n-1000000000 1000001000\n",
"4\n-1000000000 -1000000000\n-1000000000 1000000000\n1000001000 1001000000\n1000000000 -1000000000\n",
"4\n-1000000000 1000000000\n1001100001 500000000\n0000000000 -1000000000\n-500000000 -1000000000\n",
"4\n3 0\n1 0\n0 27\n10 14\n",
"4\n-1000000000 1000000000\n1001100001 500000000\n0000000000 -1000000000\n-668567170 -1000000000\n",
"5\n-1 0\n0 10\n10 1\n10 0\n3 -1\n",
"4\n5 0\n1 0\n0 27\n10 14\n",
"5\n-1 -1\n0 10\n10 1\n10 0\n3 -1\n",
"4\n5 0\n2 1\n0 17\n10 14\n",
"5\n-1 -1\n0 0\n10 1\n10 0\n6 -1\n",
"4\n5 -1\n2 1\n0 17\n10 25\n",
"5\n-1 -1\n0 0\n10 2\n10 1\n6 -1\n",
"4\n5 -1\n2 0\n0 17\n10 25\n",
"4\n7 -1\n2 1\n0 17\n10 25\n",
"4\n7 0\n2 1\n0 17\n10 25\n",
"4\n7 0\n0 1\n0 17\n10 25\n",
"4\n7 0\n0 1\n1 17\n10 25\n",
"4\n7 0\n0 0\n1 17\n10 25\n",
"5\n-1 0\n0 10\n10 10\n20 0\n10 -1\n",
"5\n6 -1\n0 0\n0 10\n10 10\n20 0\n",
"4\n-1000000000 -1000000000\n-1000000000 1000000000\n1000001000 1000000000\n1000000000 -1000000000\n",
"4\n0 0\n1 100\n101 1\n1 -100\n",
"5\n-1 0\n0 10\n10 10\n31 0\n10 -1\n",
"4\n-1000000000 -1000000000\n-1000000000 1000000001\n1000001000 1000000000\n1000000000 -1000000000\n",
"4\n1 0\n1 100\n101 1\n1 -100\n",
"5\n-1 0\n0 10\n10 10\n10 0\n10 -1\n",
"4\n3 0\n1 0\n0 27\n8 14\n",
"4\n1 -1\n1 100\n101 1\n1 -100\n",
"5\n-1 0\n0 10\n10 1\n10 0\n10 -1\n",
"4\n1 -1\n1 100\n100 1\n1 -100\n",
"4\n1 -1\n1 100\n100 1\n1 -64\n",
"4\n5 0\n2 0\n0 27\n10 14\n",
"4\n1 -1\n1 100\n101 1\n1 -64\n",
"5\n-1 -1\n0 1\n10 1\n10 0\n3 -1\n",
"4\n5 0\n2 0\n0 17\n10 14\n",
"4\n1 -1\n1 100\n101 1\n1 -3\n",
"5\n-1 -1\n0 0\n10 1\n10 0\n3 -1\n",
"4\n1 -1\n1 000\n101 1\n1 -3\n",
"4\n5 0\n2 1\n0 17\n10 25\n",
"4\n1 -1\n1 100\n101 1\n1 -2\n",
"5\n-1 -1\n0 0\n10 2\n10 0\n6 -1\n",
"4\n1 -1\n1 100\n101 2\n1 -2\n",
"4\n1 -1\n1 000\n101 2\n1 -2\n",
"4\n1 -1\n1 010\n101 2\n1 -2\n",
"4\n1 -1\n1 000\n101 2\n1 -1\n",
"4\n1 -1\n1 100\n101 2\n1 -1\n",
"4\n1 -1\n1 100\n001 2\n1 -1\n"
],
"outputs": [
"1.00000000\n",
"0.35355339\n",
"0.00000177\n",
"0.50000000\n",
"530330085.88991064\n",
"0.00001768\n",
"0.00000000\n",
"0.50000000\n",
"707106781.18654752\n",
"0.86824314\n",
"0.50000000\n",
"707106781.18654752\n",
"0.70710678\n",
"24967.13949733\n",
"0.5\n",
"176776695.29663688\n",
"707106604.4098742\n",
"1.302364713186689\n",
"1.7677669529663689\n",
"0.9922778767136676\n",
"0.0\n",
"176770802.8383395\n",
"689655172.4137931\n",
"0.894427190999916\n",
"0.649189020270599\n",
"0.35355339059327373\n",
"176770802.7794159\n",
"690000000.0\n",
"706930203.4146422\n",
"176711889.00379845\n",
"0.8411784753765535\n",
"223401634.58330497\n",
"0.3535533905932737\n",
"1.682356950753107\n",
"0.18107149208503706\n",
"1.2979650903611306\n",
"0.31687511114881484\n",
"1.1776330006588163\n",
"0.35082320772281167\n",
"1.3114549325518636\n",
"1.9675654176982917\n",
"2.1213203435596424\n",
"3.0459984420343584\n",
"2.6153846153846154\n",
"2.6925824035672523\n",
"0.5\n",
"0.5\n",
"707106604.4098742\n",
"0.5\n",
"0.5\n",
"707106604.4098742\n",
"0.0\n",
"0.0\n",
"0.894427190999916\n",
"0.0\n",
"0.0\n",
"0.0\n",
"0.0\n",
"1.302364713186689\n",
"0.0\n",
"0.18107149208503706\n",
"1.302364713186689\n",
"0.0\n",
"0.18107149208503706\n",
"0.0\n",
"1.2979650903611306\n",
"0.0\n",
"0.31687511114881484\n",
"0.0\n",
"0.0\n",
"0.0\n",
"0.0\n",
"0.0\n",
"0.0\n"
]
}
|
You are given a convex polygon P with n distinct vertices p1, p2, ..., pn. Vertex pi has coordinates (xi, yi) in the 2D plane. These vertices are listed in clockwise order.
You can choose a real number D and move each vertex of the polygon a distance of at most D from their original positions.
Find the maximum value of D such that no matter how you move the vertices, the polygon does not intersect itself and stays convex.
Input
The first line has one integer n (4 ≤ n ≤ 1 000) — the number of vertices.
The next n lines contain the coordinates of the vertices. Line i contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line).
Output
Print one real number D, which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.
Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.
Namely, let's assume that your answer is a and the answer of the jury is b. The checker program will consider your answer correct if <image>.
Examples
Input
4
0 0
0 1
1 1
1 0
Output
0.3535533906
Input
6
5 0
10 0
12 -4
10 -8
5 -8
3 -4
Output
1.0000000000
Note
Here is a picture of the first sample
<image>
Here is an example of making the polygon non-convex.
<image>
This is not an optimal solution, since the maximum distance we moved one point is ≈ 0.4242640687, whereas we can make it non-convex by only moving each point a distance of at most ≈ 0.3535533906.
|
{
"inputs": [
"8\n10 3\n100 4\n8 7\n97 2\n8 8\n3 10\n5 3\n1000000000 9\n",
"8\n10 3\n100 4\n8 7\n97 2\n8 8\n3 10\n5 3\n1000000000 9\n",
"7\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n",
"8\n10 3\n100 8\n8 7\n97 2\n8 8\n3 10\n5 3\n1000000000 9\n",
"7\n1 1\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n",
"8\n10 3\n100 4\n8 7\n97 2\n8 8\n3 3\n5 3\n1000000000 9\n",
"8\n10 3\n100 8\n8 7\n172 2\n8 8\n3 10\n5 3\n1000000000 9\n",
"8\n10 3\n100 4\n8 7\n97 2\n8 8\n3 3\n5 2\n1000000000 9\n",
"8\n10 3\n100 8\n8 7\n172 2\n8 8\n3 10\n5 3\n1000000000 18\n",
"7\n1 1\n1 2\n1 2\n0 2\n1 1\n1 2\n1 2\n",
"8\n13 3\n100 4\n8 7\n97 2\n8 8\n3 3\n5 2\n1000000000 9\n",
"8\n13 3\n110 4\n8 7\n97 2\n8 8\n3 3\n5 2\n1000000000 9\n",
"7\n1 1\n1 2\n1 2\n1 1\n1 1\n1 2\n1 2\n",
"8\n10 3\n100 8\n8 12\n172 2\n8 8\n3 2\n5 3\n1010000000 18\n",
"7\n1 1\n1 2\n2 2\n1 1\n1 1\n1 2\n1 2\n",
"8\n13 3\n110 4\n12 7\n97 2\n1 8\n3 3\n5 2\n1000000000 9\n",
"8\n10 3\n100 8\n8 12\n143 2\n8 8\n3 2\n5 3\n1010000000 18\n",
"8\n10 3\n100 8\n8 12\n143 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 3\n100 8\n16 12\n143 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 5\n100 8\n21 12\n143 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 5\n100 13\n21 12\n143 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 5\n100 6\n21 12\n143 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 3\n100 4\n8 7\n42 2\n8 8\n3 10\n5 3\n1000000000 9\n",
"7\n1 2\n1 2\n1 3\n1 2\n1 2\n1 2\n1 2\n",
"8\n10 3\n100 6\n8 7\n97 2\n8 8\n3 10\n5 3\n1000000000 9\n",
"8\n20 3\n100 8\n8 7\n97 2\n8 8\n3 10\n5 3\n1000000000 9\n",
"8\n10 3\n100 4\n9 7\n97 2\n8 8\n3 3\n5 3\n1000000000 9\n",
"8\n10 3\n100 8\n8 7\n190 2\n8 8\n3 10\n5 3\n1000000000 9\n",
"8\n19 3\n100 4\n8 7\n97 2\n8 8\n3 3\n5 2\n1000000000 9\n",
"8\n12 3\n100 8\n8 7\n172 2\n8 8\n3 10\n5 3\n1000000000 18\n",
"8\n10 3\n100 4\n8 7\n97 2\n8 8\n2 3\n5 2\n1000000000 9\n",
"8\n10 3\n110 8\n8 7\n172 2\n8 8\n3 2\n5 3\n1000000000 18\n",
"7\n1 1\n1 2\n2 2\n0 1\n1 1\n1 2\n1 2\n",
"8\n10 3\n100 8\n8 12\n172 2\n8 8\n3 2\n5 3\n1000000000 17\n",
"7\n1 1\n1 2\n1 2\n1 1\n1 1\n2 2\n1 2\n",
"8\n10 3\n100 8\n8 12\n172 2\n8 8\n3 2\n5 3\n1010000000 24\n",
"8\n10 5\n100 8\n8 12\n143 2\n8 8\n3 2\n5 3\n1010000000 18\n",
"8\n10 3\n100 8\n16 12\n143 2\n8 1\n3 2\n1 3\n1010000000 18\n",
"8\n10 5\n100 13\n21 12\n143 2\n8 8\n3 2\n1 3\n1010000000 8\n",
"8\n10 5\n100 3\n21 12\n143 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 3\n100 4\n8 7\n42 2\n8 8\n3 10\n5 3\n1000000000 15\n",
"7\n1 2\n1 2\n1 3\n1 2\n1 2\n2 2\n1 2\n",
"8\n20 3\n100 8\n8 7\n97 2\n8 8\n3 10\n5 3\n1000000000 10\n",
"7\n1 1\n1 2\n2 2\n1 2\n1 2\n1 2\n0 2\n",
"8\n10 3\n100 8\n8 7\n190 1\n8 8\n3 10\n5 3\n1000000000 9\n",
"8\n19 3\n100 4\n8 7\n97 2\n13 8\n3 3\n5 2\n1000000000 9\n",
"8\n12 3\n100 8\n8 7\n172 2\n8 11\n3 10\n5 3\n1000000000 18\n",
"8\n10 3\n110 8\n8 7\n172 2\n8 8\n3 2\n10 3\n1000000000 18\n",
"8\n13 3\n110 4\n8 7\n97 2\n18 8\n3 3\n5 2\n1000000000 9\n",
"8\n10 3\n100 8\n8 12\n172 2\n8 11\n3 2\n5 3\n1000000000 17\n",
"7\n1 1\n1 2\n1 2\n1 1\n1 2\n2 2\n1 2\n",
"8\n13 3\n110 4\n7 7\n97 2\n8 8\n3 3\n5 4\n1000000000 9\n",
"8\n13 3\n100 8\n8 12\n172 2\n8 8\n3 2\n5 3\n1010000000 24\n",
"8\n10 3\n100 8\n16 3\n143 2\n8 1\n3 2\n1 3\n1010000000 18\n",
"8\n1 3\n100 8\n16 12\n9 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 5\n100 8\n21 12\n143 2\n8 8\n3 2\n0 3\n1010000000 2\n",
"8\n10 5\n100 13\n21 12\n143 2\n10 8\n3 2\n1 3\n1010000000 8\n",
"8\n10 5\n100 6\n21 12\n143 2\n4 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 3\n100 4\n8 7\n42 2\n7 8\n3 10\n5 3\n1000000000 15\n",
"8\n20 3\n100 13\n8 7\n97 2\n8 8\n3 10\n5 3\n1000000000 10\n",
"7\n1 1\n1 2\n2 2\n1 2\n1 2\n2 2\n0 2\n",
"8\n10 3\n100 4\n0 7\n97 2\n8 8\n3 3\n5 3\n1000000010 9\n",
"8\n10 3\n100 13\n8 7\n190 1\n8 8\n3 10\n5 3\n1000000000 9\n",
"8\n19 3\n100 4\n8 7\n97 2\n26 8\n3 3\n5 2\n1000000000 9\n",
"8\n12 3\n101 8\n8 7\n172 2\n8 11\n3 10\n5 3\n1000000000 18\n",
"8\n10 3\n100 4\n8 14\n97 2\n8 1\n2 3\n5 2\n1000000000 9\n",
"8\n13 3\n110 4\n8 7\n97 2\n18 8\n3 3\n10 2\n1000000000 9\n",
"8\n10 3\n100 8\n8 12\n172 2\n8 11\n3 2\n9 3\n1000000000 17\n",
"8\n13 3\n110 4\n7 7\n97 2\n8 8\n3 2\n5 4\n1000000000 9\n",
"8\n13 3\n100 8\n8 12\n172 2\n8 4\n3 2\n5 3\n1010000000 24\n",
"7\n2 1\n1 2\n2 2\n0 1\n1 1\n1 3\n1 2\n",
"8\n1 3\n100 8\n12 12\n9 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 5\n100 8\n21 12\n143 2\n8 8\n3 3\n2 3\n1010000000 18\n",
"8\n10 5\n100 8\n21 12\n143 2\n12 8\n3 2\n0 3\n1010000000 2\n",
"8\n7 5\n100 13\n21 12\n143 2\n10 8\n3 2\n1 3\n1010000000 8\n",
"8\n10 5\n100 6\n21 11\n143 2\n4 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 3\n100 4\n8 7\n42 2\n7 8\n3 10\n3 3\n1000000000 15\n",
"8\n20 3\n100 13\n8 7\n97 2\n8 8\n3 10\n5 3\n0000000000 10\n",
"7\n1 1\n1 2\n0 2\n1 2\n1 2\n2 2\n0 2\n",
"7\n1 1\n1 2\n1 2\n0 2\n1 2\n1 2\n1 2\n",
"8\n10 3\n100 8\n8 7\n172 2\n8 8\n3 2\n5 3\n1000000000 18\n",
"7\n1 1\n1 2\n1 2\n0 1\n1 1\n1 2\n1 2\n",
"8\n10 3\n100 8\n8 12\n172 2\n8 8\n3 2\n5 3\n1000000000 18\n",
"8\n13 3\n110 4\n12 7\n97 2\n8 8\n3 3\n5 2\n1000000000 9\n",
"8\n10 3\n100 8\n21 12\n143 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"7\n1 1\n1 2\n1 2\n1 2\n1 2\n1 2\n0 2\n",
"8\n13 3\n110 4\n8 7\n97 2\n13 8\n3 3\n5 2\n1000000000 9\n",
"8\n13 3\n110 4\n12 7\n97 2\n8 8\n3 3\n5 4\n1000000000 9\n",
"7\n1 1\n1 2\n2 2\n1 1\n1 1\n1 3\n1 2\n",
"8\n13 3\n110 4\n12 7\n97 2\n1 8\n3 3\n0 2\n1000000000 9\n",
"8\n10 3\n100 8\n16 12\n9 2\n8 8\n3 2\n1 3\n1010000000 18\n",
"8\n10 3\n100 8\n21 12\n143 2\n8 8\n3 2\n2 3\n1010000000 18\n",
"8\n10 5\n100 8\n21 12\n143 2\n8 8\n3 2\n0 3\n1010000000 18\n",
"8\n10 3\n100 4\n0 7\n97 2\n8 8\n3 3\n5 3\n1000000000 9\n",
"8\n10 3\n100 4\n8 14\n97 2\n8 8\n2 3\n5 2\n1000000000 9\n",
"7\n1 1\n1 2\n2 2\n0 1\n1 1\n1 2\n0 2\n",
"7\n1 1\n1 2\n2 2\n0 1\n1 1\n1 3\n1 2\n",
"8\n13 3\n110 4\n12 7\n97 2\n2 8\n3 3\n0 2\n1000000000 9\n",
"8\n10 5\n100 8\n21 12\n143 2\n8 8\n3 2\n2 3\n1010000000 18\n",
"7\n1 2\n1 3\n1 3\n1 2\n1 2\n2 2\n1 2\n",
"8\n10 3\n110 8\n8 12\n172 2\n8 8\n3 2\n10 3\n1000000000 18\n",
"7\n1 1\n1 2\n2 2\n0 1\n1 1\n1 3\n0 2\n",
"7\n1 1\n1 2\n1 2\n1 1\n0 2\n2 2\n1 2\n"
],
"outputs": [
"yes\n2 2 6\nyes\n1 1 1 97\nno\nno\nyes\n1 1 1 1 1 1 1 1\nno\nyes\n1 1 3\nyes\n2 2 2 2 2 2 2 2 999999984\n",
"yes\n2 2 6\nyes\n1 1 1 97\nno\nno\nyes\n1 1 1 1 1 1 1 1\nno\nyes\n1 1 3\nyes\n2 2 2 2 2 2 2 2 999999984\n",
"no\nno\nno\nno\nno\nno\nno\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n1\nNO\nNO\nNO\nYES\n1\nNO\nNO\n",
"YES\n1 1 11\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1\nNO\nNO\nYES\n1\nYES\n1\nNO\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n1\nNO\nYES\n1 1\nYES\n1\nYES\n1\nNO\nNO\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nNO\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nYES\n1 1 1 1 1 1 1 1 1 1 1 5\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 2 2 2\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 76\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 95\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nYES\n1 41\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 95\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 16\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 97\nYES\n1 1 1 1 1 1 3\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 189\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1 1 17\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 8\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 103\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n1\nNO\nYES\n1 1\nNO\nYES\n1\nNO\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 999999968\n",
"YES\n1\nNO\nNO\nYES\n1\nYES\n1\nYES\n1 1\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999977\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nYES\n1 1 1 1 1 1 1 1 1 1 1 5\nNO\nYES\n8\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 2 2 2\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 76\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1009999993\n",
"YES\n2 2 2 2 2\nYES\n2 2 96\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nYES\n1 41\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 999999972\n",
"NO\nNO\nNO\nNO\nNO\nYES\n1 1\nNO\n",
"YES\n2 2 16\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 999999991\n",
"YES\n1\nNO\nYES\n1 1\nNO\nNO\nNO\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n190\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1 1 17\nYES\n1 1 1 97\nNO\nNO\nNO\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 8\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nNO\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 103\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n2 2 6\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nYES\n1 1 1 1 1 1 1 11\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nNO\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 999999968\n",
"YES\n1\nNO\nNO\nYES\n1\nNO\nYES\n1 1\nNO\n",
"YES\n1 1 11\nYES\n1 1 1 107\nYES\n1 1 1 1 1 1 1\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1 1 11\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999977\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nYES\n2 2 12\nNO\nYES\n8\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"NO\nYES\n1 1 1 1 1 1 1 93\nYES\n1 1 1 1 1 1 1 1 1 1 1 5\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1009999999\n",
"YES\n2 2 2 2 2\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 76\nNO\nNO\nYES\n1 1 1 1 1 1 1 3\nNO\nNO\nYES\n1 1 1 1 1 1 1 1009999993\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 95\nNO\nNO\nNO\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nYES\n1 41\nNO\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 999999972\n",
"YES\n2 2 16\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 76\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 999999991\n",
"YES\n1\nNO\nYES\n1 1\nNO\nNO\nYES\n1 1\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999994\n",
"YES\n2 2 6\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 76\nNO\nYES\n190\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1 1 17\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 19\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 8\nNO\nNO\nYES\n1 171\nNO\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nNO\nYES\n8\nNO\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nYES\n1 1 1 1 1 1 1 11\nYES\n1 1 1\nYES\n1 9\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nNO\nNO\nYES\n1 1 7\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 999999968\n",
"YES\n1 1 11\nYES\n1 1 1 107\nYES\n1 1 1 1 1 1 1\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1 1 11\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 5\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999977\n",
"YES\n2\nNO\nYES\n1 1\nNO\nYES\n1\nNO\nNO\n",
"NO\nYES\n1 1 1 1 1 1 1 93\nYES\n1 1 1 1 1 1 1 1 1 1 1 1\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 5\nNO\nNO\nYES\n1 1009999999\n",
"YES\n1 1 1 1 3\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 76\nNO\nNO\nYES\n1 1 1 1 1 1 1 3\nNO\nNO\nYES\n1 1 1 1 1 1 1 1009999993\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 95\nYES\n1 1 1 1 1 1 1 1 1 1 11\nNO\nNO\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nYES\n1 41\nNO\nNO\nYES\n1 1 1\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 2 2 999999972\n",
"YES\n2 2 16\nYES\n2 2 2 2 2 2 2 2 2 2 2 2 76\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nNO\n",
"YES\n1\nNO\nNO\nNO\nNO\nYES\n1 1\nNO\n",
"YES\n1\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n1\nNO\nNO\nNO\nYES\n1\nNO\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n1 1 3\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n1\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nNO\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1\nNO\nYES\n1 1\nYES\n1\nYES\n1\nNO\nNO\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nNO\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nYES\n1 1 1 1 1 1 1 1 1 1 1 5\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nYES\n1 1 1\nYES\n1 1 3\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 6\nYES\n1 1 1 97\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n1\nNO\nYES\n1 1\nNO\nYES\n1\nNO\nNO\n",
"YES\n1\nNO\nYES\n1 1\nNO\nYES\n1\nNO\nNO\n",
"YES\n1 1 11\nYES\n1 1 1 107\nNO\nNO\nNO\nYES\n1 1 1\nNO\nYES\n2 2 2 2 2 2 2 2 999999984\n",
"YES\n2 2 2 2 2\nYES\n1 1 1 1 1 1 1 93\nNO\nNO\nYES\n1 1 1 1 1 1 1 1\nNO\nNO\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1009999983\n",
"NO\nNO\nNO\nNO\nNO\nYES\n1 1\nNO\n",
"YES\n2 2 6\nYES\n1 1 1 1 1 1 1 103\nNO\nYES\n1 171\nYES\n1 1 1 1 1 1 1 1\nNO\nYES\n2 2 6\nYES\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 999999983\n",
"YES\n1\nNO\nYES\n1 1\nNO\nYES\n1\nNO\nNO\n",
"YES\n1\nNO\nNO\nYES\n1\nNO\nYES\n1 1\nNO\n"
]
}
|
You are given two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100). Represent the number n as the sum of k positive integers of the same parity (have the same remainder when divided by 2).
In other words, find a_1, a_2, …, a_k such that all a_i>0, n = a_1 + a_2 + … + a_k and either all a_i are even or all a_i are odd at the same time.
If such a representation does not exist, then report it.
Input
The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Next, t test cases are given, one per line.
Each test case is two positive integers n (1 ≤ n ≤ 10^9) and k (1 ≤ k ≤ 100).
Output
For each test case print:
* YES and the required values a_i, if the answer exists (if there are several answers, print any of them);
* NO if the answer does not exist.
The letters in the words YES and NO can be printed in any case.
Example
Input
8
10 3
100 4
8 7
97 2
8 8
3 10
5 3
1000000000 9
Output
YES
4 2 4
YES
55 5 5 35
NO
NO
YES
1 1 1 1 1 1 1 1
NO
YES
3 1 1
YES
111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111110 111111120
|
{
"inputs": [
"4 4\n2 4\n1 1\n2 3\n2 4",
"4 7\n2 4\n1 1\n2 3\n2 4",
"4 4\n2 4\n1 1\n2 0\n2 4",
"4 4\n3 4\n1 1\n2 3\n2 4",
"4 4\n2 4\n1 1\n2 0\n3 4",
"4 4\n1 4\n1 1\n2 0\n3 4",
"4 5\n0 4\n0 1\n4 5\n3 4",
"4 7\n2 4\n0 1\n2 3\n5 7",
"4 7\n1 3\n0 1\n4 1\n3 7",
"4 7\n2 4\n0 1\n2 3\n2 4",
"4 7\n2 4\n0 1\n4 3\n2 4",
"4 7\n2 4\n0 1\n4 5\n2 4",
"4 7\n2 4\n1 1\n2 1\n2 4",
"4 7\n2 4\n0 2\n2 3\n2 4",
"4 12\n2 4\n0 1\n4 3\n2 4",
"4 7\n2 4\n0 0\n4 5\n2 4",
"4 7\n2 4\n1 1\n2 1\n3 4",
"4 7\n2 4\n0 2\n2 1\n2 4",
"4 12\n0 4\n0 1\n4 3\n2 4",
"4 9\n2 4\n0 0\n4 5\n2 4",
"4 7\n1 4\n1 1\n2 1\n3 4",
"4 13\n2 4\n0 2\n2 1\n2 4",
"4 12\n0 2\n0 1\n4 3\n2 4",
"4 9\n2 4\n1 0\n4 5\n2 4",
"4 7\n1 4\n0 1\n2 1\n3 4",
"4 13\n2 6\n0 2\n2 1\n2 4",
"4 7\n1 4\n1 0\n2 1\n3 4",
"4 23\n2 6\n0 2\n2 1\n2 4",
"4 7\n1 4\n0 0\n2 1\n3 4",
"4 23\n2 3\n0 2\n2 1\n2 4",
"4 7\n1 4\n0 0\n2 1\n2 4",
"4 23\n2 3\n0 2\n2 2\n2 4",
"4 7\n1 4\n0 0\n2 2\n2 4",
"4 23\n2 3\n1 2\n2 1\n2 4",
"4 34\n2 3\n1 2\n2 1\n2 4",
"4 34\n2 3\n1 2\n2 1\n2 8",
"4 34\n2 3\n1 2\n2 2\n2 8",
"4 34\n2 3\n1 2\n2 2\n2 14",
"4 34\n2 3\n2 2\n2 2\n2 14",
"4 7\n2 4\n1 1\n0 3\n2 4",
"4 7\n2 4\n0 1\n4 3\n1 4",
"4 7\n0 4\n0 1\n4 5\n2 4",
"4 7\n2 4\n1 1\n1 1\n2 4",
"4 7\n2 4\n0 2\n2 3\n4 4",
"4 12\n2 4\n-1 1\n4 3\n2 4",
"4 7\n2 4\n-1 0\n4 5\n2 4",
"4 7\n2 4\n1 1\n0 1\n3 4",
"4 12\n0 4\n0 0\n4 3\n2 4",
"4 17\n2 4\n0 0\n4 5\n2 4",
"4 7\n1 3\n1 1\n2 1\n3 4",
"4 13\n0 4\n0 2\n2 1\n2 4",
"4 9\n0 2\n0 1\n4 3\n2 4",
"4 9\n2 4\n1 0\n2 5\n2 4",
"4 7\n1 4\n0 1\n2 2\n3 4",
"4 13\n2 6\n-1 2\n2 1\n2 4",
"4 23\n2 11\n0 2\n2 1\n2 4",
"4 23\n2 5\n0 2\n2 1\n2 4",
"4 7\n1 0\n0 0\n2 1\n2 4",
"4 7\n1 3\n0 0\n2 2\n2 4",
"4 23\n2 1\n1 2\n2 1\n2 4",
"4 34\n2 3\n1 2\n2 1\n1 4",
"4 34\n2 3\n1 1\n2 1\n2 8",
"4 34\n2 3\n0 2\n2 2\n2 8",
"4 34\n2 3\n1 2\n2 2\n2 28",
"4 61\n2 3\n2 2\n2 2\n2 14",
"4 7\n2 4\n0 1\n0 3\n2 4",
"4 7\n0 4\n0 1\n4 5\n3 4",
"4 7\n1 4\n1 1\n1 1\n2 4",
"4 7\n2 4\n0 2\n2 3\n5 4",
"4 12\n2 4\n-2 1\n4 3\n2 4",
"4 7\n2 4\n-1 0\n4 5\n2 1",
"4 7\n2 3\n1 1\n0 1\n3 4",
"4 12\n0 4\n0 0\n4 2\n2 4",
"4 17\n2 5\n0 0\n4 5\n2 4",
"4 7\n1 2\n1 1\n2 1\n3 4",
"4 13\n0 4\n0 2\n2 2\n2 4",
"4 9\n0 2\n1 1\n4 3\n2 4",
"4 9\n2 4\n1 0\n2 5\n2 1",
"4 7\n1 4\n0 1\n2 2\n3 3",
"4 13\n2 6\n-1 2\n2 1\n2 0",
"4 23\n2 11\n0 3\n2 1\n2 4",
"4 23\n2 7\n0 2\n2 1\n2 4",
"4 7\n1 0\n0 0\n2 1\n3 4",
"4 7\n1 3\n0 0\n2 2\n1 4",
"4 23\n2 1\n1 2\n2 0\n2 4",
"4 34\n2 3\n1 3\n2 1\n1 4",
"4 34\n2 3\n1 1\n2 1\n4 8",
"4 34\n2 3\n0 0\n2 2\n2 8",
"4 34\n2 3\n0 2\n2 2\n2 28",
"4 61\n2 3\n2 2\n2 2\n2 24",
"4 7\n2 4\n0 2\n0 3\n2 4",
"4 8\n1 4\n1 1\n2 0\n3 4",
"4 7\n1 4\n1 1\n1 1\n2 0",
"4 7\n2 4\n0 2\n2 0\n5 4",
"4 12\n2 2\n-2 1\n4 3\n2 4",
"4 7\n2 6\n1 1\n0 1\n3 4",
"4 12\n0 4\n0 1\n4 2\n2 4",
"4 17\n2 5\n0 0\n4 3\n2 4",
"4 7\n1 2\n1 0\n2 1\n3 4",
"4 13\n0 4\n0 2\n2 2\n2 0",
"4 9\n0 2\n1 1\n4 3\n2 5"
],
"outputs": [
"1\n3\n6\n-1",
"1\n2\n3\n4\n",
"1\n3\n4\n-1\n",
"1\n2\n5\n-1\n",
"1\n3\n4\n5\n",
"-1\n-1\n-1\n-1\n",
"1\n2\n-1\n-1\n",
"1\n2\n3\n7\n",
"1\n2\n3\n-1\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n",
"1\n2\n3\n4\n"
]
}
|
There is a grid of squares with H+1 horizontal rows and W vertical columns.
You will start at one of the squares in the top row and repeat moving one square right or down. However, for each integer i from 1 through H, you cannot move down from the A_i-th, (A_i + 1)-th, \ldots, B_i-th squares from the left in the i-th row from the top.
For each integer k from 1 through H, find the minimum number of moves needed to reach one of the squares in the (k+1)-th row from the top. (The starting square can be chosen individually for each case.) If, starting from any square in the top row, none of the squares in the (k+1)-th row can be reached, print `-1` instead.
Constraints
* 1 \leq H,W \leq 2\times 10^5
* 1 \leq A_i \leq B_i \leq W
Input
Input is given from Standard Input in the following format:
H W
A_1 B_1
A_2 B_2
:
A_H B_H
Output
Print H lines. The i-th line should contain the answer for the case k=i.
Example
Input
4 4
2 4
1 1
2 3
2 4
Output
1
3
6
-1
|
{
"inputs": [
"4\n0 0\n10 0\n10 10\n0 10",
"4\n0 0\n10 0\n10 4\n0 10",
"4\n0 0\n10 0\n10 2\n0 10",
"4\n0 0\n10 0\n10 2\n0 9",
"4\n0 0\n10 1\n10 2\n0 9",
"4\n0 0\n10 1\n10 2\n1 9",
"4\n0 0\n9 1\n10 2\n1 9",
"4\n0 0\n9 1\n10 4\n1 9",
"4\n0 0\n10 0\n14 10\n0 10",
"4\n0 0\n7 0\n10 4\n0 10",
"4\n0 0\n10 0\n10 2\n0 1",
"4\n0 0\n10 0\n19 2\n0 9",
"4\n0 0\n10 1\n10 2\n1 7",
"4\n0 -1\n9 1\n10 2\n1 9",
"4\n0 0\n9 1\n10 4\n1 7",
"4\n0 0\n10 0\n14 10\n0 19",
"4\n0 0\n7 0\n10 4\n-1 10",
"4\n0 0\n10 0\n19 3\n0 9",
"4\n0 0\n10 1\n10 2\n1 1",
"4\n0 -1\n9 0\n10 2\n1 9",
"4\n0 0\n9 1\n10 7\n1 7",
"4\n0 0\n10 0\n11 10\n0 19",
"4\n0 0\n7 0\n10 4\n-1 18",
"4\n0 0\n10 0\n19 3\n0 13",
"4\n0 0\n10 1\n10 2\n0 1",
"4\n0 -2\n9 0\n10 2\n1 9",
"4\n0 0\n10 0\n11 10\n0 22",
"4\n1 0\n7 0\n10 4\n-1 18",
"4\n0 0\n10 0\n19 3\n0 7",
"4\n-1 0\n10 0\n10 2\n0 1",
"4\n0 -2\n9 1\n10 2\n1 9",
"4\n0 0\n10 0\n11 20\n0 22",
"4\n1 0\n7 -1\n10 4\n-1 18",
"4\n-1 0\n10 0\n19 3\n0 7",
"4\n-1 0\n10 0\n6 2\n0 1",
"4\n0 0\n10 0\n11 20\n0 24",
"4\n1 0\n7 -1\n10 4\n0 18",
"4\n0 0\n10 -1\n19 3\n0 7",
"4\n-1 0\n10 1\n6 2\n0 1",
"4\n0 0\n10 0\n13 20\n0 24",
"4\n2 0\n7 -1\n10 4\n0 18",
"4\n-1 0\n10 -1\n19 3\n0 7",
"4\n-2 0\n10 1\n6 2\n0 1",
"4\n0 0\n13 0\n13 20\n0 24",
"4\n2 0\n7 -1\n15 4\n0 18",
"4\n-2 0\n10 1\n6 2\n0 2",
"4\n1 0\n13 0\n13 20\n0 24",
"4\n2 0\n7 -1\n26 4\n0 18",
"4\n1 0\n13 0\n5 20\n0 24",
"4\n2 0\n7 -1\n26 4\n0 24",
"4\n1 1\n13 0\n5 20\n0 24",
"4\n2 0\n7 -1\n26 0\n0 24",
"4\n2 0\n13 0\n5 20\n0 24",
"4\n2 1\n7 -1\n26 0\n0 24",
"4\n2 0\n13 1\n5 20\n0 24",
"4\n2 1\n7 -1\n26 0\n1 24",
"4\n2 0\n13 1\n5 34\n0 24",
"4\n1 1\n7 -1\n26 0\n1 24",
"4\n2 0\n13 0\n5 34\n0 24",
"4\n0 1\n7 -1\n26 0\n1 24",
"4\n2 0\n7 0\n5 34\n0 24",
"4\n0 1\n7 -1\n26 -1\n1 24",
"4\n2 0\n7 0\n5 18\n0 24",
"4\n0 1\n2 -1\n26 -1\n1 24",
"4\n0 0\n7 0\n5 18\n0 24",
"4\n0 1\n2 0\n26 -1\n1 24",
"4\n0 0\n7 0\n5 18\n1 24",
"4\n0 1\n0 0\n26 -1\n1 24",
"4\n0 0\n11 0\n5 18\n1 24",
"4\n0 1\n0 0\n26 -1\n1 27",
"4\n0 0\n6 0\n5 18\n1 24",
"4\n0 1\n0 0\n32 -1\n1 27",
"4\n-1 0\n6 0\n5 18\n1 24",
"4\n0 1\n0 0\n32 -1\n0 27",
"4\n-1 0\n6 0\n5 18\n2 24",
"4\n0 1\n1 0\n32 -1\n0 27",
"4\n-1 0\n6 0\n5 18\n0 24",
"4\n0 1\n1 0\n32 0\n0 27",
"4\n-1 0\n6 0\n5 21\n0 24",
"4\n0 1\n1 -1\n32 0\n0 27",
"4\n-1 0\n6 0\n5 21\n-1 24",
"4\n0 1\n0 -1\n32 0\n0 27",
"4\n-1 0\n10 0\n5 21\n-1 24",
"4\n0 1\n0 -1\n32 0\n0 41",
"4\n-1 0\n10 0\n5 21\n0 24",
"4\n-1 0\n10 0\n5 12\n0 24",
"4\n-2 0\n10 0\n5 12\n0 24",
"4\n0 3\n0 -1\n32 0\n1 41",
"4\n0 3\n0 -1\n32 0\n1 58",
"4\n1 3\n0 -1\n32 0\n1 58",
"4\n1 3\n0 0\n32 0\n1 58",
"4\n1 2\n0 0\n32 0\n1 58",
"4\n0 0\n10 0\n20 10\n0 10",
"4\n0 0\n10 0\n10 4\n0 11",
"4\n0 0\n10 0\n16 2\n0 10",
"4\n0 0\n10 0\n10 2\n0 18",
"4\n0 0\n10 1\n12 2\n1 9",
"4\n-1 0\n9 1\n10 2\n1 9",
"4\n1 0\n9 1\n10 4\n1 9",
"4\n0 0\n10 0\n14 10\n-1 10",
"4\n0 0\n7 1\n10 4\n0 10"
],
"outputs": [
"10\n14.142135623730950488",
"7.3178024859\n12.2065556157\n",
"6.7528910636\n11.6619037897\n",
"6.1868396755\n11.4127122105\n",
"6.1660587942\n10.7703296143\n",
"6.3319736848\n10.2437469572\n",
"6.3592985397\n9.7717758522\n",
"6.7506203352\n9.8478424033\n",
"10.0000000000\n16.4155227683\n",
"7.5414879701\n11.8726576637\n",
"1.5791710028\n10.1118742081\n",
"6.6602126111\n19.1022362398\n",
"5.0371385701\n9.8871706604\n",
"7.0883223329\n9.8187078984\n",
"5.4519891971\n9.8773005015\n",
"12.9141922507\n21.3018147823\n",
"7.3985616901\n12.5602547745\n",
"6.9348871619\n19.0132808228\n",
"0.9434421125\n10.1788997441\n",
"7.1486885013\n10.5022526605\n",
"6.4536519800\n11.8300406350\n",
"10.7313936266\n20.6669440454\n",
"8.1729658770\n19.2732143174\n",
"9.4993501576\n19.1923670481\n",
"0.9950371902\n10.1980390272\n",
"7.8779261391\n10.7993270615\n",
"10.8078075790\n23.3327085709\n",
"7.4359622538\n19.4575352759\n",
"5.6122092638\n19.0022050040\n",
"1.5632995346\n11.0898844534\n",
"7.8155170208\n10.1796365358\n",
"10.5347368440\n24.1374221683\n",
"7.6064905586\n20.4787207544\n",
"5.6767725460\n19.6234369992\n",
"1.7499181755\n9.4001745330\n",
"10.5607924443\n25.8736244938\n",
"7.5983861748\n20.0407181150\n",
"6.1666928800\n19.0163947345\n",
"1.2208460311\n10.0000000000\n",
"11.7315871420\n25.4961154515\n",
"6.8470629658\n20.1692507731\n",
"6.2358092575\n19.7119393255\n",
"1.1694260437\n10.0000000000\n",
"13.0000000000\n26.7956515958\n",
"10.0906086830\n19.8894218203\n",
"1.5797704667\n10.7307390393\n",
"12.4639187260\n27.0217247990\n",
"13.8056152393\n25.2352927465\n",
"8.7517159567\n25.4330548259\n",
"16.6560722899\n27.1506920150\n",
"8.6034806664\n25.1007625580\n",
"15.2803734922\n28.4107892908\n",
"8.0461130661\n25.6028698478\n",
"14.8958996453\n28.4735949158\n",
"8.1783693661\n24.9836858127\n",
"15.1870215537\n27.9654146132\n",
"9.0442809301\n33.6913539884\n",
"15.5221325143\n27.7576242139\n",
"8.9402894993\n34.0028621836\n",
"15.8418399900\n28.0635884809\n",
"5.3529688703\n34.0961519508\n",
"15.4970320685\n28.5478803455\n",
"4.6948586919\n24.7692475663\n",
"16.3832349802\n28.4701246924\n",
"5.9350608974\n24.5411007292\n",
"15.5754795625\n28.6745207264\n",
"5.6165399846\n24.2912021111\n",
"15.6623862872\n28.6426047271\n",
"7.9652754383\n24.5675090312\n",
"16.8573233451\n29.9961232856\n",
"5.0784274975\n24.2361429481\n",
"17.8258740641\n34.6950108051\n",
"5.7222123349\n24.1715871428\n",
"17.5875776052\n35.1318943412\n",
"5.4281454621\n24.0468293128\n",
"17.5532697506\n35.1448036922\n",
"6.0620320011\n24.3733973832\n",
"17.7605590535\n34.7371864022\n",
"6.0783305245\n24.4415757471\n",
"18.5361986599\n34.5457160027\n",
"6.4844125068\n24.7538664909\n",
"18.5325932244\n34.5398320783\n",
"8.6778229891\n25.2395553893\n",
"21.5035766519\n44.4775224130\n",
"8.4149910546\n24.8322496967\n",
"7.6512372707\n24.4182308941\n",
"8.3763308254\n24.3310501212\n",
"21.7190307038\n44.1128806801\n",
"22.1801323709\n60.3850782041\n",
"21.4212657165\n60.4958929772\n",
"21.2392535817\n60.0287343254\n",
"21.2333562461\n60.0309571347\n",
"10.0000000000\n21.3600093633\n",
"7.8545205930\n12.9417001706\n",
"7.2065910839\n16.1753091161\n",
"7.5735886660\n18.8378395134\n",
"6.4159876843\n11.7382528024\n",
"6.5604451378\n10.3055265812\n",
"6.6170165710\n10.0947670101\n",
"10.0000000000\n16.4359024361\n",
"7.3275553128\n10.8932669712\n"
]
}
|
Fair Chocolate-Cutting
You are given a flat piece of chocolate of convex polygon shape. You are to cut it into two pieces of precisely the same amount with a straight knife.
Write a program that computes, for a given convex polygon, the maximum and minimum lengths of the line segments that divide the polygon into two equal areas.
The figures below correspond to first two sample inputs. Two dashed lines in each of them correspond to the equal-area cuts of minimum and maximum lengths.
<image>
Figure F.1. Sample Chocolate Pieces and Cut Lines
Input
The input consists of a single test case of the following format.
$n$
$x_1$ $y_1$
...
$x_n$ $y_n$
The first line has an integer $n$, which is the number of vertices of the given polygon. Here, $n$ is between 3 and 5000, inclusive. Each of the following $n$ lines has two integers $x_i$ and $y_i$, which give the coordinates ($x_i, y_i$) of the $i$-th vertex of the polygon, in counterclockwise order. Both $x_i$ and $y_i$ are between 0 and 100 000, inclusive.
The polygon is guaranteed to be simple and convex. In other words, no two edges of the polygon intersect each other and interior angles at all of its vertices are less than $180^\circ$.
Output
Two lines should be output. The first line should have the minimum length of a straight line segment that partitions the polygon into two parts of the equal area. The second line should have the maximum length of such a line segment. The answer will be considered as correct if the values output have an absolute or relative error less than $10^{-6}$.
Sample Input 1
4
0 0
10 0
10 10
0 10
Sample Output 1
10
14.142135623730950488
Sample Input 2
3
0 0
6 0
3 10
Sample Output 2
4.2426406871192851464
10.0
Sample Input 3
5
0 0
99999 20000
100000 70000
33344 63344
1 50000
Sample Output 3
54475.580091580027976
120182.57592539864775
Sample Input 4
6
100 350
101 349
6400 3440
6400 3441
1200 7250
1199 7249
Sample Output 4
4559.2050019027964982
6216.7174287968524227
Example
Input
4
0 0
10 0
10 10
0 10
Output
10
14.142135623730950488
|
{
"inputs": [
"2\na b\na c\nc d\n\nSAMPLE",
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jmztqzhhgk\nlvvycvhfuw tuacnmroow\nbzdxlxnify goftuinook\noyndzyanjf pupkkegthi\njnqirauxks vdwzfjegog\nsgeyfnadqx deksokytli\nvpqdmejpcy qrccokdwti\ngeoudpjpox imoohodkjo\nistgnzgkyn expabfujkg\nqarmfmzawi hpnwkiudmj\nskrfyvhnsd cckqwnvxrv\nfuqithmeun cfebblaxqq\ntjyuplczrh wtjswcujbh\nkhfhdqoops wdesiofofq\nlzcosnwtjk bayxgovlyd\ncvjkwwlkyj jknxhcgooq\nhqxxxvxvsm pxijilihtc\nyltleijpii meqogjqrpa\nowyayplryk qsmmeijyev\nsfwqtseczr pdaujzzlvz\nnngbinrstc dqcokzlwvu\ndmdbzrvooe paurupcgmb\ntkjafxrpth wsnyagbnqv\nsfavfdbiec domojxjzmn\nktpgrbmmqb rgmtfahbpu\ntacldiqwmo okurvaqlqb\niulfdajhhv eteanzxixc\nxwdyfchtvg spvdjbthlj\nhyibssazaq xebwppdkim\nxcbusxxnwp dphqtalngs\nkkntiusyzs crbigmowzx\ngnjfrgunhy lbqbmfzwft\nipfytafzvy lyaqoaddhz\nhanajvfagm lbpucpmqme\nmdkymcetvj hnjgbvjngg\nmcfvbasztk lxfwpcxigy\ngtdccujwaq omnwbullgt\nkrpgiuzoax hkbexbdjuu\ndmikyazete yzczcfnmma\ntondzbjami eeupsjfkcj\nnbzantdlqn mjigonoymv\nuazyocnilm jkwdxpkprk\nekfjctnjns fsndruzogn\nvkpyhgbzvc qnknwkrvtf\nspvqoihhtv xgdcusywke\nmkklqevywi ccvyceszxp\nkczcpxicat zbubdcbats\nzujxbiwwwr yvyiwyolhp\nsuadgkwwlu aoixmrpkay\nblxbnuidoz vrcnrlqpxk\nfwpxwgmuhg jqirrtznew\nyxhtpckrue mgpzjjshuj\nkleaouoyky yxqsijpchk\ncuzmlwmkbq gccovfbjsn\nvleavmegnl amersfcuha\ntjbkqewmnf nrqxhdwcin\ncdwkinoxee lgfnkdxvmb\nrvdnhdekap gtpzfqrriu\nwoiqlwpeyq blveqmjwbr\ngbwintitvf titiwvqecc\nxlalhlycwg ldcszciczv\nbmvuvjryoj nilxbvuxls\nxkpkqelcxy locznwqhpv\nbwfekzxgon omtgitwpmi\noqplmmkyeh laudvphrsn\nsimdvfduma wyrmjiwxbb\nmdxaryukpk uneaqywyeb\nbfadldndim fxwtfbxggk\nyvtuuxsvwx qokyzvghwm\ncuqvfbrbcl kxmucauyog\noezffaqokb pavkbvmqfe\nlogjxjjiuu qzgqtyaxus\nrlymmrnzwt bseoraledr\nvwjmzejcwr pcuviafpja\nhjrhlfqbbm ekqmtlywyd\naggwunakzc rjpjbylzce\nqwisbzvkkb hifwovdnnv\noqjqtndsev kqqparlpoy\ntedhlshxuq ccdhnzicbh\nmdtzedtbfp zobjunxivg\nongiumxshk mefmcqyngg\nhihzgjyvtx zbggmbxrsl\nsjfkmuxvze qvvwluunfi\nqsmgxgujgw scrtowaqab\ncxweubnpru vieovjfmwt\nvlayxyrvpw pksafqzdqg\ninyerarxpi 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tjbkqewmnf\nktpgrbmmqb cdwkinoxee\ntacldiqwmo rvdnhdekap\niulfdajhhv woiqlwpeyq\nxwdyfchtvg gbwintitvf\nhyibssazaq xlalhlycwg\nxcbusxxnwp bmvuvjryoj\nkkntiusyzs xkpkqelcxy\ngnjfrgunhy bwfekzxgon\nipfytafzvy oqplmmkyeh\nhanajvfagm simdvfduma\nmdkymcetvj mdxaryukpk\nmcfvbasztk bfadldndim\ngtdccujwaq yvtuuxsvwx\nkrpgiuzoax cuqvfbrbcl\ndmikyazete oezffaqokb\ntondzbjami logjxjjiuu\nnbzantdlqn rlymmrnzwt\nuazyocnilm vwjmzejcwr\nekfjctnjns hjrhlfqbbm\nvkpyhgbzvc aggwunakzc\nspvqoihhtv qwisbzvkkb\nmkklqevywi oqjqtndsev\nlzcosnwtjk kkntiusyzs\ncvjkwwlkyj gnjfrgunhy\nhqxxxvxvsm ipfytafzvy\nyltleijpii hanajvfagm\nowyayplryk mdkymcetvj\nsfwqtseczr mcfvbasztk\nnngbinrstc gtdccujwaq\ndmdbzrvooe krpgiuzoax\ntkjafxrpth dmikyazete\nsfavfdbiec tondzbjami\nktpgrbmmqb nbzantdlqn\ntacldiqwmo uazyocnilm\niulfdajhhv ekfjctnjns\nxwdyfchtvg vkpyhgbzvc\nhyibssazaq spvqoihhtv\nxcbusxxnwp mkklqevywi\nlzcosnwtjk tkjafxrpth\ncvjkwwlkyj sfavfdbiec\nhqxxxvxvsm ktpgrbmmqb\nyltleijpii tacldiqwmo\nowyayplryk iulfdajhhv\nsfwqtseczr xwdyfchtvg\nnngbinrstc hyibssazaq\ndmdbzrvooe xcbusxxnwp\nlzcosnwtjk owyayplryk\ncvjkwwlkyj sfwqtseczr\nhqxxxvxvsm nngbinrstc\nyltleijpii dmdbzrvooe\nlzcosnwtjk hqxxxvxvsm\ncvjkwwlkyj yltleijpii\nlzcosnwtjk cvjkwwlkyj",
"2\na b\na c\nc d\n\nELPMAS",
"2\n` d\n` b\nb f\n\nPKESAM",
"2\na b\na c\nc e\n\nSAMPLE",
"12\nlzcosnwtjk xcjunvtpwu\ncvjkwwlkyj jyjzvkopkt\nhqxxxvxvsm oaettnnxsn\nyltleijpii taddtwjkhq\nowyayplryk gamjhfquwe\nsfwqtseczr clpbsurgox\nnngbinrstc beuwpgazlm\ndmdbzrvooe sodttxayqp\ntkjafxrpth yugxdvihim\nsfavfdbiec fimvhmtjte\nktpgrbmmqb pqstnzulvo\ntacldiqwmo qywspwioip\niulfdajhhv seauwsgswe\nxwdyfchtvg qfdfsxxcne\nhyibssazaq rlotxuhzyv\nxcbusxxnwp qwmepsphnw\nkkntiusyzs reomvztlbu\ngnjfrgunhy rbntbmolxq\nipfytafzvy mcnvknvvpz\nhanajvfagm ofcjvaapjd\nmdkymcetvj jmvtsahcbm\nmcfvbasztk owektymnhq\ngtdccujwaq rqanclxrtx\nkrpgiuzoax adnsfchncw\ndmikyazete ivujyrzqwy\ntondzbjami qwhlgqguqz\nnbzantdlqn thjpwayuch\nuazyocnilm esiavbajzh\nekfjctnjns triuzbvyod\nvkpyhgbzvc edqrghngve\nspvqoihhtv gmqvlphhdg\nmkklqevywi lerjloimbc\nkczcpxicat twncvhgbhs\nzujxbiwwwr dyyvniugax\nsuadgkwwlu jpprslbowd\nblxbnuidoz vryfaaanxs\nfwpxwgmuhg corxgyekfc\nyxhtpckrue idkmtgygwt\nkleaouoyky ibsgeoancd\ncuzmlwmkbq wgqyuhspyq\nvleavmegnl xgpnihbnqx\ntjbkqewmnf maidznwoot\ncdwkinoxee 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"2\na b\na c\nc e\n\nELPMAS",
"2\na b\na c\nc e\n\nEKPMAS",
"2\na b\na c\nb e\n\nEKPMAS",
"2\na b\na c\nb f\n\nEKPMAS",
"2\na b\na b\nb f\n\nEKPMAS",
"2\na b\na b\nb f\n\nEKPSAM",
"2\na c\na b\nb f\n\nEKPSAM",
"2\na c\na b\nb f\n\nPKESAM",
"2\na d\na b\nb f\n\nPKESAM",
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"2\na c\na c\nc d\n\nSAMPLE",
"2\na b\na c\nc e\n\nEKPLAS",
"2\na c\na b\nb f\n\nMASPKE",
"2\na c\na b\nc d\n\nSAMPLE",
"2\na b\na c\nc f\n\nEKPLAS",
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iulfdajhhv\nsfwqtseczr xwdyfchtvg\nnngbinrstc hyibssazaq\ndmdbzrvooe xcbusxxnwp\nlzcosnwtjk owyayplryk\ncvjkwwlkyj sfwqtseczr\nhqxxxvxvsm nngbinrstc\nyltleijpii dmdbzrvooe\nlzcosnwtjk hqxxxvxvsm\ncvjkwwlkyj yltleijpii\nlzcosnwtjk cvjkwwlkyj",
"2\na b\na c\nc d\n\nELPMAT",
"2\na b\na c\nc d\n\nSAMQLE",
"2\na b\na c\nb e\n\nELPMAS",
"2\na b\na c\nb d\n\nEKPMAS",
"2\na b\na b\na f\n\nEKPSAM",
"2\na d\na b\nb f\n\nMASEKP",
"2\na c\na d\nc d\n\nSAMPLE",
"2\na c\na b\nb f\n\nMASPKF",
"2\na b\na c\nc f\n\nEKPLAT",
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"2\na d\na b\nb e\n\nMASEKP",
"2\na c\na d\nc c\n\nSAMPLE",
"2\na c\na b\nb g\n\nMASPKF",
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"2\na d\na b\nb e\n\nPKESAM",
"2\na c\na d\nc c\n\nSAMLPE",
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"2\na c\na c\nc e\n\nELPMAS",
"2\na b\na c\nc f\n\nEKPMAS",
"2\na c\na b\nb f\n\nEKPMAS",
"2\na d\na b\na f\n\nPKESAM",
"2\na b\na c\nc f\n\nEKPL@S",
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"2\na b\na c\nc d\n\nSAMRLE",
"2\na b\na b\na f\n\nMASPKE",
"2\na d\na b\nb f\n\nNASEKP",
"2\na c\na d\nc e\n\nSAMPLE",
"2\na c\na b\nb f\n\nFKPSAM",
"2\na b\na c\nc f\n\nEKPLAR",
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"2\na b\na b\nb g\n\nMASPKF",
"2\na d\na b\nb e\n\nPKERAM",
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"2\na c\na b\nb f\n\nSKPMAE",
"2\na d\na b\na e\n\nPKESAM",
"2\na b\na c\nc f\n\nE@PLKS",
"2\na b\na c\nc e\n\nSAMRLE",
"2\na b\na c\na f\n\nEKPSAM",
"2\na e\na b\nb f\n\nNASEKP",
"2\na c\na d\nc e\n\nSAMOLE",
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"2\na b\na b\na g\n\nMASPKF",
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"2\na e\na b\na e\n\nPKESAM",
"2\na b\na c\nc g\n\nE@PLKS",
"2\na b\na c\nc e\n\nSAMRKE",
"2\na b\na c\na e\n\nEKPSAM",
"2\na f\na b\nb f\n\nNASEKP",
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"2\na b\na b\na g\n\nFKPSAM",
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"2\na e\na b\na e\n\nQKESAM",
"2\na b\na c\nc g\n\nSKLP@E",
"2\na b\na c\nb e\n\nEKPSAM",
"2\na e\na b\na e\n\nMASEKQ",
"2\na e\na b\na e\n\nMESAKQ",
"2\na e\na c\na e\n\nMESAKQ",
"2\na e\na c\na e\n\nMDSAKQ",
"2\na e\na c\na e\n\nMDASKQ",
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"2\na b\na c\nc d\n\nSAEPLM",
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"2\na b\na c\nc e\n\nELPLAS",
"2\na b\na c\nc c\n\nELPMAS",
"2\na b\na c\nb e\n\nSAMPKE",
"2\na b\na c\nb f\n\nSAMPKE",
"2\na b\na b\nb f\n\nSAMPKE",
"2\na c\na c\nc e\n\nSAMPLE",
"2\na b\na c\nc e\n\nEKQLAS",
"2\na c\na b\nb g\n\nMASPKE",
"2\na c\na b\nc c\n\nSAMPLE",
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lvvycvhfuw\npynjpsrzsx bzdxlxnify\nodwygzhgrr oyndzyanjf\naglhwxzmdx jnqirauxks\nvtrvehiczd sgeyfnadqx\nacayxfyujb vpqdmejpcy\nfneuvvjyol geoudpjpox\nfayrqkzron istgnzgkyn\ngxxhgnnwar qarmfmzawi\ndxqoqwyypu skrfyvhnsd\nnjnhnotjqd fuqithmeun\nqwsbfxmtbe tjyuplczrh\nytedhzyneq khfhdqoops\nlzcosnwtjk tedhlshxuq\ncvjkwwlkyj mdtzedtbfp\nhqxxxvxvsm ongiumxshk\nyltleijpii hihzgjyvtx\nowyayplryk sjfkmuxvze\nsfwqtseczr qsmgxgujgw\nnngbinrstc cxweubnpru\ndmdbzrvooe vlayxyrvpw\ntkjafxrpth inyerarxpi\nsfavfdbiec bsvmmawbgu\nktpgrbmmqb vpjoewfrgt\ntacldiqwmo sbkuygwpjo\niulfdajhhv doctpfjwxi\nxwdyfchtvg lvoifrixif\nhyibssazaq bauevpmevd\nxcbusxxnwp lhrcuiuwyk\nkkntiusyzs jnagpunmqc\ngnjfrgunhy haxgjlnoba\nipfytafzvy qdwsmwrjrx\nhanajvfagm wpwcakwvfp\nmdkymcetvj hsxrqksczi\nmcfvbasztk ozisrmxqjj\ngtdccujwaq zjfgburlyq\nkrpgiuzoax sklfbnjmjf\ndmikyazete zfxpgatogw\ntondzbjami juxzxvwqik\nnbzantdlqn aqqbbwhdnp\nuazyocnilm irkskpxaug\nekfjctnjns fpziwdrdan\nvkpyhgbzvc wuvyutiuxb\nspvqoihhtv ubjpxcqigd\nmkklqevywi wuoihaqvmc\nkczcpxicat qmnnwgawxb\nzujxbiwwwr iogwrtqirw\nsuadgkwwlu lbzhygvwud\nblxbnuidoz hjoxhquyfx\nfwpxwgmuhg iphtabnsrg\nyxhtpckrue rjhmvnqkwe\nkleaouoyky hvfpzwrlmi\ncuzmlwmkbq oygfqtcijv\nvleavmegnl rrwweagfsb\ntjbkqewmnf tjpyerbrrt\ncdwkinoxee phoqsgfkwc\nrvdnhdekap mvzabofbhp\nwoiqlwpeyq isjszafcie\ngbwintitvf epszrlpehe\nxlalhlycwg fkpkotwksn\nbmvuvjryoj jyzhdoabqb\nxkpkqelcxy qxsscghlgp\nbwfekzxgon nmfaorfazu\noqplmmkyeh fyyhtupqyp\nsimdvfduma ktujclislm\nmdxaryukpk pynjpsrzsx\nbfadldndim odwygzhgrr\nyvtuuxsvwx aglhwxzmdx\ncuqvfbrbcl vtrvehiczd\noezffaqokb acayxfyujb\nlogjxjjiuu fneuvvjyol\nrlymmrnzwt fayrqkzron\nvwjmzejcwr gxxhgnnwar\nhjrhlfqbbm dxqoqwyypu\naggwunakzc njnhnotjqd\nqwisbzvkkb qwsbfxmtbe\noqjqtndsev ytedhzyneq\nlzcosnwtjk kczcpxicat\ncvjkwwlkyj zujxbiwwwr\nhqxxxvxvsm suadgkwwlu\nyltleijpii blxbnuidoz\nowyayplryk fwpxwgmuhg\nsfwqtseczr yxhtpckrue\nnngbinrstc kleaouoyky\ndmdbzrvooe cuzmlwmkbq\ntkjafxrpth vleavmegnl\nsfavfdbiec tjbkqewmnf\nktpgrbmmqb cdwkinoxee\ntacldiqwmo rvdnhdekap\niulfdajhhv woiqlwpeyq\nxwdyfchtvg gbwintitvf\nhyibssazaq xlalhlycwg\nxcbusxxnwp bmvuvjryoj\nkkntiusyzs xkpkqelcxy\ngnjfrgunhy bwfekzxgon\nipfytafzvy oqplmmkyeh\nhanajvfagm simdvfduma\nmdkymcetvj mdxaryukpk\nmcfvbasztk bfadldndim\ngtdccujwaq yvtuuxsvwx\nkrpgiuzoax cuqvfbrbcl\ndmikyazete oezffaqokb\ntondzbjami logjxjjiuu\nnbzantdlqn rlymmrnzwt\nuazyocnilm vwjmzejcwr\nekfjctnjns hjrhlfqbbm\nvkpyhgbzvc aggwunakzc\nspvqoihhtv qwisbzvkkb\nmkklqevywi oqjqtndsev\nlzcosnwtjk kkntiusyzs\ncvjkwwlkyj gnjfrgunhy\nhqxxxvxvsm ipfytafzvy\nyltleijpii hanajvfagm\nowyayplryk mdkymcetvj\nsfwqtseczr mcfvbasztk\nnngbinrstc gtdccujwaq\ndmdbzrvooe krpgiuzoax\ntkjafxrpth dmikyazete\nsfavfdbiec tondzbjami\nktpgrbmmqb nbzantdlqn\ntacldiqwmo uazyocnilm\niulfdajhhv ekfjctnjns\nxwdyfchtvg vkpyhgbzvc\nhyibssazaq spvqoihhtv\nxcbusxxnwp mkklqevywi\nlzcosnwtjk tkjafxrpth\ncvjkwwlkyj sfavfdbiec\nhqxxxvxvsm ktpgrbmmqb\nyltleijpii tacldiqwmo\nowyayplryk iulfdajhhv\nsfwqtseczr xwdyfchtvg\nnngbinrstc hyibssazaq\ndmdbzrvooe xcbusxxnwp\nlzcosnwtjk owyayplryk\ncvjkwwlkyj sfwqtseczr\nhqxxxvxvsm nngbinrstc\nyltleijpii dmdbzrvooe\nlzcosnwtjk hqxxxvxvsm\ncvjkwwlkyj yltleijpii\nlzcosnwtjk cvjkwwlkyj",
"2\na b\na c\nc d\n\nDLPMAT",
"2\na b\na c\nc c\n\nSAMQLE"
],
"outputs": [
"a\n",
"fovjpmznym\n",
"lzcosnwtjk\n",
"fovjpmznym\n",
"lzcosnwtjk\n",
"a\n",
"`\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"fovjpmznym\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"fovjpmznym\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"fovjpmznym\n",
"lzcosnwtjk\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"a\n",
"lzcosnwtjk\n",
"a\n",
"a\n"
]
}
|
Several drivers had lined up for the Drag Racing Competition at the Tokyo Drift Street. Dom had organized the competition, but he was not available during all the races and hence he did not know their results. In the drag race match, 2 drivers race against each other and one of them is the winner, and the loser gets eliminated - there were no ties. The competition takes place as a knockout tournament. There are a total of N rounds, and the number of players in the tournament are 2^N. Dom's friend Letty gave him the results of all the races in this format:
A B - denoting: Match was between A and B, and the winner was A.
Note: The results are not ordered.
Input:
First line contains a single positive integer N.
2^N - 1 lines follow - Each line contains details of a match.
Output:
Print the name of the driver who won the Drag Racing Competition.
Constraints:
1 ≤ N ≤ 15
Names of drivers do not contain more than 15 characters.
(Candidates solving the question in Python or C++ will be given preference)
SAMPLE INPUT
2
a b
a c
c d
SAMPLE OUTPUT
a
Explanation
Consider [a, b, c, d] to be the drivers.
c eliminates d.
a eliminates c.
a eliminates b.
Hence, a is the winner.
|
{
"inputs": [
"9 4\n",
"8 3\n",
"1 1\n",
"26 6\n",
"3 4\n",
"2 4\n",
"2 3\n",
"800019998 40000\n",
"77792 2\n",
"123456789 13456\n",
"147268968 2\n",
"4 3\n",
"7 2\n",
"2 1\n",
"7 3\n",
"999961559 44720\n",
"3 2\n",
"3 3\n",
"20492 2\n",
"1000000000 10\n",
"5 2\n",
"1 3\n",
"33989 18\n",
"3 1\n",
"1000000000 29\n",
"1000000000 1\n",
"13 4\n",
"1 88999\n",
"13736 3\n",
"813491792 78123\n",
"4 1\n",
"49725 4\n",
"4 2\n",
"16 4\n",
"2 2\n",
"140089944 2\n",
"85300 2\n",
"849600011 46\n",
"1000000000 30\n",
"2333 3\n",
"1000000000 3\n",
"4 4\n",
"3 8\n",
"1000000000 100000\n",
"1 2\n",
"42180 2\n",
"1 4\n",
"6 4\n",
"77792 3\n",
"147268968 4\n",
"11 2\n",
"14 3\n",
"34025 2\n",
"1000100000 10\n",
"33989 27\n",
"1000001000 29\n",
"14623 3\n",
"5 1\n",
"28877 4\n",
"201743995 2\n",
"85300 3\n",
"1356764191 46\n",
"1000000000 39\n",
"2333 6\n",
"1010000000 3\n",
"10 3\n",
"42180 4\n",
"9 3\n",
"13 3\n",
"11 4\n",
"77792 4\n",
"147268968 1\n",
"18 3\n",
"14 4\n",
"1031 2\n",
"0000100000 10\n",
"33989 48\n",
"0000001000 29\n",
"14623 5\n",
"10 1\n",
"44565 4\n",
"6583280 2\n",
"85300 4\n",
"1356764191 69\n",
"1000000000 70\n",
"10 4\n",
"42180 5\n",
"19 4\n",
"64582 4\n",
"18 1\n",
"27 4\n",
"2002 2\n",
"0000100000 18\n",
"21213 48\n",
"0000101000 29\n",
"6 3\n",
"14623 4\n",
"15 1\n",
"17119 4\n",
"2 8\n",
"2 6\n",
"8945386 13456\n",
"5 3\n",
"999961559 76187\n",
"1 7\n",
"1 5\n",
"2 5\n",
"1283498613 78123\n",
"7 4\n",
"16 7\n",
"0 3\n",
"7 5\n",
"6 8\n",
"1000010000 100000\n",
"1 6\n",
"3 6\n",
"0 8\n",
"4 8\n",
"15298847 13456\n",
"1601439176 76187\n",
"0 7\n",
"1 10\n",
"4 5\n",
"588650690 78123\n",
"1 8\n",
"16 10\n",
"13 5\n",
"18 6\n",
"1 9\n",
"9 6\n",
"0 5\n",
"5 4\n",
"0 15\n",
"378052 13456\n",
"1601439176 75240\n",
"2 10\n",
"625302413 78123\n"
],
"outputs": [
"NO\n",
"NO\n",
"YES\n1 ",
"YES\n1 2 4 5 6 8 ",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n38895 38897 ",
"YES\n2447 2448 2449 2450 2451 2452 2453 2454 2455 2456 2457 2458 2459 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 2470 2471 2472 2473 2474 2475 2476 2477 2478 2479 2480 2481 2482 2483 2484 2485 2486 2487 2488 2489 2490 2491 2492 2493 2494 2495 2496 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 2542 2543 2544 2545 2546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 2585 2586 2587 2588 2589 2590 2591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 2634 2635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648 2649 2650 2651 2652 2653 2654 2655 2656 2657 2658 2659 2660 2661 2662 2663 2664 2665 2666 2667 2668 2669 2670 2671 2672 2673 2674 2675 2676 2677 2678 2679 2680 2681 2682 2683 2684 2685 2686 2687 2688 2689 2690 2691 2692 2693 2694 2695 2696 2697 2698 2699 2700 2701 2702 2703 2704 2705 2706 2707 2708 2709 2710 2711 2712 2713 2714 2715 2716 2717 2718 2719 2720 2721 2722 2723 2724 2725 2726 2727 2728 2729 2730 2731 2732 2733 2734 2735 2736 2737 2738 2739 2740 2741 2742 2743 2744 2745 2746 2747 2748 2749 2750 2751 2752 2753 2754 2755 2756 2757 2758 2759 2760 2761 2762 2763 2764 2765 2766 2767 2768 2769 2770 2771 2772 2773 2774 2775 2776 2777 2778 2779 2780 2781 2782 2783 2784 2785 2786 2787 2788 2789 2790 2791 2792 2793 2794 2795 2796 2797 2798 2799 2800 2801 2802 2803 2804 2805 2806 2807 2808 2809 2810 2811 2812 2813 2814 2815 2816 2817 2818 2819 2820 2821 2822 2823 2824 2825 2826 2827 2828 2829 2830 2831 2832 2833 2834 2835 2836 2837 2838 2839 2840 2841 2842 2843 2844 2845 2846 2847 2848 2849 2850 2851 2852 2853 2854 2855 2856 2857 2858 2859 2860 2861 2862 2863 2864 2865 2866 2867 2868 2869 2870 2871 2872 2873 2874 2875 2876 2877 2878 2879 2880 2881 2882 2883 2884 2885 2886 2887 2888 2889 2890 2891 2892 2893 2894 2895 2896 2897 2898 2899 2900 2901 2902 2903 2904 2905 2906 2907 2908 2909 2910 2911 2912 2913 2914 2915 2916 2917 2918 2919 2920 2921 2922 2923 2924 2925 2926 2927 2928 2929 2930 2931 2932 2933 2934 2935 2936 2937 2938 2939 2940 2941 2942 2943 2944 2945 2946 2947 2948 2949 2950 2951 2952 2953 2954 2955 2956 2957 2958 2959 2960 2961 2962 2963 2964 2965 2966 2967 2968 2969 2970 2971 2972 2973 2974 2975 2976 2977 2978 2979 2980 2981 2982 2983 2984 2985 2986 2987 2988 2989 2990 2991 2992 2993 2994 2995 2996 2997 2998 2999 3000 3001 3002 3003 3004 3005 3006 3007 3008 3009 3010 3011 3012 3013 3014 3015 3016 3017 3018 3019 3020 3021 3022 3023 3024 3025 3026 3027 3028 3029 3030 3031 3032 3033 3034 3035 3036 3037 3038 3039 3040 3041 3042 3043 3044 3045 3046 3047 3048 3049 3050 3051 3052 3053 3054 3055 3056 3057 3058 3059 3060 3061 3062 3063 3064 3065 3066 3067 3068 3069 3070 3071 3072 3073 3074 3075 3076 3077 3078 3079 3080 3081 3082 3083 3084 3085 3086 3087 3088 3089 3090 3091 3092 3093 3094 3095 3096 3097 3098 3099 3100 3101 3102 3103 3104 3105 3106 3107 3108 3109 3110 3111 3112 3113 3114 3115 3116 3117 3118 3119 3120 3121 3122 3123 3124 3125 3126 3127 3128 3129 3130 3131 3132 3133 3134 3135 3136 3137 3138 3139 3140 3141 3142 3143 3144 3145 3146 3147 3148 3149 3150 3151 3152 3153 3154 3155 3156 3157 3158 3159 3160 3161 3162 3163 3164 3165 3166 3167 3168 3169 3170 3171 3172 3173 3174 3175 3176 3177 3178 3179 3180 3181 3182 3183 3184 3185 3186 3187 3188 3189 3190 3191 3192 3193 3194 3195 3196 3197 3198 3199 3200 3201 3202 3203 3204 3205 3206 3207 3208 3209 3210 3211 3212 3213 3214 3215 3216 3217 3218 3219 3220 3221 3222 3223 3224 3225 3226 3227 3228 3229 3230 3231 3232 3233 3234 3235 3236 3237 3238 3239 3240 3241 3242 3243 3244 3245 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14521 14522 14523 14524 14525 14526 14527 14528 14529 14530 14531 14532 14533 14534 14535 14536 14537 14538 14539 14540 14541 14542 14543 14544 14545 14546 14547 14548 14549 14550 14551 14552 14553 14554 14555 14556 14557 14558 14559 14560 14561 14562 14563 14564 14565 14566 14567 14568 14569 14570 14571 14572 14573 14574 14575 14576 14577 14578 14579 14580 14581 14582 14583 14584 14585 14586 14587 14588 14589 14590 14591 14592 14593 14594 14595 14596 14597 14598 14599 14600 14601 14602 14603 14604 14605 14606 14607 14608 14609 14610 14611 14612 14613 14614 14615 14616 14617 14618 14619 14620 14621 14622 14623 14624 14625 14626 14627 14628 14629 14630 14631 14632 14633 14634 14635 14636 14637 14638 14639 14640 14641 14642 14643 14644 14645 14646 14647 14648 14649 14650 14651 14652 14653 14654 14655 14656 14657 14658 14659 14660 14661 14662 14663 14664 14665 14666 14667 14668 14669 14670 14671 14672 14673 14674 14675 14676 14677 14678 14679 14680 14681 14682 14683 14684 14685 14686 14687 14688 14689 14690 14691 14692 14693 14694 14695 14696 14697 14698 14699 14700 14701 14702 14703 14704 14705 14706 14707 14708 14709 14710 14711 14712 14713 14714 14715 14716 14717 14718 14719 14720 14721 14722 14723 14724 14725 14726 14727 14728 14729 14730 14731 14732 14733 14734 14735 14736 14737 14738 14739 14740 14741 14742 14743 14744 14745 14746 14747 14748 14749 14750 14751 14752 14753 14754 14755 14756 14757 14758 14759 14760 14761 14762 14763 14764 14765 14766 14767 14768 14769 14770 14771 14772 14773 14774 14775 14776 14777 14778 14779 14780 14781 14782 14783 14784 14785 14786 14787 14788 14789 14790 14791 14792 14793 14794 14795 14796 14797 14798 14799 14800 14801 14802 14803 14804 14805 14806 14807 14808 14809 14810 14811 14812 14813 14814 14815 14816 14817 14818 14819 14820 14821 14822 14823 14824 14825 14826 14827 14828 14829 14830 14831 14832 14833 14834 14835 14836 14837 14838 14839 14840 14841 14842 14843 14844 14845 14846 14847 14848 14849 14850 14851 14852 14853 14854 14855 14856 14857 14858 14859 14860 14861 14862 14863 14864 14865 14866 14867 14868 14869 14870 14871 14872 14873 14874 14875 14876 14877 14878 14879 14880 14881 14882 14883 14884 14885 14886 14887 14888 14889 14890 14891 14892 14893 14894 14895 14896 14897 14898 14899 14900 14901 14902 14903 14904 14905 14906 14907 14908 14909 14910 14911 14912 14913 14914 14915 14916 14917 14918 14919 14920 14921 14922 14923 14924 14925 14926 14927 14928 14929 14930 14931 14932 14933 14934 14935 14936 14937 14938 14939 14940 14941 14942 14943 14944 14945 14946 14947 14948 14949 14950 14951 14952 14953 14954 14955 14956 14957 14958 14959 14960 14961 14962 14963 14964 14965 14966 14967 14968 14969 14970 14971 14972 14973 14974 14975 14976 14977 14978 14979 14980 14981 14982 14983 14984 14985 14986 14987 14988 14989 14990 14991 14992 14993 14994 14995 14996 14997 14998 14999 15000 15001 15002 15003 15004 15005 15006 15007 15008 15009 15010 15011 15012 15013 15014 15015 15016 15017 15018 15019 15020 15021 15022 15023 15024 15025 15026 15027 15028 15029 15030 15031 15032 15033 15034 15035 15036 15037 15038 15039 15040 15041 15042 15043 15044 15045 15046 15047 15048 15049 15050 15051 15052 15053 15054 15055 15056 15057 15058 15059 15060 15061 15062 15063 15064 15065 15066 15067 15068 15069 15070 15071 15072 15073 15074 15075 15076 15077 15078 15079 15080 15081 15082 15083 15084 15085 15086 15087 15088 15089 15090 15091 15092 15093 15094 15095 15096 15097 15098 15099 15100 15101 15102 15103 15104 15105 15106 15107 15108 15109 15110 15111 15112 15113 15114 15115 15116 15117 15118 15119 15120 15121 15122 15123 15124 15125 15126 15127 15128 15129 15130 15131 15132 15133 15134 15135 15136 15137 15138 15139 15140 15141 15142 15143 15144 15145 15146 15147 15148 15149 15150 15151 15152 15153 15154 15155 15156 15157 15158 15159 15160 15161 15162 15163 15164 15165 15166 15167 15168 15169 15170 15171 15172 15173 15174 15175 15176 15177 15178 15179 15180 15181 15182 15183 15184 15185 15186 15187 15188 15189 15190 15191 15192 15193 15194 15195 15196 15197 15198 15199 15200 15201 15202 15203 15204 15205 15206 15207 15208 15209 15210 15211 15212 15213 15214 15215 15216 15217 15218 15219 15220 15221 15222 15223 15224 15225 15226 15227 15228 15229 15230 15231 15232 15233 15234 15235 15236 15237 15238 15239 15240 15241 15242 15243 15244 15245 15246 15247 15248 15249 15250 15251 15252 15253 15254 15255 15256 15257 15258 15259 15260 15261 15262 15263 15264 15265 15266 15267 15268 15269 15270 15271 15272 15273 15274 15275 15276 15277 15278 15279 15280 15281 15282 15283 15284 15285 15286 15287 15288 15289 15290 15291 15292 15293 15294 15295 15296 15297 15298 15299 15300 15301 15302 15303 15304 15305 15306 15307 15308 15309 15310 15311 15312 15313 15314 15315 15316 15317 15318 15319 15320 15321 15322 15323 15324 15325 15326 15327 15328 15329 15330 15331 15332 15333 15334 15335 15336 15337 15338 15339 15340 15341 15342 15343 15344 15345 15346 15347 15348 15349 15350 15351 15352 15353 15354 15355 15356 15357 15358 15359 15360 15361 15362 15363 15364 15365 15366 15367 15368 15369 15370 15371 15372 15373 15374 15375 15376 15377 15378 15379 15380 15381 15382 15383 15384 15385 15386 15387 15388 15389 15390 15391 15392 15393 15394 15395 15396 15397 15398 15399 15400 15401 15402 15403 15404 15405 15406 15407 15408 15409 15410 15411 15412 15413 15414 15415 15416 15417 15418 15419 15420 15421 15422 15423 15424 15425 15426 15427 15428 15429 15430 15431 15432 15433 15434 15435 15436 15437 15438 15439 15440 15441 15442 15443 15444 15445 15446 15447 15448 15449 15450 15451 15452 15453 15454 15455 15456 15457 15458 15459 15460 15461 15462 15463 15464 15465 15466 15467 15468 15469 15470 15471 15472 15473 15474 15475 15476 15477 15478 15479 15480 15481 15482 15483 15484 15485 15486 15487 15488 15489 15490 15491 15492 15493 15494 15495 15496 15497 15498 15499 15500 15501 15502 15503 15504 15505 15506 15507 15508 15509 15510 15511 15512 15513 15514 15515 15516 15517 15518 15519 15520 15521 15522 15523 15524 15525 15526 15527 15528 15529 15530 15531 15532 15533 15534 15535 15536 15537 15538 15539 15540 15541 15542 15543 15544 15545 15546 15547 15548 15549 15550 15551 15552 15553 15554 15555 15556 15557 15558 15559 15560 15561 15562 15563 15564 15565 15566 15567 15568 15569 15570 15571 15572 15573 15574 15575 15576 15577 15578 15579 15580 15581 15582 15583 15584 15585 15586 15587 15588 15589 15590 15591 15592 15593 15594 15595 15596 15597 15598 15599 15600 15601 15602 15603 15604 15605 15606 15607 15608 15609 15610 15611 15612 15613 15614 15615 15616 15617 15618 15619 15620 15621 15622 15623 15624 15625 15626 15627 15628 15629 15630 15631 15632 15633 15634 15635 15636 15637 15638 15639 15640 15641 15642 15643 15644 15645 15646 15647 15648 15649 15650 15651 15652 15653 15654 15655 15656 15657 15658 15659 15660 15661 15662 15663 15664 15665 15666 15667 15668 15669 15670 15671 15672 15673 15674 15675 15676 15677 15678 15679 15680 15681 15682 15683 15684 15685 15686 15687 15688 15689 15690 15691 15692 15693 15694 15695 15696 15697 15698 15699 15700 15701 15702 15703 15704 15705 15706 15707 15708 15709 15710 15711 15712 15713 15714 15715 15716 15717 15718 15719 15720 15721 15722 15723 15724 15725 15726 15727 15728 15729 15730 15731 15732 15733 15734 15735 15736 15737 15738 15739 15740 15741 15742 15743 15744 15745 15746 15747 15748 15749 15750 15751 15752 15753 15754 15755 15756 15757 15758 15759 15760 15761 15762 15763 15764 15765 15766 15767 15768 15769 15770 15771 15772 15773 15774 15775 15776 15777 15778 15779 15780 15781 15782 15783 15784 15785 15786 15787 15788 15789 15790 15791 15792 15793 15794 15795 15796 15797 15798 15799 15800 15801 15802 15803 15804 15805 15806 15807 15808 15809 15810 15811 15812 15813 15814 15815 15816 15817 15818 15819 15820 15821 15822 15823 15824 15825 15826 15827 15828 15829 15830 15831 15832 15833 15834 15835 15836 15837 15838 15839 15840 15841 15842 15843 15844 15845 15846 15847 15848 15849 15850 15851 15852 15853 15854 15855 15856 15857 15858 15859 15860 15861 15862 15863 15864 15865 15866 15867 15868 15869 15870 15871 15872 15873 15874 15875 15876 15877 15878 15879 15880 15881 15882 15883 15884 15885 15886 15887 15888 15889 15890 15891 15892 15893 15894 15895 15896 15897 15898 15899 15900 15901 15902 15903 ",
"YES\n73634483 73634485 ",
"NO\n",
"YES\n3 4 ",
"YES\n2 ",
"YES\n1 2 4 ",
"NO\n",
"YES\n1 2 ",
"NO\n",
"YES\n10245 10247 ",
"YES\n99999995 99999996 99999997 99999998 99999999 100000001 100000002 100000003 100000004 100000005 ",
"YES\n2 3 ",
"NO\n",
"YES\n1879 1880 1881 1882 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 ",
"YES\n3 ",
"YES\n34482744 34482745 34482746 34482747 34482748 34482749 34482750 34482751 34482752 34482753 34482754 34482756 34482757 34482758 34482759 34482760 34482761 34482762 34482763 34482764 34482765 34482766 34482767 34482768 34482769 34482770 34482771 34482772 34482773 ",
"YES\n1000000000 ",
"YES\n1 2 4 6 ",
"NO\n",
"YES\n4577 4578 4581\n",
"NO\n",
"YES\n4 ",
"YES\n12429 12431 12432 12433 ",
"NO\n",
"YES\n2 3 4 7\n",
"NO\n",
"YES\n70044971 70044973 ",
"YES\n42649 42651 ",
"YES\n18469542 18469543 18469545 18469546 18469547 18469548 18469549 18469550 18469551 18469552 18469553 18469554 18469555 18469556 18469557 18469558 18469559 18469560 18469561 18469562 18469563 18469564 18469565 18469566 18469567 18469568 18469569 18469570 18469571 18469572 18469573 18469574 18469575 18469576 18469577 18469578 18469579 18469580 18469581 18469582 18469583 18469584 18469585 18469586 18469587 18469588 ",
"YES\n33333318 33333319 33333320 33333321 33333322 33333324 33333325 33333326 33333327 33333328 33333329 33333330 33333331 33333332 33333333 33333334 33333335 33333336 33333337 33333338 33333339 33333340 33333341 33333342 33333343 33333344 33333345 33333346 33333347 33333348 ",
"YES\n776 777 780\n",
"YES\n333333332 333333333 333333335 ",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n21089 21091 ",
"NO\n",
"NO\n",
"YES\n25929 25931 25932\n",
"YES\n36817240 36817241 36817243 36817244\n",
"YES\n5 6\n",
"YES\n3 5 6\n",
"YES\n17012 17013\n",
"YES\n100009995 100009996 100009997 100009998 100009999 100010001 100010002 100010003 100010004 100010005\n",
"YES\n1245 1246 1247 1248 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272\n",
"YES\n34482779 34482780 34482781 34482782 34482783 34482784 34482785 34482786 34482787 34482788 34482789 34482790 34482791 34482792 34482793 34482794 34482795 34482796 34482797 34482798 34482799 34482800 34482801 34482802 34482803 34482804 34482806 34482807 34482808\n",
"YES\n4873 4874 4876\n",
"YES\n5\n",
"YES\n7217 7219 7220 7221\n",
"YES\n100871997 100871998\n",
"YES\n28432 28433 28435\n",
"YES\n29494851 29494852 29494853 29494854 29494855 29494856 29494857 29494858 29494859 29494860 29494861 29494862 29494863 29494864 29494865 29494866 29494867 29494868 29494869 29494870 29494871 29494872 29494873 29494874 29494875 29494876 29494877 29494878 29494879 29494880 29494881 29494882 29494883 29494884 29494885 29494886 29494888 29494889 29494890 29494891 29494892 29494893 29494894 29494895 29494896 29494897\n",
"YES\n25641006 25641007 25641008 25641009 25641010 25641011 25641012 25641013 25641014 25641015 25641016 25641017 25641018 25641019 25641021 25641022 25641023 25641024 25641025 25641026 25641027 25641028 25641029 25641030 25641031 25641032 25641033 25641034 25641035 25641036 25641037 25641038 25641039 25641040 25641041 25641042 25641043 25641044 25641045\n",
"YES\n386 387 388 389 391 392\n",
"YES\n336666665 336666667 336666668\n",
"YES\n2 3 5\n",
"YES\n10543 10544 10546 10547\n",
"YES\n2 3 4\n",
"YES\n3 4 6\n",
"YES\n1 2 3 5\n",
"YES\n19446 19447 19449 19450\n",
"YES\n147268968\n",
"YES\n5 6 7\n",
"YES\n2 3 4 5\n",
"YES\n515 516\n",
"YES\n9995 9996 9997 9998 9999 10001 10002 10003 10004 10005\n",
"YES\n684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732\n",
"YES\n20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 37 38 39 40 41 42 43 44 45 46 47 48 49\n",
"YES\n2922 2923 2925 2926 2927\n",
"YES\n10\n",
"YES\n11139 11141 11142 11143\n",
"YES\n3291639 3291641\n",
"YES\n21323 21324 21326 21327\n",
"YES\n19663215 19663216 19663217 19663218 19663219 19663220 19663221 19663222 19663223 19663224 19663225 19663226 19663227 19663228 19663229 19663230 19663231 19663232 19663233 19663234 19663235 19663236 19663237 19663238 19663239 19663240 19663241 19663242 19663243 19663244 19663245 19663246 19663247 19663248 19663249 19663250 19663251 19663252 19663253 19663254 19663255 19663256 19663257 19663258 19663259 19663260 19663261 19663262 19663263 19663264 19663265 19663266 19663267 19663268 19663269 19663270 19663271 19663272 19663273 19663275 19663276 19663277 19663278 19663279 19663280 19663281 19663282 19663283 19663284\n",
"YES\n14285679 14285680 14285681 14285682 14285683 14285684 14285685 14285686 14285687 14285688 14285689 14285690 14285691 14285692 14285693 14285695 14285696 14285697 14285698 14285699 14285700 14285701 14285702 14285703 14285704 14285705 14285706 14285707 14285708 14285709 14285710 14285711 14285712 14285713 14285714 14285715 14285716 14285717 14285718 14285719 14285720 14285721 14285722 14285723 14285724 14285725 14285726 14285727 14285728 14285729 14285730 14285731 14285732 14285733 14285734 14285735 14285736 14285737 14285738 14285739 14285740 14285741 14285742 14285743 14285744 14285745 14285746 14285747 14285748 14285749\n",
"YES\n1 2 3 4\n",
"YES\n8434 8435 8436 8437 8438\n",
"YES\n3 4 5 7\n",
"YES\n16144 16145 16146 16147\n",
"YES\n18\n",
"YES\n5 6 7 9\n",
"YES\n1000 1002\n",
"YES\n5547 5548 5549 5550 5551 5552 5553 5554 5555 5556 5557 5558 5559 5560 5561 5562 5563 5565\n",
"YES\n418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466\n",
"YES\n3468 3469 3470 3471 3472 3473 3474 3476 3477 3478 3479 3480 3481 3482 3483 3484 3485 3486 3487 3488 3489 3490 3491 3492 3493 3494 3495 3496 3497\n",
"YES\n1 2 3\n",
"YES\n3654 3655 3656 3658\n",
"YES\n15\n",
"YES\n4278 4279 4280 4282\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
}
|
Polycarp has to solve exactly n problems to improve his programming skill before an important programming competition. But this competition will be held very soon, most precisely, it will start in k days. It means that Polycarp has exactly k days for training!
Polycarp doesn't want to procrastinate, so he wants to solve at least one problem during each of k days. He also doesn't want to overwork, so if he solves x problems during some day, he should solve no more than 2x problems during the next day. And, at last, he wants to improve his skill, so if he solves x problems during some day, he should solve at least x+1 problem during the next day.
More formally: let [a_1, a_2, ..., a_k] be the array of numbers of problems solved by Polycarp. The i-th element of this array is the number of problems Polycarp solves during the i-th day of his training. Then the following conditions must be satisfied:
* sum of all a_i for i from 1 to k should be n;
* a_i should be greater than zero for each i from 1 to k;
* the condition a_i < a_{i + 1} ≤ 2 a_i should be satisfied for each i from 1 to k-1.
Your problem is to find any array a of length k satisfying the conditions above or say that it is impossible to do it.
Input
The first line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 10^5) — the number of problems Polycarp wants to solve and the number of days Polycarp wants to train.
Output
If it is impossible to find any array a of length k satisfying Polycarp's rules of training, print "NO" in the first line.
Otherwise print "YES" in the first line, then print k integers a_1, a_2, ..., a_k in the second line, where a_i should be the number of problems Polycarp should solve during the i-th day. If there are multiple answers, you can print any.
Examples
Input
26 6
Output
YES
1 2 4 5 6 8
Input
8 3
Output
NO
Input
1 1
Output
YES
1
Input
9 4
Output
NO
|
{
"inputs": [
"5 5\n1 2 1 1 2\n1 2\n1 3\n2 4\n2 5\n1 2 3\n1 1 2\n2 1\n2 2\n2 4\n",
"10 10\n137 197 856 768 825 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n418 45 865 869 745 901 177 773 854 462\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 6 246\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 981\n1 2 868\n2 7\n",
"10 10\n137 197 856 768 825 894 86 174 218 299\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n418 49 865 869 745 901 177 773 854 462\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 6 246\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 981\n1 2 868\n2 7\n",
"5 5\n1 2 1 1 2\n1 2\n1 3\n1 4\n2 5\n1 2 3\n1 1 2\n2 1\n2 2\n2 4\n",
"10 10\n137 197 856 768 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"5 5\n1 3 1 1 2\n1 2\n1 3\n1 4\n2 5\n1 2 3\n1 1 2\n2 1\n2 2\n2 4\n",
"10 10\n137 197 856 1409 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"5 5\n1 3 1 1 2\n1 2\n1 3\n1 4\n2 5\n1 2 3\n1 1 2\n2 1\n2 4\n2 4\n",
"10 10\n418 45 865 869 745 901 177 773 854 462\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 6 68\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 981\n1 2 868\n2 7\n",
"5 5\n2 2 1 1 2\n1 2\n1 3\n2 4\n2 5\n1 2 3\n1 1 2\n2 1\n2 2\n2 4\n",
"10 10\n137 197 856 768 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 5\n1 7 244\n",
"5 5\n2 2 1 2 2\n1 2\n1 3\n2 4\n2 5\n1 2 3\n1 1 2\n2 1\n2 2\n2 4\n",
"10 10\n137 197 856 768 1384 894 86 174 218 299\n7 8\n4 7\n8 9\n8 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 3\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n418 45 865 869 745 901 177 773 854 462\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 6 246\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 1556\n1 2 868\n2 7\n",
"10 10\n137 197 856 960 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n418 49 865 869 745 901 177 773 854 462\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 1 246\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 981\n1 2 868\n2 7\n",
"10 10\n137 197 856 1056 1384 894 86 174 218 299\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n418 45 865 869 745 901 96 773 854 462\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 6 246\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 1556\n1 2 868\n2 7\n",
"10 10\n137 197 856 960 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 1 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n137 197 856 960 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n3 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 1 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n137 265 856 1585 367 894 86 174 218 326\n7 8\n1 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 748\n2 3\n1 7 244\n",
"10 10\n435 45 865 869 745 901 177 773 854 48\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 6 68\n1 7 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 981\n1 2 868\n2 7\n",
"10 10\n137 197 856 768 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n137 265 856 1409 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 265 856 1409 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n2 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 197 856 768 1384 894 86 174 218 299\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n137 197 856 1409 367 127 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 265 856 1409 367 894 86 174 218 326\n6 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 197 856 768 1384 894 86 174 218 299\n7 8\n4 7\n8 9\n8 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n137 197 856 768 367 894 86 174 218 100\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 5\n1 7 244\n",
"10 10\n137 265 856 1409 367 894 86 174 218 326\n6 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 6 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 197 856 768 1384 894 82 174 218 299\n7 8\n4 7\n8 9\n8 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 3\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n137 197 856 768 825 894 86 174 218 299\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n2 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n137 197 856 768 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 9 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 197 856 1409 367 1322 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 265 856 1409 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 748\n2 3\n1 7 244\n",
"10 10\n435 45 865 869 745 901 177 773 854 462\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 6 68\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 981\n1 2 868\n2 7\n",
"10 10\n137 265 856 1409 367 894 86 174 218 326\n6 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 330\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 197 856 768 367 894 86 174 218 110\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 5\n1 7 244\n",
"10 10\n137 265 856 1409 367 894 86 174 218 326\n6 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 6 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 705\n2 3\n1 7 244\n",
"10 10\n137 197 856 768 1384 894 82 111 218 299\n7 8\n4 7\n8 9\n8 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 3\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 4\n1 7 244\n",
"10 10\n418 49 865 869 745 901 177 773 1499 462\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 1 246\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 981\n1 2 868\n2 7\n",
"10 10\n137 197 856 768 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 9 972\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 197 856 1409 174 1322 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 265 856 1409 367 894 86 174 218 326\n7 8\n1 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 748\n2 3\n1 7 244\n",
"10 10\n435 45 865 869 745 901 177 773 854 48\n4 8\n1 4\n3 6\n1 5\n1 10\n5 9\n1 2\n4 7\n1 3\n2 2\n1 6 68\n1 4 296\n1 2 378\n1 8 648\n2 6\n1 5 288\n1 6 981\n1 2 868\n2 7\n",
"10 10\n137 197 856 768 367 894 86 174 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 9 1674\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n",
"10 10\n137 197 856 1409 174 1322 86 94 218 326\n7 8\n4 7\n8 9\n7 10\n1 2\n2 4\n3 6\n3 5\n2 3\n1 9 624\n2 1\n2 4\n1 6 505\n1 8 467\n1 3 643\n2 1\n1 8 631\n2 3\n1 7 244\n"
],
"outputs": [
"3\n3\n0\n",
"137\n768\n137\n768\n",
"45\n1147\n-119\n",
"137\n768\n137\n768\n",
"49\n1147\n-119\n",
"3\n3\n-1\n",
"137\n768\n137\n1499\n",
"3\n4\n-1\n",
"137\n1409\n137\n1499\n",
"3\n-1\n-1\n",
"45\n969\n-119\n",
"4\n3\n0\n",
"137\n768\n137\n-276\n",
"4\n3\n1\n",
"137\n856\n137\n768\n",
"45\n1147\n-119\n",
"137\n960\n137\n960\n",
"49\n1147\n127\n",
"137\n1056\n137\n1056\n",
"45\n1147\n-200\n",
"137\n960\n780\n1603\n",
"137\n960\n780\n317\n",
"137\n1585\n137\n1499\n",
"45\n969\n473\n",
"137\n768\n137\n768\n",
"137\n1409\n137\n1499\n",
"137\n1409\n137\n1499\n",
"137\n768\n137\n768\n",
"137\n1409\n137\n1499\n",
"137\n1409\n137\n1499\n",
"137\n768\n137\n768\n",
"137\n768\n137\n-276\n",
"137\n1409\n137\n1499\n",
"137\n856\n137\n768\n",
"137\n768\n137\n768\n",
"137\n768\n137\n1499\n",
"137\n1409\n137\n1499\n",
"137\n1409\n137\n1499\n",
"45\n969\n-119\n",
"137\n1409\n137\n1499\n",
"137\n768\n137\n-276\n",
"137\n1409\n137\n1499\n",
"137\n856\n137\n768\n",
"49\n1147\n127\n",
"137\n768\n137\n1499\n",
"137\n1409\n137\n1499\n",
"137\n1409\n137\n1499\n",
"45\n969\n-119\n",
"137\n768\n137\n1499\n",
"137\n1409\n137\n1499\n"
]
}
|
Iahub likes trees very much. Recently he discovered an interesting tree named propagating tree. The tree consists of n nodes numbered from 1 to n, each node i having an initial value ai. The root of the tree is node 1.
This tree has a special property: when a value val is added to a value of node i, the value -val is added to values of all the children of node i. Note that when you add value -val to a child of node i, you also add -(-val) to all children of the child of node i and so on. Look an example explanation to understand better how it works.
This tree supports two types of queries:
* "1 x val" — val is added to the value of node x;
* "2 x" — print the current value of node x.
In order to help Iahub understand the tree better, you must answer m queries of the preceding type.
Input
The first line contains two integers n and m (1 ≤ n, m ≤ 200000). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 1000). Each of the next n–1 lines contains two integers vi and ui (1 ≤ vi, ui ≤ n), meaning that there is an edge between nodes vi and ui.
Each of the next m lines contains a query in the format described above. It is guaranteed that the following constraints hold for all queries: 1 ≤ x ≤ n, 1 ≤ val ≤ 1000.
Output
For each query of type two (print the value of node x) you must print the answer to the query on a separate line. The queries must be answered in the order given in the input.
Examples
Input
5 5
1 2 1 1 2
1 2
1 3
2 4
2 5
1 2 3
1 1 2
2 1
2 2
2 4
Output
3
3
0
Note
The values of the nodes are [1, 2, 1, 1, 2] at the beginning.
Then value 3 is added to node 2. It propagates and value -3 is added to it's sons, node 4 and node 5. Then it cannot propagate any more. So the values of the nodes are [1, 5, 1, - 2, - 1].
Then value 2 is added to node 1. It propagates and value -2 is added to it's sons, node 2 and node 3. From node 2 it propagates again, adding value 2 to it's sons, node 4 and node 5. Node 3 has no sons, so it cannot propagate from there. The values of the nodes are [3, 3, - 1, 0, 1].
You can see all the definitions about the tree at the following link: http://en.wikipedia.org/wiki/Tree_(graph_theory)
|
{
"inputs": [
"abc\nddd\n",
"abcdef\nabcdeg\n",
"abacaba\nubuduba\n",
"izybggxalv\nrbqjamqnyg\n",
"abacabadaba\ndabacabaaba\n",
"aaaaaa\nzzzzzz\n",
"aac\nbbb\n",
"jvmzmvqexcqycjcpuqimvyovcffrdwtexpqhxswzytoaokvnexkzgycpmbgvsnyifkwvfbirtwnprmrlotlnhkogjlmxmgruklcuqstwfwoswux\nvzsmohqcjpzdhfyjbljviodktdsfbmaujgtsryzlcwdvccykofgxibzrxoqrvfarjduntkenwwqwuvzzxamztghkusejmucljoedfrqpcwunkru\n",
"aaaabbbcccdeeffffgghhhiiiiijjjjjjjkklllmmnnnnnnooopppqqqqssttuuvvvvwwwxyyzzzzzz\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"abcde\nzzzzz\n",
"ftmhkyguxvbuqaiuxbmj\nftmhkyguxvbuqaiuxbmk\n",
"qszbyqbjgs\nqszbyqbjgt\n",
"aaaabbbccddddeeeeffffffggggggghhhiijjjjjjjkkkllmmmmmmmmmnnnopppppppqqqqrrrrsssttttuuuuuvvvvvvwwwwwxxxxxyyyyyyyzzz\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"dkvctjuqhtotnlwkoiaegcbsigoqvfbjtbhsniksnsauinmcoffbyberonxcpsucpacnaopnjfytkbaqpsxvjppjxzcsrlqkufjt\ndkvctjuqhtotnlwkoiaegcbsigoqvfbjtbhsniksnsauinmcoffbyberonxcpsucpacnaopnjfytkbaqpsxvjppjxzcsrlqkufju\n",
"acceeffghhijjjklmmoqqqssstuuwwxyy\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"acehlmnssx\nzzzzzzzzzz\n",
"a\nc\n",
"qdgvzritpdtoqkq\nvlulirhbfjbcmdp\n",
"wdtzolgzsx\nxnlokxihzw\n",
"hoazcxoypk\njdmafdaqwm\n",
"aaa\nccc\n",
"aaaccc\nbbbbbb\n",
"ujfawuezgiy\nvuqvvsivvwe\n",
"izybggxalv\nrbqjanqmyg\n",
"abacabaeaba\ndabacabaaba\n",
"aaaaaa\nzzzzyz\n",
"jvmzmvqexcqycjcpuqimvyovcffrdwtexpqhxswzytoaokvnexkzgycpmbgvsnyifkwvfbirtwnprmrlotlnhkogjlmxmgruklcuqstwfwoswux\nvzsmohqcjpzdhfyjbljviodktdsfbmaujgtssyzlcwdvccykofgxibzrxoqrvfarjduntkenwwqwuvzzxamztghkusejmucljoedfrqpcwunkru\n",
"aaaabbbcccdeeffffgghhhiiiiijjjjjjjkklllmmonnnnnooopppqqqqssttuuvvvvwwwxyyzzzzzz\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"dbcae\nzzzzz\n",
"aaaabbbccddddeeeeffffffghggggghhhiijjjjjjjkkkllmmmmmmmmmnnnopppppppqqqqrrrrsssttttuuuuuvvvvvvwwwwwxxxxxyyyyyyyzzz\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"dkvctjuqhtotnlwkoiaegcbsigoqvfbjtbhsniksnsauinmcoffbyberonxcpsucpacnaopnjfytkbaqpsxvjppjxzcsrlqkufjt\nujfukqlrsczxjppjvxspqabktyfjnpoancapcuspcxnorebybffocmniuasnskinshbtjbfvqogisbcgeaiokwlntothqujtcvkd\n",
"acehlmnssx\nzzzzzzyzzz\n",
"qdgvzritpdtoqkp\nvlulirhbfjbcmdp\n",
"wdtzolgzsy\nxnlokxihzw\n",
"aaccac\nbbbbbb\n",
"ujeawuezgiy\nvuqvvsivvwe\n",
"aac\nddd\n",
"abcdef\ngedcba\n",
"abacaba\nubudtba\n",
"aaabaa\nzzzzyz\n",
"jvmzmvqexcqycjcpuqimvyovcffrdwtexpqhxswzytoaokvnexkzgycpmbgvsnxifkwvfbirtwnprmrlotlnhkogjlmxmgruklcuqstwfwoswux\nvzsmohqcjpzdhfyjbljviodktdsfbmaujgtssyzlcwdvccykofgxibzrxoqrvfarjduntkenwwqwuvzzxamztghkusejmucljoedfrqpcwunkru\n",
"eacbd\nzzzzz\n",
"aaaabbbccddddeeeefqffffghggggghhhiijjjjjjjkkkllmmmmmmmmmnnnopppppppqqqfrrrrsssttttuuuuuvvvvvvwwwwwxxxxxyyyyyyyzzz\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"dkvctjtqhtotnlwkoiaegcbsigoqvfbjtbhsniksnsauinmcoffbyberonxcpsucpacnaopnjfytkbaqpsxvjppjxzcsrlqkufjt\nujfukqlrsczxjppjvxspqabktyfjnpoancapcuspcxnorebybffocmniuasnskinshbtjbfvqogisbcgeaiokwlntothqujtcvkd\n",
"yyxwmuutsssqqqomwlkjjjihhgffeecca\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"wdtzolszgy\nxnlokxihzw\n",
"aadcac\nbbbbbb\n",
"yyxwmuutsssqqqowmlkjjjihhgffeecca\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"qdgvtrizpdtoqkp\nvlclirhbfjbumdp\n",
"baacaaa\nubudtba\n",
"yyxwmuutsssqqqowmljjjjihhgffeecca\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"qdgutrizpdtoqkp\nvlclirhbfjbumdp\n",
"wotzdlszgy\nxnlokxjhzw\n",
"aca\nded\n",
"abaeabacaba\ndaabcabaaaa\n",
"dkvctjtqhtotnlwkoiaegcbsigoqvfbjtbhsniksnsauinmcoffbyberonxcpsucpacnaopnjfytkbaqpsxvjppjxzcsrlqkufjt\nuifukqlrsczxjppjvxspqabktyfjnpoancapcuspcxnorebybffocmniuasoskinsibtjbfvqogisbcgeaiokwlntothqujtcvkd\n",
"yyxwmvutsssqqqowmljjjjihhgffeecca\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"wotzdslzgy\nxnlokxjhzw\n",
"yyxwwuutsssqqqommlkjjjihhgffeecca\nzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\n",
"aaa\ncbc\n",
"abacabaeaba\ndaaacabaaba\n",
"acehlmossx\nzzzzzzyzzz\n",
"qdgvzritpdtoqkp\nvlclirhbfjbumdp\n",
"aaa\nbcc\n",
"ujeawuezgiy\nvuqvvsiuvwe\n",
"aac\nded\n",
"abcdef\ngecdba\n",
"bbacaaa\nubudtba\n",
"abacabaeaba\ndaaacabaaaa\n",
"aaabaa\nzzzzxz\n",
"eacbd\nzzyzz\n",
"dkvctjtqhtotnlwkoiaegcbsigoqvfbjtbhsniksnsauinmcoffbyberonxcpsucpacnaopnjfytkbaqpsxvjppjxzcsrlqkufjt\nujfukqlrsczxjppjvxspqabktyfjnpoancapcuspcxnorebybffocmniuasnskinsibtjbfvqogisbcgeaiokwlntothqujtcvkd\n",
"acehlmossw\nzzzzzzyzzz\n",
"wdtzolszgy\nxnlokxjhzw\n",
"caa\nded\n",
"abacabaeaba\ndaabcabaaaa\n",
"dkvctjtqhtotnlwkoiaegcbsigoqvfbjtbhsniksnsauinmcoffbyberonxcpsucpacnaopnjfytkbaqpsxvjppjxzcsrlqkufjt\nujfukqlrsczxjppjvxspqabktyfjnpoancapcuspcxnorebybffocmniuasoskinsibtjbfvqogisbcgeaiokwlntothqujtcvkd\n",
"acehlmossw\nzzzyzzzzzz\n",
"baacaaa\nubuetba\n"
],
"outputs": [
"5",
"0",
"64",
"183497",
"5586",
"0",
"1",
"845854724",
"56953494",
"119",
"0",
"0",
"362472550",
"0",
"615090736",
"1814399",
"0",
"862600433",
"229771",
"116556",
"0",
"9",
"1730501",
"183497\n",
"5209\n",
"0\n",
"845854724\n",
"986002514\n",
"39\n",
"819409284\n",
"198572959\n",
"1814399\n",
"959891537\n",
"169291\n",
"7\n",
"883781\n",
"2\n",
"719\n",
"64\n",
"3\n",
"787431374\n",
"21\n",
"615027939\n",
"444343862\n",
"651345440\n",
"169285\n",
"19\n",
"573995375\n",
"961050737\n",
"8\n",
"893498849\n",
"463749909\n",
"109045\n",
"1\n",
"5104\n",
"657435778\n",
"870209309\n",
"109021\n",
"0\n",
"0\n",
"5209\n",
"1814399\n",
"959891537\n",
"0\n",
"883781\n",
"2\n",
"719\n",
"21\n",
"5209\n",
"3\n",
"21\n",
"444343862\n",
"1814399\n",
"169285\n",
"0\n",
"5209\n",
"444343862\n",
"1814399\n",
"8\n"
]
}
|
At the Byteland State University marks are strings of the same length. Mark x is considered better than y if string y is lexicographically smaller than x.
Recently at the BSU was an important test work on which Vasya recived the mark a. It is very hard for the teacher to remember the exact mark of every student, but he knows the mark b, such that every student recieved mark strictly smaller than b.
Vasya isn't satisfied with his mark so he decided to improve it. He can swap characters in the string corresponding to his mark as many times as he like. Now he want to know only the number of different ways to improve his mark so that his teacher didn't notice something suspicious.
More formally: you are given two strings a, b of the same length and you need to figure out the number of different strings c such that:
1) c can be obtained from a by swapping some characters, in other words c is a permutation of a.
2) String a is lexicographically smaller than c.
3) String c is lexicographically smaller than b.
For two strings x and y of the same length it is true that x is lexicographically smaller than y if there exists such i, that x1 = y1, x2 = y2, ..., xi - 1 = yi - 1, xi < yi.
Since the answer can be very large, you need to find answer modulo 109 + 7.
Input
First line contains string a, second line contains string b. Strings a, b consist of lowercase English letters. Their lengths are equal and don't exceed 106.
It is guaranteed that a is lexicographically smaller than b.
Output
Print one integer — the number of different strings satisfying the condition of the problem modulo 109 + 7.
Examples
Input
abc
ddd
Output
5
Input
abcdef
abcdeg
Output
0
Input
abacaba
ubuduba
Output
64
Note
In first sample from string abc can be obtained strings acb, bac, bca, cab, cba, all of them are larger than abc, but smaller than ddd. So the answer is 5.
In second sample any string obtained from abcdef is larger than abcdeg. So the answer is 0.
|
{
"inputs": [
"14",
"10",
"13",
"15",
"12",
"25",
"17",
"32",
"16",
"42",
"22",
"20",
"33",
"48",
"51",
"29",
"24",
"27",
"55",
"49",
"54",
"39",
"36",
"43",
"60",
"38",
"103",
"46",
"79",
"74",
"61",
"86",
"113",
"67",
"200",
"78",
"100",
"66",
"140",
"121",
"320",
"76",
"147",
"101",
"107",
"269",
"229",
"303",
"137",
"142",
"111",
"443",
"383",
"217",
"842",
"381",
"467",
"57",
"206",
"265",
"527",
"82",
"191",
"124",
"120",
"64",
"116",
"182",
"209",
"106",
"144",
"94",
"88",
"92",
"90",
"129",
"118",
"160",
"70",
"201",
"71",
"146",
"154",
"371",
"109",
"98",
"84",
"241",
"457",
"193",
"262",
"134",
"170",
"480",
"253",
"150",
"204",
"337",
"162",
"757",
"174",
"363",
"1018",
"361"
],
"outputs": [
"1\n",
"0\n",
"1\n",
"7\n",
"0\n",
"924\n",
"28\n",
"5005\n",
"7\n",
"38760\n",
"210\n",
"84\n",
"8008\n",
"100947\n",
"177100\n",
"3003\n",
"462\n",
"1716\n",
"296010\n",
"134596\n",
"230230\n",
"27132\n",
"12376\n",
"54264\n",
"475020\n",
"18564\n",
"18009460\n",
"74613\n",
"3262623\n",
"1947792\n",
"593775\n",
"5245786\n",
"32468436\n",
"1107568\n",
"120529249\n",
"2760681\n",
"13983816\n",
"906192\n",
"119877472\n",
"50063860\n",
"398506989\n",
"2324784\n",
"170230452\n",
"15890700\n",
"22957480\n",
"177979760\n",
"666926094\n",
"888600657\n",
"109453344\n",
"131115985\n",
"28989675\n",
"111163147\n",
"291483359\n",
"913554181\n",
"32193075\n",
"334682835\n",
"267522932\n",
"376740\n",
"346548658\n",
"547258390\n",
"968158960\n",
"3838380\n",
"869107785\n",
"55525372\n",
"45057474\n",
"736281\n",
"36288252\n",
"622614630\n",
"517381573\n",
"20358520\n",
"143218999\n",
"9366819\n",
"6096454\n",
"8145060\n",
"7059052\n",
"74974368\n",
"40475358\n",
"277962685\n",
"1344904\n",
"192052393\n",
"1623160\n",
"156238908\n",
"218618940\n",
"301564503\n",
"25827165\n",
"12271512\n",
"4496388\n",
"652745439\n",
"587920886\n",
"927048304\n",
"963411965\n",
"90858768\n",
"406481544\n",
"988895639\n",
"925156747\n",
"185250786\n",
"267339913\n",
"530983208\n",
"300500200\n",
"141575099\n",
"470155077\n",
"913567028\n",
"857373624\n",
"424719499\n"
]
}
|
Chef loves arrays. But he really loves a specific kind of them - Rainbow Arrays.
The array is a Rainbow Array if it has such a structure:
The first a1 elements equal to 1.
The next a2 elements equal to 2.
The next a3 elements equal to 3.
The next a4 elements equal to 4.
The next a5 elements equal to 5.
The next a6 elements equal to 6.
The next a7 elements equal to 7.
The next a6 elements equal to 6.
The next a5 elements equal to 5.
The next a4 elements equal to 4.
The next a3 elements equal to 3.
The next a2 elements equal to 2.
The next a1 elements equal to 1.
ai is a positive integer, the variables with the same index (a1 in the first statement and a1 in the last one, for example) are equal.
There are no any other elements in array.
For example, {1,1,2,2,2,3,4,5,5,6,7,7,7,6,5,5,4,3,2,2,2,1,1} is a Rainbow Array.
The array {1,2,3,4,5,6,7,6,6,5,4,3,2,1} is not a Rainbow Array, because the sizes of the blocks with the element 6 are different.
Please help Chef to count the number of different Rainbow Arrays that contain exactly N elements.
Input
The first line contains a single integer N.
Output
Output the number of different Rainbow Arrays with N elements, modulo 10^9+7.
Constraints
1 ≤ N ≤ 10^6
Example
Input #1:
10
Output #1:
0
Input #2:
13
Output #2:
1
Input #3:
14
Output #3:
1
Input #4:
15
Output #4:
7
|
{
"inputs": [
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n110 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 0 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n110 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -14\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -18 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-127 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -144 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n6 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-8 -79 -20\n3 3\n110 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-122 -40 -50 -8\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -7\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -11\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -18 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 3\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -30 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 5\n-100 -20 -100\n-100 -20 -20\n-100 -60 -9\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-18 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-127 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-224 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-174 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -38\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -31\n-7 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-147 -20 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-127 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -144 12\n-250 -130 -330 -18\n-56 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-100 -20 -63\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-146 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-33 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -20 -30\n-100 -20 2\n-46 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -165\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -38 -30\n-100 -20 2\n-127 -20 -20\n4 5\n883 5 4\n0 -380 -250 -312\n-90 2 -144 12\n-250 -130 -330 -18\n-56 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-100 -20 -63\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-146 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-33 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -20 -49\n-100 -20 2\n-46 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -165\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
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"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-174 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -31\n-7 -100 -20\n3 3\n100 3 3\n-135 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -26\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-32 -20 -100\n-100 -25 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n6 3\n100 19 3\n-147 -20 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-250 -62 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-187 -20 -100\n-100 -20 -100\n-174 -20 -100\n3 3\n100 10 10\n-38 -20 -100\n-100 -20 -20\n-100 -60 -45\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -31\n-7 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-12 -60 -9\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-127 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -144 12\n-250 -130 -330 -18\n-56 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-120 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -7\n3 3\n101 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -172 -11\n3 3\n100 1 3\n-100 0 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-250 -130 -330 -166\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-120 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-10 -20 -20\n-100 -60 -7\n3 3\n101 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -172 -11\n3 3\n100 3 3\n-100 0 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 5\n-10 -380 -250 -325\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-120 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -13 -20\n-100 -60 -7\n3 3\n101 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -172 -11\n3 3\n100 3 3\n-100 0 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -325\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-411 -10 -39 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -38 -30\n-100 -20 2\n-127 -20 -20\n4 5\n883 5 4\n1 -380 -250 -312\n-90 2 -144 12\n-250 -130 -330 -18\n-56 -47 -50 -19\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-100 -20 -100\n-117 -20 -15\n3 3\n000 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-147 -3 -100\n-20 -20 -20\n-20 -124 -30\n3 3\n100 3 3\n-100 -20 -30\n-72 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-207 -107 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-188 -20 -100\n-117 -20 -15\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-122 -60 -20\n3 3\n100 19 3\n-147 -3 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-72 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -42 8\n-207 -107 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-153 -60 -8\n3 3\n100 19 3\n-172 -20 -100\n-20 -20 -20\n-10 -100 -20\n3 3\n100 3 3\n-100 -38 -30\n-100 -20 2\n-127 0 -20\n4 5\n883 5 4\n1 -380 -250 -312\n-90 2 -144 12\n-250 -130 -330 -29\n-58 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -3 -100\n-100 -20 -100\n-117 -20 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-153 -60 -20\n3 3\n100 19 3\n-172 -20 -100\n-20 -20 -20\n-10 -100 -8\n3 3\n110 3 3\n-100 -38 -30\n-100 -20 2\n-127 0 -20\n4 5\n883 5 4\n1 -380 -250 -312\n-90 2 -144 12\n-250 -130 -330 -29\n-56 -28 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -50\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -223 -250\n-59 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -10 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n000 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -106\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-4 -257 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -48 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 10\n-100 -26 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -38\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-250 -130 -330 -120\n-177 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -7 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -8 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -5\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -190\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -24 -20\n-20 -83 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -25\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n6 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-8 -79 -36\n3 3\n110 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -46 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -24\n-100 -60 -1\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -11\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -741 -250 -312\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 0\n-100 -20 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 5\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 6\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-18 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-127 -20 -20\n4 5\n1500 5 4\n-16 -380 -250 -312\n-90 2 -80 8\n-224 -130 -330 -120\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -18 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-106 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n0 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 3\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -10\n-250 -10 -30 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-32 -20 -100\n-100 -25 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -15\n4 5\n1500 3 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 4\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n6 3\n100 19 3\n-147 -20 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-250 -62 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-33 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -28 -30\n-100 -20 2\n-46 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-35 -40 -45 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -20 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-12 -60 -9\n3 3\n100 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-127 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -144 12\n-250 -130 -330 -18\n-56 -40 -50 -25\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-120 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -7\n3 3\n101 19 3\n-100 -20 -100\n-20 -20 -20\n-20 -172 -11\n3 3\n100 1 3\n-100 0 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -107\n-90 2 -80 8\n-250 -130 -330 -166\n-120 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n6 3\n100 10 7\n-100 -20 -100\n-125 -29 -20\n-78 -60 -20\n3 3\n110 10 3\n-100 -20 -100\n-20 -20 -20\n-8 -29 -20\n3 3\n110 3 3\n-100 -8 0\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -6\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -24 -100\n-100 -20 -63\n-130 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-146 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-33 -20 -100\n-20 -33 -20\n-20 -79 -20\n3 3\n111 3 3\n-100 -20 -30\n-100 -20 2\n-46 -20 -15\n4 5\n1500 5 4\n-10 -380 -250 -162\n-90 2 -80 8\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -10 -32 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-100 -20 -100\n-117 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -32\n-100 -60 -20\n3 3\n100 19 3\n-147 -3 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-274 -168 -330 -120\n-120 -48 -50 -20\n-250 -5 -10 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-49 -20 -100\n-227 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -40 -20\n-100 -60 -20\n3 3\n100 19 3\n-147 -3 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n100 3 3\n-100 -20 -30\n-72 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -312\n-90 2 -80 8\n-207 -168 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-100 -22 -100\n-117 -20 -15\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-147 -3 -100\n-20 -20 -20\n-20 -124 -14\n3 3\n100 3 3\n-100 -20 -30\n-72 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -226 -312\n-90 2 -80 8\n-207 -168 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-117 -2 -195\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 19 3\n-172 -20 -100\n-20 -20 -20\n-10 -100 -20\n3 3\n110 3 3\n-100 -38 -30\n-100 -20 2\n-127 -20 -20\n4 5\n883 5 4\n1 -380 -250 -312\n-90 2 -144 12\n-467 -130 -330 -29\n-56 -40 -50 -20\n-250 -10 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -25 -100\n-100 -20 -35\n-117 -29 -15\n3 3\n100 10 10\n-100 -20 -100\n-100 -20 -20\n-122 -60 -20\n3 3\n110 19 3\n-289 -3 -100\n-20 -20 -20\n-20 -124 -20\n3 3\n000 3 3\n-78 -20 -30\n-72 -20 2\n-100 -20 -20\n4 5\n89 5 4\n-10 -380 -250 -253\n-90 2 -80 8\n-207 -107 -330 -120\n-120 -48 -50 -20\n-250 -5 -20 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n110 10 10\n-100 -20 -100\n-100 -20 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -100 -20\n3 3\n100 3 3\n-100 -20 -30\n-100 -20 2\n-100 -20 -20\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 8\n-250 -130 -330 -106\n-120 -40 -50 -20\n-250 -8 -13 -150\n0 0",
"3 3\n100 10 10\n-100 -20 -100\n-100 -20 -100\n-100 -20 -100\n3 3\n100 10 10\n-100 -20 -100\n-100 -4 -20\n-100 -60 -20\n3 3\n100 10 3\n-100 -20 -100\n-20 -20 -20\n-20 -79 -20\n3 3\n110 3 3\n-100 -20 -30\n-22 -20 2\n-100 -20 -14\n4 5\n1500 5 4\n-10 -380 -250 -250\n-90 2 -80 1\n-250 -130 -330 -120\n-120 -40 -50 -12\n-250 -4 -32 -150\n0 0"
],
"outputs": [
"60\n80\nNA\n50\n390",
"60\n80\nNA\n50\n376\n",
"60\n80\nNA\n50\n388\n",
"60\n80\nNA\n50\n394\n",
"60\n80\nNA\n50\n390\n",
"60\n80\nNA\n50\nNA\n",
"60\n80\nNA\n44\n394\n",
"58\n80\nNA\n50\n376\n",
"60\n80\nNA\n50\n454\n",
"60\n40\nNA\n50\n388\n",
"60\n80\nNA\n50\n378\n",
"60\n80\nNA\n45\n394\n",
"60\n67\nNA\n50\n390\n",
"58\n80\nNA\n50\n386\n",
"64\n80\nNA\n45\n394\n",
"60\n69\nNA\n50\n390\n",
"60\n98\nNA\n50\n388\n",
"65\n80\nNA\n50\n390\n",
"60\n80\nNA\n50\n352\n",
"64\n80\nNA\n45\n439\n",
"60\n80\nNA\n50\n342\n",
"64\n80\nNA\n64\n439\n",
"60\n80\nNA\n50\n270\n",
"65\n80\nNA\nNA\n390\n",
"60\n80\nNA\n50\n258\n",
"74\n80\nNA\nNA\n390\n",
"74\n76\nNA\nNA\n390\n",
"60\n80\nNA\n50\n383\n",
"60\n70\nNA\n50\n388\n",
"60\n80\nNA\n50\n384\n",
"60\n80\nNA\n50\n386\n",
"60\n87\nNA\n50\n390\n",
"60\n80\nNA\nNA\n390\n",
"60\nNA\nNA\n50\n390\n",
"60\n80\nNA\n54\n388\n",
"60\n80\nNA\n50\n280\n",
"60\n71\nNA\n50\n390\n",
"NA\n80\nNA\n50\n390\n",
"53\n80\nNA\n50\n390\n",
"50\n80\nNA\n50\n454\n",
"64\n80\nNA\nNA\n394\n",
"60\n40\nNA\n50\n397\n",
"64\n80\nNA\n45\n399\n",
"60\n67\nNA\n50\n436\n",
"64\n80\nNA\n56\n439\n",
"60\n67\nNA\n50\n409\n",
"65\n80\nNA\n50\n380\n",
"60\n96\nNA\n50\n342\n",
"64\n80\nNA\n57\n439\n",
"60\n80\nNA\n50\n222\n",
"65\n80\nNA\nNA\n260\n",
"65\n80\nNA\nNA\n377\n",
"65\n76\nNA\nNA\n390\n",
"60\n70\nNA\n50\n314\n",
"60\n80\nNA\n50\n437\n",
"60\n80\nNA\n44\n554\n",
"52\n80\nNA\n50\n386\n",
"47\n80\nNA\n50\n376\n",
"60\n80\nNA\nNA\n388\n",
"60\n80\nNA\nNA\n380\n",
"58\n80\nNA\n50\n280\n",
"60\n100\nNA\n54\n388\n",
"60\n40\nNA\n50\n384\n",
"NA\n80\nNA\nNA\n390\n",
"60\n80\nNA\n50\n294\n",
"69\n80\nNA\n45\n394\n",
"60\n80\n40\nNA\n390\n",
"60\n100\nNA\n50\n388\n",
"60\n69\nNA\n50\n352\n",
"60\n67\nNA\nNA\n436\n",
"60\n67\nNA\n50\n280\n",
"60\n60\nNA\n50\n409\n",
"60\n80\nNA\n50\n277\n",
"65\nNA\nNA\n50\n390\n",
"65\n80\nNA\n50\n352\n",
"60\n68\nNA\n50\n270\n",
"43\n80\nNA\n50\n258\n",
"60\n80\nNA\n50\n345\n",
"60\n70\nNA\nNA\n314\n",
"60\n80\nNA\n50\n382\n",
"60\n86\nNA\n50\n390\n",
"47\n80\nNA\n50\n375\n",
"60\n80\nNA\n55\n388\n",
"60\n40\nNA\n45\n384\n",
"60\n65\nNA\n50\n390\n",
"NA\n80\nNA\nNA\n396\n",
"58\n80\nNA\n50\n390\n",
"69\n80\nNA\n45\nNA\n",
"60\n100\n40\nNA\n390\n",
"64\n80\nNA\n45\n389\n",
"60\n69\nNA\n50\n357\n",
"60\n67\nNA\nNA\n363\n",
"60\n40\nNA\n20\n388\n",
"64\n80\nNA\n45\n376\n",
"65\n92\nNA\n50\n380\n",
"65\n100\nNA\n50\n390\n",
"67\n80\nNA\n50\n390\n",
"42\n80\nNA\n50\n270\n",
"74\n80\nNA\nNA\nNA\n",
"60\n80\nNA\n50\n369\n",
"60\n64\nNA\n44\n554\n"
]
}
|
Aizu has an ancient legend of buried treasure. You have finally found the place where the buried treasure is buried. Since we know the depth of the buried treasure and the condition of the strata to be dug, we can reach the buried treasure at the lowest cost with careful planning. So you decided to create a program that reads the condition of the formation and calculates the route to reach the buried treasure depth at the lowest cost.
The state of the formation is represented by cells arranged in a two-dimensional grid, and the position of each cell is represented by the coordinates (x, y). Let the upper left be (1,1), and assume that the x coordinate increases as it goes to the right and the y coordinate increases as it goes deeper down. You choose one of the cells with the smallest y-coordinate and start digging from there, then dig into one of the cells with the largest y-coordinate. There are two types of cells in the formation:
1. A cell filled with soil. There is a fixed cost for each cell to dig.
2. Oxygen-filled cell. There is no need to dig, and each cell can be replenished with a fixed amount of oxygen. The oxygen in the cell that has been replenished with oxygen is exhausted and cannot be replenished again. Also, when you reach this cell, you must replenish oxygen.
Only left, right, and down cells can be dug from a cell. Once you have dug a cell, you can move it left or right, but you cannot move it up.
You must carry an oxygen cylinder with you when excavating. The moment the oxygen cylinder reaches zero, you will not be able to move, excavate, or replenish oxygen. The remaining amount is decremented by 1 each time you move the cell. Even if the remaining amount of the oxygen cylinder is 0 and the depth of the buried treasure is reached, it is not considered to have been reached. In addition, oxygen can be replenished in cells that have accumulated oxygen, but the excess capacity is discarded.
Create a program that inputs the size of the formation, the excavation cost, the capacity of the oxygen cylinder, the amount of oxygen in the initial state, and the information of the formation, and outputs the minimum cost to reach the deepest cell. However, if the minimum cost exceeds the excavation cost, or if you cannot reach the buried treasure no matter how you dig, please output "NA".
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by two zero lines. Each dataset is given in the following format.
W H
f m o
c1,1 c2,1 ... cW,1
c1,2 c2,2 ... cW,2
...
c1, H c2, H ... cW, H
The horizontal size W of the formation and the vertical size H (3 ≤ W, H ≤ 10) are given in the first line. The second line is the integer f (1 ≤ f ≤ 10000) that represents your excavation cost, the integer m (3 ≤ m ≤ 50) that represents the capacity of the oxygen cylinder, and the integer o that represents the amount of oxygen you have in the initial state. o ≤ m) is given.
The following H line is given the geological information ci, j. ci, j represents the cell information for coordinates (i, j) and is given in the following format:
If the value is negative, the cell is full of soil and the value represents the cost.
If the value is positive, it is a cell filled with oxygen, and the value represents the amount of oxygen.
However, there are no more than 50 cells in which oxygen has accumulated.
The number of datasets does not exceed 50.
Output
Print the minimum cost or NA on one line for each dataset.
Example
Input
3 3
100 10 10
-100 -20 -100
-100 -20 -100
-100 -20 -100
3 3
100 10 10
-100 -20 -100
-100 -20 -20
-100 -60 -20
3 3
100 10 3
-100 -20 -100
-20 -20 -20
-20 -100 -20
3 3
100 3 3
-100 -20 -30
-100 -20 2
-100 -20 -20
4 5
1500 5 4
-10 -380 -250 -250
-90 2 -80 8
-250 -130 -330 -120
-120 -40 -50 -20
-250 -10 -20 -150
0 0
Output
60
80
NA
50
390
|
{
"inputs": [
"16\nnandu \nkanth\nkalyan\ndhiraj\nkanth\nkalyan\nbaala\nkt\nbaala\njayanth\nsampu\nbaala\nkanth\nkalyan\nbaala\nkt\n\nSAMPLE",
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"16\nnandu \nkanth\nkalyan\ndhiraj\nkanth\nkalyan\nbaala\nkt\nbalaa\njayanth\nsampu\nbaala\nkanth\nkalyan\nbaala\nkt\n\nSAMPLE",
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"16\nnandu \nkanth\nkalyan\ndhiraj\nkanth\nkalyan\nalaab\nkt\nbalaa\njayanth\nsampu\nbaala\nkanth\nkalyan\nbaala\nkt\n\nSAMPLE",
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"16\nnandu \nkanth\nkalyan\ndhiraj\nkanth\nkalyan\nalaab\nkt\nbalaa\njayanth\nsampu\nbabla\nkanth\nkalyan\nbaala\nkt\n\nSAMPLE",
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"16\nnandu \nkanth\nkalyan\ndhiraj\nkanth\nkalyan\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\nkt\n\nSAMPLE",
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"16\nnandu \nkanth\nkalyan\ndhiraj\nkanth\nnaylak\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\nkt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\ndhiraj\nkanth\nnaylak\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\nkt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\ndhiraj\nkanth\nnaylak\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\ndhir`j\nkanth\nnaylak\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\ndhri`j\nkanth\nnaylak\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\nkanth\nnaylak\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\nkaoth\nnaylak\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\nkaoth\nkalyan\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nkalyan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\nkaoth\nkalyan\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nyalkan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakth\nkalyan\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nyalkan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakth\nkblyan\nalaab\nkt\nbalaa\njayanth\nsampu\nbaalb\nkanth\nyalkan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakth\nkblyan\nalaab\nkt\naalab\njayanth\nsampu\nbaalb\nkanth\nyalkan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakuh\nkblyan\nalaab\nkt\naalab\njayanth\nsampu\nbaalb\nkanth\nyalkan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakuh\nkblyan\nalaab\nkt\n`alab\njayanth\nsampu\nbaalb\nkanth\nyalkan\nbaala\njt\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakuh\nkblyan\nalaab\nkt\n`alab\njayanth\nsampu\nbaalb\nkanth\nyalkan\nbaala\ntj\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakuh\nkblyan\nalaab\nku\n`alab\njayanth\nsampu\nbaalb\nkanth\nyalkan\nbaala\ntj\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakuh\nkblyan\nalaab\nku\n`alab\njayanth\nsampu\nbbalb\nkanth\nyalkan\nbaala\ntj\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakuh\nkblyan\nalaab\nku\n`alab\njayanth\nsampu\nbbblb\nkanth\nyalkan\nbaala\ntj\n\nSAMPLE",
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"16\nnandu \nhtnak\nkalyan\nj`irhd\noakuh\nkblyan\nalaab\nuk\n`alab\njayanth\nsampu\nbbblb\nkanth\nyalkan\nbaala\ntj\n\nSAMPLE",
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tcdqdlshcjegksuxlvaqpjluxgwhlppzkokgrrgejuhxikouimarqesxiletzkhtaswlk\nxngthyybcnlkmfjzpxxrtijhndbwmpitffwrscbivzuijbkhgcoeeigehjrowrzdxadeib\nohlgjrsikhyozkrhgwjislospuuepcqiyqlwnokujsioubpjzbtbznaumtvzwjeykkjuri\nhvbbckhomkcqmixrcladcsrvphsdsktwzwhnbppjdmdsxuwjraqbaveutrmejhrabtbkoz\nfplzojsbsmezakavpzhdzemgwzfgrxbkvvmpschtiheyktfphtbuvqspubnvjuyitqpsqr\nbkdudzhrpeizmsihwwjatewdsdnjnhhnbyqisqdikzxdjqzkwqpdmbzjuprjwotmknhzhp\ngzrkauuwaejyxzasajravlnvmhvqkryaruhuhficbrwcmiafxrbvvbaoojkjvddffzzkpt\nkofcjrykvkefooesijfwpdyrdpcbhqedxwxhdxbeciwsqwlrayswxblheiizszqvxefaca\nxydrdwbirfqfvkbbyrgnhlabkgauruzejlicnutcatfmaqxfoegzxtwirqtsfeznmudahp\noksypfxjybegnzyczibrrppuwdackqfoqjshfbbwhpmupyiozegoozegxudgjfkoxkthgs\nkimsuspesktykkvuzjcelnahfghzunuuimryzfrirudbbonogvwshellxjglppknnrdahs\nafewcoupatdnwqfzatirueymnvrasoswdfrmvbchfntguyrhgkofumzpbzjiwpjmmjpmqq\ndwbimztwswwutqxzorviinxnujizihutvjcxwjcqkajaljhxqxkejkskpkwtkuouectgwt\nxcwetlqnjwavyemknhvfzvsxwnhuvkgohuutqjkzialibehuhsqbvycnbwtgurcqzvuztt\nwgogosycpjpsxrsuoicqepmsrslhjyrpjrqyjkgcqwkokufquuzxqukrqmuobdccffyxau\neaaoystxpypoithbtpvwdklabmoidgzzrgcoxbfdkfgpoysbauifytjuxopzwhpwhquipm\nkvrbdbqmhebxfojzxkyxivnkxqsnnrykzfhiqfzjkvcicbxqivrddpvwlqxpndaweygzrr\nofyotouubaamrwvalqbevvakualuvzlpdyfmcfwcrhbsmrsidquzcgrrzvnftqmgknggnl\nkdysqsbiugxlkvdaadorcigxcomswewcaibjkapsuugnlyvnfmxmkckyazclsftqzqpjun\nkpixfsftympfloibojtfiuadkoxwsnveauxzpurzdmfcelyntgpbzxgtxdudiwoiehljlf\naovpiopjapilbzuuqpaxwisbykjwogxjweqsadrmtjaazixxswntsilmsvsurblgvqsllo\noqnyntgqvxinrbhncktmktqdwprskyrwjphepyxyguufnjpmhtrwngisryxhvdyomujbrr\nrpntljxrtrzkoihrxlqynpskddcxxuexkupmwkcllglhemnvziawviezufqayemoaymmxw\nnhpqzfkbuwxygmibhfxhojqfmwmjhzqekilmxiimoqpzwcfhfwwmtiurntqoxuksiibsgl\ngoupvddlwubfwlquuddjyfmrxctaegholwhljmoyhaibnjtqqvtxtrrtpzapdplkupjrwv\nzbbgcwnhzcvqgssupkzwyxelqjbufnputnkuqsgokzzhsstxgjdmvudziuidtacdzqsfjj\nkhbtclkeirdyjkgtbsnferyunzrklinnwzjogpkeffgdowelkhxyxfjeegbdcexnjwykqx\ntijqmeivvcshyvhyygklcbiymgktrbxwcamwmjqygzovaultksuptkpdimztvvlkvkaiem\naqpmcovqjpyhmhzsrklqstgskwbmudevyajnasfcbnyvgsswwjassyqrzqutwmfvtxbmzs\nxsywibcwqodraufbpgotfbnwxgvgddywsvylolhilqpdqunzzjfspdbiewsgeebubdikmq\ntpbcxwfszxwelafyolubfygjulcqoyqswiokejfldewfoyraniknlsaonqzassgpbtqmpn\nkxekxogcxpqasonhpoelfnlhcpzcpszjrfosbrqdzvullmxeqlqqpcbceqypxivmbafdip\nzmrgpiqyfofwkwafsxihaefgoscoeoirponzdkakpkksgjytfcmhaiibgspvhmdzgossve\nzldhjuuuhpyioqqjpxtsljixuccrjwjdpykyavzmplftdremcybyksasaytwbvhgshclzb\njgalfseoeliqvhlbljwdouoqkcqazfflsnopeeihtiztoczebnafqmedylflfvrkbwtrty\nlqqoxrmlimluyrxsstdohitusyswlxbbpnfagdzjylqxtzzhdwarwsisekpnirrcbjaylb\ntieucfeoqkqdcyontjoavkhodpwqhwyczxnljfzorqdapocafbiknjzcvvyrbxhpiaqmss\nzariwcvmjnbwbtrernzkkzujziuysepkzgalnzocexcjwppyzzclvkatnhnstbkktqekox\nqijabkrbvixqvsscsmtgbjzannesrblcxbebhorzlgugpihnivgbcsladarecnacxbukem\naceyhfyekbxzfdzzsbetmfxazrhxuwmftmjptitwavmrefhzukaocrofyzatjdswzdgxev\nezikkojjgjackrasqcqdrbtaqwitjbytxxzgtctqouloxomduailksoboctybodtntlori\nnqightfaicwudbgpkirmvjcjbrsznigxarwrbdsrnriopvrsdrphmdklwvwspacylzabax\nvigevnhnnzlkznsyevyavpvqvecmxiylyjuqtxjhzhxkrimngghjenlwnwhtbtvfzurjgu",
"16\nnandu \nhtnak\nkalyan\nj`irhd\noakuh\nkblzan\nalaab\nuk\n`alab\njayanth\nsampu\nbbblb\nkanth\nyalkan\nbaala\ntj\n\nSAPMLE",
"50\nphqchumeaynllfdxfirg\nvsbxggbwkfnqduxwfnfo\nyvrnprxggperpjktrsvz\nstmwcysyycqpevikeffm\nznimkkasvwsrenzkycxf\nxtlsgypsfadpooefxzbc\noejuvpvaboygpoeylfqb\nnyljvrvipyamoehwqnqr\nqpmxujjloovaowuxwhms\nncbxcoksfzkvatxdknly\njyhfixjswnkkufnuxxzr\nzbmnmgqooketlyhnkoau\ngzqrcddiuteyojwaiyzp\nvscmpsajlfvgubfaaovl\nzylntrkdcpwsrtesjwhd\nizcobzcnfwlqiitvdwvx\nhrcbldvgylwgbusbmbor\nxtlhcsmpxohgmgnkeufc\nxotogbgxpeyanfetcuke\npzshkljugggekjdqzjen\npevqgxiepjsrdzjazujl\nxbywibozwmikmqfbhhcl\nduunfsksrsrtekmqdcyz\njeeuhmsqrcozijipfion\needdpszrnavymmtatbdz\nqsoemuvnpppsuacbazux\nmhecthlegrpunkdmbppw\neqtgjoparmowzdqyoxyt\njbbhawdydcprjbxphonh\npkwqyuqrqzhnbnfuvqnh\nqlrzjpxiogvliexdzuzo\nsrkrtsvojbrzmwzpowkj\nilefraamidgpnpuuhgxp\nqnjwjmwaxxmnsnhhlqqr\ndslguxzntjctozftlduz\nsmzcnockvfajfrmxotho\nwkbjzwucwljfrimpmyhc\nhzriwkbarxbgfcbceyhj\nugicwtbvtrehbbxpxifb\nbukgztockcqfckgcbfvx\nmjrmbsztsshfroefwsjr\nxjhguzyupzwweiqurpix\niqgldquveoowtcudhnef\nnjhaimuczfskuiduburi\nzezdkvcfbakyucdrbtws\ntpidukuhjzefczzzbfkq\ndpqzikfobucdhthxdjgk\njelrlpaxamceroswitdp\ntpcclifkeljytihrcqay\nbnefxnxvgzedyyhngzcd"
],
"outputs": [
"baala\ndhiraj\njayanth\nkalyan\nkanth\nkt\nnandu \nsampu\n",
"bnefxnxvgzedyyhngycd\ndpqzikfobucdhthxdjgk\nduunfsksrsrtekmqdcyz\needdpszrnavymmtatbdz\neqtgjoparmowzdqyoxyt\ngzqrcddiuteiojwayyzp\nhrcbldvgylwgbusbmbor\nhzriwkbarxbgfcbceyhj\nilefraamdigpnpuuhgxp\niqflduuveoowqcudhnef\nizcobzcnfwlqijtvdwvx\njbbhawdydcprjbxphooh\njeeuhmsrqcozijipfion\njelrlpaxamceroswitdp\njyhfixjswnkkufnuxxzr\nlchhbfqmkimwzobiwybx\nmhecthlegrpunkdmbppw\nmjrmbsztsshfroefwsjr\nncbxcoksfzkvatxdknly\nnjhaimuczfskuiduburi\nnpljvrvipyamyehwqnqr\noejuvpvaboygpoeylfpb\npevqgxiepjsrdzjazujl\nphqghumeaylnlfdxfirc\npkwqyuhrqzhnbnfuvqnq\npzshkljugggekjdqzjen\nqlrzjpxiogvliexdzuzo\nqnjwjmwaxxmnsnhhlqqr\nqpmxujjloovaowuxwhms\nqsoemuvnpppsuacbazux\nsmzcnockvfajfrmxotho\nsrkrusvojbrzmwzpowkj\nstmwcysyycqpevikeffm\nswtbrecuykabfcvkdzez\ntoidukuhjzefczzzbfkq\ntpcclifkeljytihrcqay\nugixwtbvtrehbbcpxifb\nvscmpsajlfvgubfaaovl\nvscxggbwkfnqduxwfnfo\nwkbjzwucwljfrimpmyhc\nxjhguzyupzwweiqurpix\nxotogbgxpeyanfetcuke\nxtlhcsmpxohgmgnkeufd\nxtlsgypsfadpooefxzbc\nxvfbcgkcfqckcotzgkub\nzbmnmgqooketlyhnkoau\nznimkkasvwsrenzkycxf\nzudltfzotcjtnzxuglsd\nzvsrtkjprepggxrpnrvy\nzylntrkdcpwsrtesjwhd\n",
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"baala\nbalaa\ndhiraj\njayanth\nkalyan\nkanth\nkt\nnandu \nsampu\n",
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"alaab\nbaala\nbalaa\ndhiraj\njayanth\nkalyan\nkanth\nkt\nnandu \nsampu\n",
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"alaab\nbaala\nbabla\nbalaa\ndhiraj\njayanth\nkalyan\nkanth\nkt\nnandu \nsampu\n",
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"alaab\nbaala\nbaalb\nbalaa\ndhiraj\njayanth\nkalyan\nkanth\nkt\nnandu \nsampu\n",
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"alaab\nbaala\nbaalb\nbalaa\ndhiraj\njayanth\nkalyan\nkanth\nkt\nnandu \nnaylak\nsampu\n",
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"alaab\nbaala\nbaalb\nbalaa\ndhiraj\nhtnak\njayanth\nkalyan\nkanth\nkt\nnandu \nnaylak\nsampu\n",
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"alaab\nbaala\nbaalb\nbalaa\ndhiraj\nhtnak\njayanth\njt\nkalyan\nkanth\nkt\nnandu \nnaylak\nsampu\n",
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"alaab\nbaala\nbaalb\nbalaa\ndhir`j\nhtnak\njayanth\njt\nkalyan\nkanth\nkt\nnandu \nnaylak\nsampu\n",
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"alaab\nbaala\nbaalb\nbalaa\nhtnak\nj`irhd\njayanth\njt\nkalyan\nkanth\nkt\nnandu \nnaylak\nsampu\n",
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"alaab\nbaala\nbaalb\nbalaa\nhtnak\nj`irhd\njayanth\njt\nkalyan\nkanth\nkaoth\nkt\nnandu \nsampu\n",
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"alaab\nbaala\nbaalb\nbalaa\nhtnak\nj`irhd\njayanth\njt\nkalyan\nkanth\nkaoth\nkt\nnandu \nsampu\nyalkan\n",
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"alaab\nbaala\nbaalb\nbalaa\nhtnak\nj`irhd\njayanth\njt\nkalyan\nkanth\nkt\nnandu \noakth\nsampu\nyalkan\n",
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"`alab\nalaab\nbaala\nbaalb\nhtnak\nj`irhd\njayanth\njt\nkalyan\nkanth\nkblyan\nkt\nnandu \noakuh\nsampu\nyalkan\n",
"bnefxnxvgzedyyhngzcd\nbukgztockcqfckgcbfvx\ndpqzikfobucdhthxdjgk\nduunfsksrsrtekmqdcyz\needdpszrnavymmtatbdz\neqtgjoparmowzdqyoxyt\ngzqrcddiuteiojwayyzp\nhrcbldvgylwgbusbmbor\nhzriwkbarxbgfcbceyhj\nilefraamidgpnpuuhgxp\niqfldquveoowtcudhnef\nizcobzcnfwlqiitvdwvx\njbbhawdydcprjbxphooh\njeeuhmsqrcozijipfion\njelrlpaxamceroswitdp\njyhfixjswnkkufnuxxzr\nmhecthlegrpunkdmbppw\nmjrmbsztsshfroefwsjr\nncbxcoksfzkvatxdknly\nnjhaimuczfskuiduburi\nnyljvrvipyampehwqnqr\noejuvpvaboygpoeylfqb\npevqgxiepjsrdzjazujl\nphqchumeaylnlfdxfirg\npkwqyuqrqzhnbnfuvqnh\npzshkljugggekjdqzjen\nqlrzjpxiogvliexdzuzo\nqnjwjmwaxxmnsnhhlqqr\nqpmxujjloovaowuxwhms\nqsoemuvnpppsuacbazux\nsmzcnockvfajfrmxotho\nsrkrtsvojbrzmwzpowkj\nstmwcysyycqpevikeffm\nswtbrdcuykabfcvkdzez\ntpcclifkeljytihrcqay\ntpidukuhjzefczzzbfkq\nugicwtbvtrehbbxpxifb\nvsbxggbwkfnqduxwfnfo\nvscmpsajlfvgubfaaovl\nwkbjzwucwljfrimpmyhc\nxbywibozwmikmqfbhhcl\nxjhguzyupzwweiqurpix\nxotogbgxpeyanfetcuke\nxtlhcsmpxohgmgnkeufc\nxtlsgypsfadpooefxzbc\nyvrnprxggperpjktrsvz\nzbmnmgqooketlyhnkoau\nznimkkasvwsrenzkycxf\nzudltfzotcjtnzxuglsd\nzylntrkdcpwsrtesjwhd\n",
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"`alab\nalaab\nbaala\nbaalb\nhtnak\nj`irhd\njayanth\nkalyan\nkanth\nkblyan\nkt\nnandu \noakuh\nsampu\ntj\nyalkan\n",
"bnefxnxvgzedyyhngzcd\nbukgztockcqfckgcbfvx\ndpqzikfobucdhthxdjgk\nduunfsksrsrtekmqdcyz\needdpszrnavymmtatbdz\neqtgjoparmowzdqyoxyt\ngzqrcddiuteiojwayyzp\nhrcbldvgylwgbusbmbor\nhzriwkbarxbgfcbceyhj\nilefraamidgpnpuuhgxp\niqfldquveoowtcudhnef\nizcobzcnfwlqiitvdwvx\njbbhawdydcprjbxphooh\njeeuhmsqrcozijipfion\njelrlpaxamceroswitdp\njyhfixjswnkkufnuxxzr\nmhecthlegrpunkdmbppw\nmjrmbsztsshfroefwsjr\nncbxcoksfzkvatxdknly\nnjhaimuczfskuiduburi\nnyljvrvipyampehwqnqr\noejuvpvaboygpoeylfqb\npevqgxiepjsrdzjazujl\nphqchumeaynllfdxfirg\npkwqyuqrqzhnbnfuvqnh\npzshkljugggekjdqzjen\nqlrzjpxiogvliexdzuzo\nqnjwjmwaxxmnsnhhlqqr\nqpmxujjloovaowuxwhms\nqsoemuvnpppsuacbazux\nsmzcnockvfajfrmxotho\nsrkrtsvojbrzmwzpowkj\nstmwcysyycqpevikeffm\nswtbrdcuykabfcvkdzez\ntpcclifkeljytihrcqay\ntpidukuhjzefczzzbfkq\nugicwtbvtrehbbxpxifb\nvsbxggbwkfnqduxwfnfo\nvscmpsajlfvgubfaaovl\nwkbjzwucwljfrimpmyhc\nxbywibozwmikmqfbhhcl\nxjhguzyupzwweiqurpix\nxotogbgxpeyanfetcuke\nxtlhcsmpxohgmgnkeufc\nxtlsgypsfadpooefxzbc\nyvrnprxggperpjktrsvz\nzbmnmgqooketlyhnkoau\nznimkkasvwsrenzkycxf\nzudltfzotcjtnzxuglsd\nzylntrkdcpwsrtesjwhd\n",
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"`alab\nalaab\nbaala\nbaalb\nhtnak\nj`irhd\njayanth\nkalyan\nkanth\nkblyan\nku\nnandu \noakuh\nsampu\ntj\nyalkan\n",
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"`alab\nalaab\nbaala\nbbalb\nhtnak\nj`irhd\njayanth\nkalyan\nkanth\nkblyan\nku\nnandu \noakuh\nsampu\ntj\nyalkan\n",
"bnefxnxvgzedyyhngzcd\nbukgztockcqfckgcbfvx\ndpqzikfobucdhthxdjgk\nduunfsksrsrtekmqdcyz\needdpszrnavymmtatbdz\neqtgjoparmowzdqyoxyt\ngzqrcddiuteyojwaiyzp\nhrcbldvgylwgbusbmbor\nhzriwkbarxbgfcbceyhj\nilefraamidgpnpuuhgxp\niqgldquveoowtcudhnef\nizcobzcnfwlqiitvdwvx\njbbhawdydcprjbxphooh\njeeuhmsqrcozijipfion\njelrlpaxamceroswitdp\njyhfixjswnkkufnuxxzr\nmhecthlegrpunkdmbppw\nmjrmbsztsshfroefwsjr\nncbxcoksfzkvatxdknly\nnjhaimuczfskuiduburi\nnyljvrvipyampehwqnqr\noejuvpvaboygpoeylfqb\npevqgxiepjsrdzjazujl\nphqchumeaynllfdxfirg\npkwqyuqrqzhnbnfuvqnh\npzshkljugggekjdqzjen\nqlrzjpxiogvliexdzuzo\nqnjwjmwaxxmnsnhhlqqr\nqpmxujjloovaowuxwhms\nqsoemuvnpppsuacbazux\nsmzcnockvfajfrmxotho\nsrkrtsvojbrzmwzpowkj\nstmwcysyycqpevikeffm\nswtbrdcuykabfcvkdzez\ntpcclifkeljytihrcqay\ntpidukuhjzefczzzbfkq\nugicwtbvtrehbbxpxifb\nvsbxggbwkfnqduxwfnfo\nvscmpsajlfvgubfaaovl\nwkbjzwucwljfrimpmyhc\nxbywibozwmikmqfbhhcl\nxjhguzyupzwweiqurpix\nxotogbgxpeyanfetcuke\nxtlhcsmpxohgmgnkeufc\nxtlsgypsfadpooefxzbc\nyvrnprxggperpjktrsvz\nzbmnmgqooketlyhnkoau\nznimkkasvwsrenzkycxf\nzudltfzotcjtnzxuglsd\nzylntrkdcpwsrtesjwhd\n",
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"`alab\nalaab\nbaala\nbbblb\nhtnak\nj`irhd\njayanth\nkalyan\nkanth\nkblyan\nku\nnandu \noakuh\nsampu\ntj\nyalkan\n",
"bnefxnxvgzedyyhngzcd\nbukgztockcqfckgcbfvx\ndpqzikfobucdhthxdjgk\ndslguxzntjctozftlduz\nduunfsksrsrtekmqdcyz\needdpszrnavymmtatbdz\neqtgjoparmowzdqyoxyt\ngzqrcddiuteyojwaiyzp\nhrcbldvgylwgbusbmbor\nhzriwkbarxbgfcbceyhj\nilefraamidgpnpuuhgxp\niqgldquveoowtcudhnef\nizcobzcnfwlqiitvdwvx\njbbhawdydcprjbxphooh\njeeuhmsqrcozijipfion\njelrlpaxamceroswitdp\njyhfixjswnkkufnuxxzr\nmhecthlegrpunkdmbppw\nmjrmbsztsshfroefwsjr\nncbxcoksfzkvatxdknly\nnjhaimuczfskuiduburi\nnyljvrvipyampehwqnqr\noejuvpvaboygpoeylfqb\npevqgxiepjsrdzjazujl\nphqchumeaynllfdxfirg\npkwqyuqrqzhnbnfuvqnh\npzshkljugggekjdqzjen\nqlrzjpxiogvliexdzuzo\nqnjwjmwaxxmnsnhhlqqr\nqpmxujjloovaowuxwhms\nqsoemuvnpppsuacbazux\nsmzcnockvfajfrmxotho\nsrkrtsvojbrzmwzpowkj\nstmwcysyycqpevikeffm\nswtbrdcuykabfcvkdzez\ntpcclifkeljytihrcqay\ntpidukuhjzefczzzbfkq\nugicwtbvtrehbbxpxifb\nvsbxggbwkfnqduxwfnfo\nvscmpsajlfvgubfaaovl\nwkbjzwucwljfrimpmyhc\nxbywibozwmikmqfbhhcl\nxjhguzyupzwweiqurpix\nxotogbgxpeyanfetcuke\nxtlhcsmpxohgmgnkeufc\nxtlsgypsfadpooefxzbc\nyvrnprxggperpjktrsvz\nzbmnmgqooketlyhnkoau\nznimkkasvwsrenzkycxf\nzylntrkdcpwsrtesjwhd\n",
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"`alab\nalaab\nbaala\nbbblb\nhtnak\nj`irhd\njayanth\nkalyan\nkanth\nkblyan\nnandu \noakuh\nsampu\ntj\nuk\nyalkan\n",
"bnefxnxvgzedyyhngzcd\nbukgztockcqfckgcbfvx\ndpqzikfobucdhthxdjgk\ndslguxzntjctozftlduz\nduunfsksrsrtekmqdcyz\needdpszrnavymmtatbdz\neqtgjoparmowzdqyoxyt\ngzqrcddiuteyojwaiyzp\nhrcbldvgylwgbusbmbor\nhzriwkbarxbgfcbceyhj\nilefraamidgpnpuuhgxp\niqgldquveoowtcudhnef\nizcobzcnfwlqiitvdwvx\njbbhawdydcprjbxphooh\njeeuhmsqrcozijipfion\njelrlpaxamceroswitdp\njyhfixjswnkkufnuxxzr\nmhecthlegrpunkdmbppw\nmjrmbsztsshfroefwsjr\nncbxcoksfzkvatxdknly\nnjhaimuczfskuiduburi\nnyljvrvipyamoehwqnqr\noejuvpvaboygpoeylfqb\npevqgxiepjsrdzjazujl\nphqchumeaynllfdxfirg\npkwqyuqrqzhnbnfuvqnh\npzshkljugggekjdqzjen\nqlrzjpxiogvliexdzuzo\nqnjwjmwaxxmnsnhhlqqr\nqpmxujjloovaowuxwhms\nqsoemuvnpppsuacbazux\nsmzcnockvfajfrmxotho\nsrkrtsvojbrzmwzpowkj\nstmwcysyycqpevikeffm\nswtbrdcuykabfcvkdzez\ntpcclifkeljytihrcqay\ntpidukuhjzefczzzbfkq\nugicwtbvtrehbbxpxifb\nvsbxggbwkfnqduxwfnfo\nvscmpsajlfvgubfaaovl\nwkbjzwucwljfrimpmyhc\nxbywibozwmikmqfbhhcl\nxjhguzyupzwweiqurpix\nxotogbgxpeyanfetcuke\nxtlhcsmpxohgmgnkeufc\nxtlsgypsfadpooefxzbc\nyvrnprxggperpjktrsvz\nzbmnmgqooketlyhnkoau\nznimkkasvwsrenzkycxf\nzylntrkdcpwsrtesjwhd\n",
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wfpofmptfbmryphhsmhyagg\nxrajvprecwgxxpswcgmmvedewdmfnqwcuqdsciliqecihluilgmfcswtwkkxlcbhqkvcsw\nxroikdevlqmrszvsscpwjdtanmjjtheaygxhnqmgnzeylxofywzowcvfapzucltlzgjjlv\nxsrrfcnribfrqivgdkybcvomvleeglkvbmhklxesljqjibfapjivfvtcdslmfjmqhssqbf\nxswdyzivgplnuagweoplvuzfjyzezhvrjcdbrujxcmqudxswbolugtxzggrrbpgqrwwnvc\nxsywibcwqodraufbpgotfbnwxgvgddywsvylolhilqpdqunzzjfspdbiewsgeebubdikmq\nxthqjupousdbnczvsunpylzysvcpqmxjppopwggcbqrzdkhgyavkpqbrmlazuepmqlxiwm\nxtwddlwhmpxsgvuwspliodqlnoojgqgqhtczgabuilsdfptquhwpmgiaylaixnqzlqyrbq\nxuwjxnpqjnbkcpdmokalxapemvbqlzsvxzkutappwgzpdpyzkzcvbntcvfxsxpjaoxtfhv\nxvfhqfawkfdjpyeevdggatfiekixeyrfcpxscjkcfgqmyhjmjtimdspizhwzizcyuceglm\nxwkduooercteeqdvdlrwamnkyxjsxpfdlzehbgkvypxfsmqhibngjtgrkpferayxdznpgk\nxwolxcvmjjccsvlbrfqhddnymuyueowdpeqlaiejnntnmogteqpemeiqfxkgjtoepfovtb\nxxfysfbtklydqsbnoedooaejjdbigedbtddlaxklpmlgcfhfhpwtpbijzpbrqaltazdkvv\nxxytgokrcxaetauqgndmphwzyiayabjrqgeppxyjsttyzuvldvybsuxkbmfzvrtnovidzn\nxydrdwbirfqfvkbbyrgnhlabkgauruzejlicnutcatfmaqxfoegzxtwirqtsfeznmudahp\nxyqnynigcrdniiwkfgtjtpnyvgxxcuhkrhrwjcnrfirdoejokxzkurspsmygxrfxifyncn\nxzorzgvktiazlzynkmwbcrujpdzqsgqlaomtkvbhgfseiexvjvwwkasymwiammkempnjqc\nyayhuldzbtdiwxvgqeemwlvgkinrlpuujushfjzwjeagxasaqetoloffimzplnudeffgac\nybvebyerlkqqbasqgxnvfhbxyetaerlhhfhetdlvcdzfkpfkhwgrkibxgwlohblnqcvovt\nycwmfyaqqiannyhqouizveavgzjwoblsgwnkvjlnivqcwvzxtcthynmuxqkwwmtfisgglg\nyddqrxnvkiyadvloyemcycfcpyuwkzebcjaedsbvqqijqlgjycjpkpxflceoniyvqvurdi\nyddtqvmvlknoqxopbtbehdcjjqrxrqbtelliscxaheqfjsecpkdykaopsaqtssqoaooyiz\nydhacwyhsgewzmtgonzltjhgauhnihreqgjfwkjsmtpjhaefqzaauldrchjccdyrfvvriv\nyehktusdgzxlaeykexqgqoevjtframuqgbdnrsmbxrvbtfglowffctujtzqwzggtlbhrop\nyfyezjftqnohgonclkiybcigqzubszjfhlckcmvdjujreqhwjgzhywtoslbxwozopccjbz\nygqkxrwdvrkcoytxkcweagydmhrpyquimwrbvezzvvjpgihcyfqzvadtdfyemfqvynbdlr\nygqlkrxedsbnmzgegepveunlpivgnokxzlozbguyrbotmgdwqzannvikxchcqqodbispmu\nyhphljzhezohmiurcpblvwaajiqugtaoqmemjlhgoxprurtymkktdbnoxwttgeeqimlhcz\nyjiigrmogvbyyygiwupinjjufihfihtdxsexaalqvthrvgwovldosgzopootghkkccjqjd\nyjnecxsjjbhiqnvocdenqmwilxxzoqfotpikpqudmomikppzhdhfqsgbxiisyzwnhxyfvy\nyjytctxrhkvhksugmbztftuaqffjpvhzkxtlrvmtuvziskmypqviditwskiuimambsyvlc\nykajapprerdhscscgeqioksbonxrtlgtfgbijkdijccmtpmlnlhylolfgjueptzjcufyze\nykkpactyyfdisisactabnjvsnuykoinlvfahfhwcquagpmzvtezuijoqmiixvyassdmwoa\nykxrqftwtweddvlqjcujdgfgvewqwcqagwjuzoqyeynsxudffunvboeyrdxykmqccqxgym\nylqnbmtovuugvpqlbqqiastpragvapcxdkuqfghxuirtctitfpnjuahzvpzbuhxvgcuexm\nymedewdmmadbrrmyzufwbecgfvlxetwaxidibgvhrguzmdfmpvtpbdohvlzmiovriwkbhb\nymsqoruzpqmalrmwvvfdlggmlxdokhkmmlqfxbnuwectnvpncmituemctnsyjmdgqvzsdz\nyntermgkiacmdvldpcpqliagvcwcztkxdbpouivbfdpmhzsmewkgumqdrrwgqpgadqztnx\nyonpibdlrusctaztcrrmvamaohvttlswmlfwncayhcdqbtahiayxsljonybsenwchkiurg\nyoobniyvokxdnusvnqqqrpimtwwxyfrmyffqinsfhvlzmauzeeoymudaktnyqaphldqbjh\nyorhmmdsimabarvwxahmhlukpzqltppmsxlbqrdpsgawmvofcgjhxirbjhtepodutwsftv\nypphqlheqdhtfnddvgkvbmivtdzsaxkgygvuzjxhrmtqqmscxiahhaheleikytagzeicxl\nyqktdmkapspbmykoylpnzoipzwdmkrbhdntdkvpdelorqcjkqzzpinoqluibjgnqqlfewi\nyqtoldcxreprsegxilmqxckvzmusoizypwucoqzarfziqfhmjgcudhpugzsdccddnchrgm\nyrhjhyjmlfrxqiwsxzudremwsmrruxoeifbxcgjintkthxrnnuagunrpnnnyvnlhavvtvz\nyrvdchmswmutwxfqhxrpadwtqcotvxqzxrrblbwweaqwornertvgxbvwxisjwvoigfrtzs\nyrwawprdpvajshgzuxuiaxucflgafxqvnvxudbtztqploegyrlbfvafnrwaxatgvbvxcgt\nyugtedogfurkxiyqufotiajmwhyilthmoevlwlrxpwpzhsvbfzvtvhwycfznmaomafsyvy\nyurkfcnzbnbpwnawnuqdntifmythcvdhjhwcubwtjajuorvrijxhesaazpkqjgtjwubdxb\nyurpzfjayhuyawfqtmqotraxtkwlumqmtboulugfdnprmpkxksctunyolnkmqvhvxqyjjg\nyurttptcagfivhrfomidtwrxmtleztkkpvagrgbahjqrdppvtizcoskrxixldixdwmdwee\nyvfoudwhfxarkanzfngeuolaivunrheaqrdnarbsvxeutczzwibowhgcxskfuuburuqlrb\nyvwbjfdffaetigrwyycraudcksxpcsosggdnlvhcyozvrncxdgnulpfdxfhnsmiwrefwpw\nywjxeshoihmlgvxiljvwllfpnjzywcpamevwtygfphifubttnwnphdbytwodclrjprseqw\nywmvykpwxlzionemyrdbvowpgwmooqrlntgrrtzhzlolmcgvruncmawflyqrtbbohdymig\nywyffcvtgtzvgejzfiejqgmixbdpktzdlyqdwztchbuslzkftquixrehfxgulpmdyzvkxn\nyxrnxsxrzletbqexkrqoiernaplqyjpqoubvjsebalwnksvloidzfpirwycztwzzvewxot\nyxzukjwocyhzqjzdhtbrrrllktchfnctpirnawonydwwvuabuqcimcnlhqodemakmunmax\nyyemaliuvlnfrsicmlhluhxoynireajmtqwdujpkaxixugagkzbqmjtigbbeqsolqykdby\nyzkwrsvrdtsgtadinpgbpcbdifkmummrwsjxvibuzoznunfcivuxrczwwwyilfxijgdnzj\nyzsswuxmfxgzeffeglunwzpkvxhvzfoserdgpznvzkfbvixmlmzhegciyzvrtaobjuhqdz\nzariwcvmjnbwbtrernzkkzujziuysepkzgalnzocexcjwppyzzclvkatnhnstbkktqekox\nzbbgcwnhzcvqgssupkzwyxelqjbufnputnkuqsgokzzhsstxgjdmvudziuidtacdzqsfjj\nzbindgpfkrocsonunranqtzcadvtesdvrdprozprbxnolgkljltqxtgvdzggcxmlazzugk\nzbkvhsapbbkdycjuzqbpzptougkzuwugysowppnfwfzwkiidkggbownxopgkwqxyoyvvnt\nzbvcalbcvasbikjtnnaciwpvfphqocgijfxdoatzyjzjeyfoyeudxzdpmtfhkknqezftio\nzckqjjdyxwbbjtxkewauerqrexiltfhulidrwysbertmbzccapsnhjaexlncerxfgdhrad\nzcmvmxmvkdhdctqesjbiwfutdgbwjoxqgbzzssokllhaxbbsepkjevwrusgrlnicuwonav\nzdgmchnxloymoflnbrtkvxwkvcovwdhgkmuneqlirrcjcjagszkjibettfswvqufknachw\nzdsfdvyilxymegdvinbjgothxgnliregbnzabhnvcnpjkxhowzpsvlcdxxztuxtwllskji\nzebvieremkydqvaeuxwmwuhndzvjmjsdjhqionbuexjzojeqjzzrsrzomzznurpsbhnihe\nzecvqifccptswmhiiemlbyufeltczfbawgfgwfkimwngsptxxpvgwawcaoglvpqfwcsdyx\nzeycqwxllnnbfnonushmvdmplykyisjhhvszhjpfswwbolzummwrhylyjlbuwxywxyqsjb\nzgdtnhmivnnkclgarygydqdhltrsthidzyqazfnovktqcotchcolineiytymrjscyoeivd\nzggfkoqrezgctqiqofqfqtssfwuqbysrtfwpoyqediumvefmnsgxczrduunaqxkfxinhso\nzgyrfvsqpcnwezgibboqqmuvvjneptwbwdoxkqenngacqgvjlqxzaagptqwdbjhrltakcy\nzhcgnttcerswetzytqvcmkvzzlnwdzvianltohtjwbdxwbcrdlfzmuaitumzjdlfwyrabx\nzhgiqlepifzxzabcwuleyqxuoziwfcztkssysmagitujrlnicfiazavydtzfhnacqgloow\nzhmwurfjxrqnsymlnscvckioszozsllcbuwgatefumgmflzbjesamgxqvkpyhhtxpiouxd\nzifawftzqgemnhpqyictmoyfpcvkcaodakjacqauzyowdzsfqhkplfbyzmnimdlxmjydax\nziggwcfaejwmmtlbjqdowkrmterjfumflbuazkvhgcwwnmkorlydoisxhrwcibvnxfezzx\nzijlastetzwmkgdnswezxkhkxwrmvoeuuvcltbmbfihlycwwqrwaygifcgczxisixirpzg\nzikwanvngdfyfttelcxyayvdbyhlkhwvvfhilgbxzebzvxrjhwbeokrnevwdlqsecivzoi\nzimryrkecdqzlyemsssqmivpbywesonnvultkjjzthqilbntcvczvjkuetxcknhxrfzqsx\nzjiqrmvzadvlhnxydircnwlmcytsdrwfbtcizcibpnyddwssrgamwlptedbnjtbqnoafjb\nzkospbjlzwihhcgsihcsavajnmllfydjagcmujzxaydrohgzzxvshmcooworgvzowcvreq\nzkziktsikwowkavxfbektcybzylgxnnwyofuawghavgszuqfjfihdxlbkfaimhkemzynmv\nzldhjuuuhpyioqqjpxtsljixuccrjwjdpykyavzmplftdremcybyksasaytwbvhgshclzb\nzlerqooveibtuakbmuzaqviouhhdenowzyxezbqzqpgnhobduwbzbdftzrainjruucocig\nzlrqhlqkysmroykkbhgoqzssfnjmpyzdgwlgodfuortkvunhvnkfivvxxablmnblwdooug\nzlxkyfrllomgvpsnevmidmrpbhepwgdmezxcdptwokiioxhopmtrbqbpdiqhohvetjedbj\nzmqqzzcgblpchgflyvruihbpbklklbcxqjxhemqpugkflvhmosixpbeysebafvactijuab\nzmrgpiqyfofwkwafsxihaefgoscoeoirponzdkakpkksgjytfcmhaiibgspvhmdzgossve\nzmurqdzcbjypdauqxhrjrcgcuoecvhvqwlspibwcxvdmpdwwthtdkjmrfyiegfhfzkehiv\nznhruouvmhrjvkdofhdtyplznfqgopquyfzdbncbmyaatfqnvygwflobrdirgqnzsicxpe\nznjbzouqgzkijndwbcjzsfjnacvackktmscubzlwesiqwqlwhgfuusvbardpwkbfxuauyt\nznklwlmzboiaevdvkkiaualcupfkucuozfeuphohvxcaegxyrzgtjwfaqfrzoofhyorsla\nzoltzdwtdadcsjbopruyaqdsjgmfjhbfiizgixxvwrhrvyzrlrgfdgeqhwheidhvjgootu\nzpodabtnkbqddpibhikzvnjrhjhgbivpwssltjrnemtpjhjrondmoovqrquvnzjuxpmtet\nzpqdpkqdsjhyzuiyzykjkiwxsocsitjizwjsndbxjxrxlwiukkqfjypgjljsjcuztktobk\nzpyfmdlqlwqiodcwfygkivbujfinzyhcejcjojonhgustqjfnecolocmfhpzxtgfpmuscr\nzqjholpbpqbptlkfeapndiptwrlzkcsqphmsfyiyxhqiwmkftwaypdrgqjhjazobjiiznd\nzqwpnthicyqzhfbzqgambaqwcgafdlbsxfzxxynskvbayzbuecaabuiihrusylazgefmyx\nztkvzcgkmijoohmzicndfudzgrvofnxjboojiegewbacgbpaloptookenlazjttykwipem\nztzzgqulftvqyujbhazwbbqhdgofwyrxvewjybbrkkskbixngyuiisyqchwpqshlbwhxhg\nzvtkfqqynnvheasuyijwgavtjcicruzqykrxybaotufmtvkpcezzczmocmvrlxcjnktjqb\nzxjfnzqjxasiaiciuihfmqfrqvwfwosatplyhjvfvifvbkulzxnihbfgtkeacqjvklmbra\nzyhyguhjjguxhzyplwiirestldulakyqquqgqccslrcgsqhvdehnjljkwomipksjeqxfwh\nzylntrkdcpwsrtesjwhdizcobzcnfwlqijtvdwvxhrcbldvgylwgbusbmborxtlhcsmpxo\n",
"`alab\nalaab\nbaala\nbbblb\nhtnak\nj`irhd\njayanth\nkalyan\nkanth\nkblzan\nnandu \noakuh\nsampu\ntj\nuk\nyalkan\n",
"bnefxnxvgzedyyhngzcd\nbukgztockcqfckgcbfvx\ndpqzikfobucdhthxdjgk\ndslguxzntjctozftlduz\nduunfsksrsrtekmqdcyz\needdpszrnavymmtatbdz\neqtgjoparmowzdqyoxyt\ngzqrcddiuteyojwaiyzp\nhrcbldvgylwgbusbmbor\nhzriwkbarxbgfcbceyhj\nilefraamidgpnpuuhgxp\niqgldquveoowtcudhnef\nizcobzcnfwlqiitvdwvx\njbbhawdydcprjbxphonh\njeeuhmsqrcozijipfion\njelrlpaxamceroswitdp\njyhfixjswnkkufnuxxzr\nmhecthlegrpunkdmbppw\nmjrmbsztsshfroefwsjr\nncbxcoksfzkvatxdknly\nnjhaimuczfskuiduburi\nnyljvrvipyamoehwqnqr\noejuvpvaboygpoeylfqb\npevqgxiepjsrdzjazujl\nphqchumeaynllfdxfirg\npkwqyuqrqzhnbnfuvqnh\npzshkljugggekjdqzjen\nqlrzjpxiogvliexdzuzo\nqnjwjmwaxxmnsnhhlqqr\nqpmxujjloovaowuxwhms\nqsoemuvnpppsuacbazux\nsmzcnockvfajfrmxotho\nsrkrtsvojbrzmwzpowkj\nstmwcysyycqpevikeffm\ntpcclifkeljytihrcqay\ntpidukuhjzefczzzbfkq\nugicwtbvtrehbbxpxifb\nvsbxggbwkfnqduxwfnfo\nvscmpsajlfvgubfaaovl\nwkbjzwucwljfrimpmyhc\nxbywibozwmikmqfbhhcl\nxjhguzyupzwweiqurpix\nxotogbgxpeyanfetcuke\nxtlhcsmpxohgmgnkeufc\nxtlsgypsfadpooefxzbc\nyvrnprxggperpjktrsvz\nzbmnmgqooketlyhnkoau\nzezdkvcfbakyucdrbtws\nznimkkasvwsrenzkycxf\nzylntrkdcpwsrtesjwhd\n"
]
}
|
Bob gives you a list of N strings and a task to solve. The task is to remove all the duplicate strings from the list and print the resulting list of strings in a sorted order.
Input:
The first line contains an integer N. Then next N lines contain a string Si.
Output:
Print the sorted list.
Constraints:
1 ≤ |N| ≤ 5000
1 ≤ |Si| ≤ 100
SAMPLE INPUT
16
nandu
kanth
kalyan
dhiraj
kanth
kalyan
baala
kt
baala
jayanth
sampu
baala
kanth
kalyan
baala
kt
SAMPLE OUTPUT
baala
dhiraj
jayanth
kalyan
kanth
kt
nandu
sampu
|
{
"inputs": [
"6\n1 1 2 2 1 1\n",
"6\n1 3 2 5 4 6\n",
"5\n1 2 1 2 1\n",
"1\n44884539\n",
"1\n56946342\n",
"6\n1 2 2 2 1 1\n",
"6\n1 3 2 5 2 6\n",
"1\n91135303\n",
"6\n1 2 2 1 1 1\n",
"6\n2 3 2 5 2 6\n",
"1\n19087161\n",
"6\n1 2 1 1 1 1\n",
"6\n2 3 2 8 2 6\n",
"1\n11456862\n",
"1\n16711056\n",
"1\n19954346\n",
"1\n19649781\n",
"1\n231392\n",
"1\n265022\n",
"1\n483249\n",
"1\n362792\n",
"1\n292478\n",
"1\n503918\n",
"1\n111825\n",
"1\n181675\n",
"1\n352374\n",
"1\n311322\n",
"1\n533424\n",
"1\n982063\n",
"1\n353415\n",
"1\n627673\n",
"1\n36646\n",
"1\n48850\n",
"1\n77788\n",
"1\n52568\n",
"1\n79814\n",
"1\n61062\n",
"1\n118480\n",
"1\n55299\n",
"1\n57778\n",
"1\n46504\n",
"1\n31848\n",
"1\n39215\n",
"1\n15650\n",
"1\n3380\n",
"1\n3693\n",
"1\n3440\n",
"1\n4355\n",
"1\n3537\n",
"1\n1873\n",
"1\n3020\n",
"1\n2054\n",
"1\n2543\n",
"1\n3230\n"
],
"outputs": [
"0\n1 1 2 2 1 1 ",
"1\n1 2 3 4 5 6 ",
"2\n1 1 1 1 1 ",
"0\n44884539 ",
"0\n56946342 \n",
"0\n1 2 2 2 1 1 \n",
"2\n1 2 2 3 5 6 \n",
"0\n91135303 \n",
"0\n1 2 2 1 1 1 \n",
"2\n2 2 2 3 5 6 \n",
"0\n19087161 \n",
"1\n1 1 1 1 1 1 \n",
"2\n2 2 2 3 6 6 \n",
"0\n11456862 \n",
"0\n16711056 \n",
"0\n19954346 \n",
"0\n19649781 \n",
"0\n231392 \n",
"0\n265022 \n",
"0\n483249 \n",
"0\n362792 \n",
"0\n292478 \n",
"0\n503918 \n",
"0\n111825 \n",
"0\n181675 \n",
"0\n352374 \n",
"0\n311322 \n",
"0\n533424 \n",
"0\n982063 \n",
"0\n353415 \n",
"0\n627673 \n",
"0\n36646 \n",
"0\n48850 \n",
"0\n77788 \n",
"0\n52568 \n",
"0\n79814 \n",
"0\n61062 \n",
"0\n118480 \n",
"0\n55299 \n",
"0\n57778 \n",
"0\n46504 \n",
"0\n31848 \n",
"0\n39215 \n",
"0\n15650 \n",
"0\n3380 \n",
"0\n3693 \n",
"0\n3440 \n",
"0\n4355 \n",
"0\n3537 \n",
"0\n1873 \n",
"0\n3020 \n",
"0\n2054 \n",
"0\n2543 \n",
"0\n3230 \n"
]
}
|
Berland — is a huge country with diverse geography. One of the most famous natural attractions of Berland is the "Median mountain range". This mountain range is n mountain peaks, located on one straight line and numbered in order of 1 to n. The height of the i-th mountain top is a_i.
"Median mountain range" is famous for the so called alignment of mountain peaks happening to it every day. At the moment of alignment simultaneously for each mountain from 2 to n - 1 its height becomes equal to the median height among it and two neighboring mountains. Formally, if before the alignment the heights were equal b_i, then after the alignment new heights a_i are as follows: a_1 = b_1, a_n = b_n and for all i from 2 to n - 1 a_i = median(b_{i-1}, b_i, b_{i+1}). The median of three integers is the second largest number among them. For example, median(5,1,2) = 2, and median(4,2,4) = 4.
Recently, Berland scientists have proved that whatever are the current heights of the mountains, the alignment process will stabilize sooner or later, i.e. at some point the altitude of the mountains won't changing after the alignment any more. The government of Berland wants to understand how soon it will happen, i.e. to find the value of c — how many alignments will occur, which will change the height of at least one mountain. Also, the government of Berland needs to determine the heights of the mountains after c alignments, that is, find out what heights of the mountains stay forever. Help scientists solve this important problem!
Input
The first line contains integers n (1 ≤ n ≤ 500 000) — the number of mountains.
The second line contains integers a_1, a_2, a_3, …, a_n (1 ≤ a_i ≤ 10^9) — current heights of the mountains.
Output
In the first line print c — the number of alignments, which change the height of at least one mountain.
In the second line print n integers — the final heights of the mountains after c alignments.
Examples
Input
5
1 2 1 2 1
Output
2
1 1 1 1 1
Input
6
1 3 2 5 4 6
Output
1
1 2 3 4 5 6
Input
6
1 1 2 2 1 1
Output
0
1 1 2 2 1 1
Note
In the first example, the heights of the mountains at index 1 and 5 never change. Since the median of 1, 2, 1 is 1, the second and the fourth mountains will have height 1 after the first alignment, and since the median of 2, 1, 2 is 2, the third mountain will have height 2 after the first alignment. This way, after one alignment the heights are 1, 1, 2, 1, 1. After the second alignment the heights change into 1, 1, 1, 1, 1 and never change from now on, so there are only 2 alignments changing the mountain heights.
In the third examples the alignment doesn't change any mountain height, so the number of alignments changing any height is 0.
|
{
"inputs": [
"2\n3\n1 2 3\n2\n42 42",
"2\n3\n1 4 3\n2\n42 42",
"2\n3\n1 4 3\n2\n42 28",
"2\n3\n1 4 3\n2\n38 42",
"2\n3\n1 0 3\n2\n38 42",
"2\n3\n1 -1 3\n2\n38 42",
"2\n3\n1 0 1\n2\n38 42",
"2\n3\n2 0 1\n2\n38 42",
"2\n3\n1 4 3\n2\n42 7",
"2\n3\n1 0 3\n2\n61 42",
"2\n3\n2 0 1\n2\n38 36",
"2\n3\n1 4 3\n2\n47 7",
"2\n3\n1 0 2\n2\n61 42",
"2\n3\n2 0 1\n2\n38 10",
"2\n3\n1 4 3\n2\n20 7",
"2\n3\n1 0 2\n2\n61 17",
"2\n3\n1 4 3\n2\n20 8",
"2\n3\n1 0 2\n2\n1 17",
"2\n3\n1 4 3\n2\n20 2",
"2\n3\n0 -2 0\n2\n75 42",
"2\n3\n1 4 3\n2\n7 2",
"2\n3\n0 -2 -1\n2\n75 42",
"2\n3\n1 4 3\n2\n13 2",
"2\n3\n0 -3 -1\n2\n75 42",
"2\n3\n1 4 3\n2\n42 8",
"2\n3\n1 2 0\n2\n42 42",
"2\n3\n1 -1 3\n2\n38 12",
"2\n3\n1 0 3\n2\n42 7",
"2\n3\n1 0 5\n2\n61 42",
"2\n3\n0 -1 3\n2\n38 32",
"2\n3\n2 0 1\n2\n38 8",
"2\n3\n1 0 1\n2\n61 42",
"2\n3\n2 -1 1\n2\n38 10",
"2\n3\n1 4 3\n2\n39 7",
"2\n3\n1 2 3\n2\n20 8",
"2\n3\n1 4 6\n2\n20 2",
"2\n3\n0 -2 0\n2\n59 42",
"2\n3\n1 5 3\n2\n13 2",
"2\n3\n1 4 6\n2\n42 8",
"2\n3\n1 2 0\n2\n42 80",
"2\n3\n1 -1 3\n2\n38 6",
"2\n3\n1 4 3\n2\n28 7",
"2\n3\n1 2 3\n2\n20 12",
"2\n3\n1 -3 0\n2\n38 42",
"2\n3\n1 4 6\n2\n20 0",
"2\n3\n0 -2 1\n2\n59 42",
"2\n3\n1 -2 -1\n2\n60 42",
"2\n3\n1 2 3\n2\n13 2",
"2\n3\n1 4 3\n2\n61 8",
"2\n3\n2 2 0\n2\n42 80",
"2\n3\n1 -1 3\n2\n38 4",
"2\n3\n1 -1 4\n2\n42 7",
"2\n3\n1 4 3\n2\n28 6",
"2\n3\n1 2 3\n2\n20 23",
"2\n3\n1 4 2\n2\n20 0",
"2\n3\n0 -2 1\n2\n39 42",
"2\n3\n1 0 3\n2\n13 2",
"2\n3\n1 4 4\n2\n61 8",
"2\n3\n1 -1 3\n2\n17 4",
"2\n3\n1 -1 4\n2\n42 0",
"2\n3\n1 4 2\n2\n28 6",
"2\n3\n0 -2 0\n2\n39 42",
"2\n3\n1 0 3\n2\n8 2",
"2\n3\n1 2 4\n2\n61 8",
"2\n3\n1 -2 3\n2\n17 4",
"2\n3\n1 -1 3\n2\n42 0",
"2\n3\n1 4 2\n2\n14 6",
"2\n3\n1 -1 3\n2\n47 0",
"2\n3\n1 -2 3\n2\n47 0",
"2\n3\n1 4 2\n2\n14 14",
"2\n3\n1 -2 2\n2\n47 0",
"2\n3\n1 -3 2\n2\n47 0",
"2\n3\n1 -1 2\n2\n47 0",
"2\n3\n1 2 2\n2\n42 42",
"2\n3\n1 4 3\n2\n69 28",
"2\n3\n1 4 3\n2\n51 42",
"2\n3\n1 -2 3\n2\n38 42",
"2\n3\n0 -1 3\n2\n38 53",
"2\n3\n2 -1 1\n2\n38 36",
"2\n3\n1 7 3\n2\n47 7",
"2\n3\n1 0 2\n2\n61 7",
"2\n3\n0 -2 1\n2\n71 42",
"2\n3\n0 -3 -1\n2\n75 16",
"2\n3\n1 2 0\n2\n24 42",
"2\n3\n2 -1 3\n2\n38 12",
"2\n3\n1 -1 3\n2\n42 7",
"2\n3\n2 0 1\n2\n38 13",
"2\n3\n1 4 3\n2\n14 7",
"2\n3\n0 -2 0\n2\n38 77",
"2\n3\n0 -1 0\n2\n59 42",
"2\n3\n1 -4 -1\n2\n75 42",
"2\n3\n1 0 6\n2\n42 8",
"2\n3\n1 -1 3\n2\n38 7",
"2\n3\n1 4 3\n2\n38 7",
"2\n3\n1 -3 0\n2\n38 61",
"2\n3\n1 0 6\n2\n20 0",
"2\n3\n0 -1 1\n2\n59 42",
"2\n3\n1 -1 3\n2\n38 5",
"2\n3\n0 -2 1\n2\n39 14",
"2\n3\n1 4 4\n2\n61 1",
"2\n3\n1 -1 3\n2\n17 8"
],
"outputs": [
"3\n0\n",
"5\n0\n",
"5\n14\n",
"5\n4\n",
"4\n4\n",
"6\n4\n",
"2\n4\n",
"3\n4\n",
"5\n35\n",
"4\n19\n",
"3\n2\n",
"5\n40\n",
"3\n19\n",
"3\n28\n",
"5\n13\n",
"3\n44\n",
"5\n12\n",
"3\n16\n",
"5\n18\n",
"4\n33\n",
"5\n5\n",
"3\n33\n",
"5\n11\n",
"5\n33\n",
"5\n34\n",
"3\n0\n",
"6\n26\n",
"4\n35\n",
"6\n19\n",
"5\n6\n",
"3\n30\n",
"2\n19\n",
"5\n28\n",
"5\n32\n",
"3\n12\n",
"8\n18\n",
"4\n17\n",
"6\n11\n",
"8\n34\n",
"3\n38\n",
"6\n32\n",
"5\n21\n",
"3\n8\n",
"7\n4\n",
"8\n20\n",
"5\n17\n",
"4\n18\n",
"3\n11\n",
"5\n53\n",
"4\n38\n",
"6\n34\n",
"7\n35\n",
"5\n22\n",
"3\n3\n",
"4\n20\n",
"5\n3\n",
"4\n11\n",
"6\n53\n",
"6\n13\n",
"7\n42\n",
"4\n22\n",
"4\n3\n",
"4\n6\n",
"4\n53\n",
"8\n13\n",
"6\n42\n",
"4\n8\n",
"6\n47\n",
"8\n47\n",
"4\n0\n",
"7\n47\n",
"9\n47\n",
"5\n47\n",
"2\n0\n",
"5\n41\n",
"5\n9\n",
"8\n4\n",
"5\n15\n",
"5\n2\n",
"8\n40\n",
"3\n54\n",
"5\n29\n",
"5\n59\n",
"3\n18\n",
"7\n26\n",
"6\n35\n",
"3\n25\n",
"5\n7\n",
"4\n39\n",
"2\n17\n",
"8\n33\n",
"7\n34\n",
"6\n31\n",
"5\n31\n",
"7\n23\n",
"7\n20\n",
"3\n17\n",
"6\n33\n",
"5\n25\n",
"6\n60\n",
"6\n9\n"
]
}
|
Little chief has his own restaurant in the city. There are N workers there. Each worker has his own salary. The salary of the i-th worker equals to Wi (i = 1, 2, ..., N). Once, chief decided to equalize all workers, that is, he wants to make salaries of all workers to be equal. But for this goal he can use only one operation: choose some worker and increase by 1 salary of each worker, except the salary of the chosen worker. In other words, the chosen worker is the loser, who will be the only worker, whose salary will be not increased during this particular operation. But loser-worker can be different for different operations, of course. Chief can use this operation as many times as he wants. But he is a busy man. That's why he wants to minimize the total number of operations needed to equalize all workers. Your task is to find this number.
Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. The first line of each test case contains a single integer N denoting the number of workers. The second line contains N space-separated integers W1, W2, ..., WN denoting the salaries of the workers.
Output
For each test case, output a single line containing the minimum number of operations needed to equalize all workers.
Constraints
1 ≤ T ≤ 100
1 ≤ N ≤ 100
0 ≤ Wi ≤ 10000 (10^4)
Example
Input:
2
3
1 2 3
2
42 42
Output:
3
0
Explanation
Example Case 1. Chief can equalize all salaries in 3 turns:
Turn ID
IDs of involved workers
Salaries after the move
1
1 2
2 3 3
2
1 2
3 4 3
3
1 3
4 4 4
Example Case 2. All salaries are already equal. He doesn't need to do anything.
|
{
"inputs": [
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nThursday Friday Saturday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 4\n7 3\nMonday Tuesday Wednesday\n9 4\nTuhrsday Friday Saturday yadnuS\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 0\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday daysTue Wednesday\n6 2\nybdhrusT Friday yadsutSa Sun`dy\n0 0",
"2 0\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 4\n7 3\nMonday Tuesday Wednesday\n9 4\nTuhrsday Friday Saturday yadnuS\n0 0",
"2 3\n1 3\nMonday Tuesday yadsendeW\n1 4\nThursday Friday Saturday Sunday\n0 0\n14 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday yadsutSa Sun`dy\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesdax\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nThursday Friday Saturday yadnuS\n0 0",
"2 2\n4 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 2\n5 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n4 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 2\n5 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aStusday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday yadsendeW\n9 4\nThursday Friday Saturday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday aRturday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTuhrsday Friday Saturday yadnuS\n0 0",
"2 2\n2 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 2\n5 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 2\nTsurhday Friday aStusday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday yadsendeW\n9 4\nThursday Friday Saturday yadnuS\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tufsday Wednesday\n9 4\nTuhrsday Friday Saturday yadnuS\n0 0",
"2 2\n5 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n15 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 2\n2 3\nMonday Uuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 4\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n3 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesdax\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n15 4\nThursday Friday Saturday yadnuS\n0 0",
"2 2\n4 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nyadnoM Tuesday Wednesday\n9 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n2 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday atSurday Sunday\n0 0",
"2 2\n7 3\nMonday yadseuT Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n14 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aStusday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n13 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday aRturday Sunday\n0 0",
"2 2\n2 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMoneay Tuesday Wednesday\n9 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 2\n5 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n10 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 4\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadsTue Wednesday\n6 2\nTsurhday Friday aStusday Sunday\n0 0",
"2 1\n5 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n15 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n3 4\nThursday Friday Saturdya Sunday\n2 2\n7 3\nMonday Tuesday Wednesdax\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n4 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nyadnoM Tuesday Wednesday\n2 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 2\n7 3\nMonday yadseuT Wedoesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n14 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n5 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aStusday Sunday\n0 0",
"2 2\n12 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n13 3\nMonday Tuesday Wednesday\n9 4\nTsurhday Friday aRturday Sunday\n0 0",
"2 2\n5 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMondby Tuesday Wednesday\n10 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 4\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday Tuesday Wednesday\n6 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadsTue Wednesday\n6 2\nTsurhday Friday aStusday Sunday\n0 0",
"2 1\n5 3\nMonday Tuesday Wednesday\n13 4\nThursday Friday Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n15 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n4 4\nThursday Friday Saturdya Sunday\n2 2\n7 3\nMonday Tuesday Wednesdax\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n4 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 1\n7 3\nyadnoM Tuesday Wednesday\n2 4\nTsurhday Friday Saturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wedoesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n12 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n13 3\nMonday Tuesday Vednesday\n9 4\nTsurhday Friday aRturday Sunday\n0 0",
"2 4\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nyadnoM Tuesday Wednesday\n6 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 3\n7 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadsTue Wednesday\n6 2\nTsurhday Friday aStusday Sunday\n0 0",
"2 1\n5 3\nMonday Tuesday Wednesday\n13 4\nThursday yadirF Saturday Sunday\n2 2\n7 3\nMonday Tuesday Wednesday\n15 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n4 4\nThursday Frid`y Saturdya Sunday\n2 2\n7 3\nMonday Tuesday Wednesdax\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n7 3\nMonday Tuesday Wedoesday\n8 4\nThursday Friday Sasurday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n12 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saturday Sunday\n2 2\n13 3\nMonday Tuesday Vednesday\n0 4\nTsurhday Friday aRturday Sunday\n0 0",
"2 4\n7 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n7 3\nyadnoM Tuesday Wednesday\n6 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 3\n7 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n7 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday aStusday Sunday\n0 0",
"2 1\n5 3\nMonday Tuesday Wednesday\n13 4\nThursday yadirF Saturday Snuday\n2 2\n7 3\nMonday Tuesday Wednesday\n15 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n4 4\nThursday Fird`y Saturdya Sunday\n2 2\n7 3\nMonday Tuesday Wednesdax\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n7 3\nMondby Tuesday Wedoesday\n8 4\nThursday Friday Sasurday Sunday\n2 0\n7 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n12 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saaurdty Sunday\n2 2\n13 3\nMonday Tuesday Vednesday\n0 4\nTsurhday Friday aRturday Sunday\n0 0",
"2 4\n7 3\nMonday Tuescay Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n7 3\nyadnoM Tuesday Wednesday\n6 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 3\n7 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n14 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday aStusday Sunday\n0 0",
"2 1\n5 3\nMonday Tuesday Wednesday\n13 4\nThursday yadirF Saturday Snudax\n2 2\n7 3\nMonday Tuesday Wednesday\n15 4\nTsurhday Friday aSuurday Sunday\n0 0",
"2 2\n6 3\nMonday Tuesday Wednesday\n4 4\nThursday Fird`y Saturdya Sunday\n2 2\n10 3\nMonday Tuesday Wednesdax\n9 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n7 3\nMondby Tuesday Wedoesday\n8 4\nThursday Friday Sasurday Sunday\n2 0\n3 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n12 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saaurdty Sunday\n2 2\n13 3\nMonday Tuesday Vednesday\n0 4\nTsurhday yadirF aRturday Sunday\n0 0",
"2 4\n7 3\nMonday Tuescay Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n7 3\nMonday Tuesday Wednesday\n6 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 3\n7 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n14 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday aStusday Sunady\n0 0",
"2 2\n7 3\nMpndby Tuesday Wedoesday\n8 4\nThursday Friday Sasurday Sunday\n2 0\n3 3\nMonday yadseuT Wednesday\n6 4\nTsurhday Friday aSturday Sunday\n0 0",
"2 2\n12 3\nMonday Tuesday Wednesday\n8 4\nThursday Friday Saaurdty Sunday\n2 2\n13 3\nMonday yadseuT Vednesday\n0 4\nTsurhday yadirF aRturday Sunday\n0 0",
"2 4\n7 3\nMonday Tuescay Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n7 3\nMonday Tuesday Wednesday\n0 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 3\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n14 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday aStusday Sunady\n0 0",
"2 2\n12 3\nMonday Tuesday Wednesday\n0 4\nThursday Friday Saaurdty Sunday\n2 2\n13 3\nMonday yadseuT Vednesday\n0 4\nTsurhday yadirF aRturday Sunday\n0 0",
"2 4\n7 3\nMonday yacseuT Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n7 3\nMonday Tuesday Wednesday\n0 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 3\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n14 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday yadsutSa Sunady\n0 0",
"2 4\n7 3\nMonday yacseuT Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n7 3\nMonday Tuesday Weanesddy\n0 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 3\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n14 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday yadsutSa Sun`dy\n0 0",
"2 4\n7 3\nMonday yacseuT Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n6 3\nMonday Tuesday Weanesddy\n0 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday Saturday Sunday\n2 0\n14 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday yadsutSa Sun`dy\n0 0",
"2 4\n7 3\nMonday yacseuT Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n6 3\nMonday Tuesday Weaoesddy\n0 4\nTsurhday Griday aSturday Sunday\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nMonday yadsTue Wednesday\n6 2\nTsurhdby Friday yadsutSa Sun`dy\n0 0",
"2 4\n7 3\nMonday yacseuT Wednesday\n8 4\nThursday Friday yadrutaS Sunday\n2 0\n6 3\nMonday Tuesday Weaoesddy\n0 4\nyadhrusT Griday aSturday Sunday\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday yadsTue Wednesday\n6 2\nTsurhdby Friday yadsutSa Sun`dy\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday yadsTue Wednesday\n6 2\nybdhrusT Friday yadsutSa Sun`dy\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday daysTue Wednesday\n6 2\nybdhrusT Friday yadsutSa Sun`dy\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday d`ysTue Wednesday\n6 2\nybdhrusT Friday yadsutSa Sun`dy\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday d`ysTue Wednesday\n6 2\nybdhrusT Friday aStusday Sun`dy\n0 0",
"2 0\n1 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday d`ysTue Wednesday\n6 4\nybdhrusT Friday aStusday Sun`dy\n0 0",
"2 0\n0 3\nMonday Tuesday Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday d`ysTue Wednesday\n6 4\nybdhrusT Friday aStusday Sun`dy\n0 0",
"2 0\n0 3\nMonday Tuescay Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday d`ysTue Wednesday\n6 4\nybdhrusT Friday aStusday Sun`dy\n0 0",
"2 0\n0 3\nMonday Tuescay Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday d`ysuTe Wednesday\n6 4\nybdhrusT Friday aStusday Sun`dy\n0 0",
"2 0\n0 3\nMonday Ttescay Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday d`ysuTe Wednesday\n6 4\nybdhrusT Friday aStusday Sun`dy\n0 0",
"2 0\n0 3\nMonday Ttescay Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 0\n14 3\nLonday s`yduTe Wednesday\n6 4\nybdhrusT Friday aStusday Sun`dy\n0 0",
"2 0\n0 3\nMonday Ttescay Wednesday\n1 4\nThursday Friday yadrutaS Sunday\n2 1\n14 3\nLonday s`yduTe Wednesday\n6 4\nybdhrusT Friday aStusday Sun`dy\n0 0"
],
"outputs": [
"Yes\nNo",
"Yes\nNo\n",
"No\nNo\n",
"Yes\nYes\n",
"No\n",
"No\nYes\n",
"Yes\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"Yes\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n",
"No\nNo\n"
]
}
|
You are working as a private teacher. Since you are giving lessons to many pupils, you are very busy, especially during examination seasons. This season is no exception in that regard.
You know days of the week convenient for each pupil, and also know how many lessons you have to give to him or her. You can give just one lesson only to one pupil on each day. Now, there are only a limited number of weeks left until the end of the examination. Can you finish all needed lessons?
Input
The input consists of multiple data sets. Each data set is given in the following format:
N W
t1 c1
list-of-days-of-the-week
t2 c2
list-of-days-of-the-week
...
tN cN
list-of-days-of-the-week
A data set begins with a line containing two integers N (0 < N ≤ 100) and W (0 < W ≤ 1010 ). N is the number of pupils. W is the number of remaining weeks. The following 2N lines describe information about the pupils. The information for each pupil is given in two lines. The first line contains two integers ti and ci. ti (0 < ti ≤ 1010 ) is the number of lessons that the i-th pupil needs. ci (0 < ci ≤ 7) is the number of days of the week convenient for the i-th pupil. The second line is the list of ci convenient days of the week (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday).
The end of input is indicated by a line that contains two zeros. This line should not be processed.
Output
For each data set, print “Yes” if you can finish all lessons, or “No” otherwise.
Example
Input
2 2
6 3
Monday Tuesday Wednesday
8 4
Thursday Friday Saturday Sunday
2 2
7 3
Monday Tuesday Wednesday
9 4
Thursday Friday Saturday Sunday
0 0
Output
Yes
No
|
{
"inputs": [
"3 \n1200\n500\n242",
"3 \n1200\n360\n242",
"3 \n1200\n360\n255",
"3 \n1200\n493\n380",
"3 \n1200\n806\n380",
"3 \n1200\n32\n380",
"3 \n1200\n30\n380",
"3 \n1200\n30\n99",
"3 \n1200\n30\n158",
"3 \n1200\n12\n158",
"3 \n1200\n24\n158",
"3 \n391\n24\n158",
"3 \n391\n43\n158",
"3 \n391\n43\n188",
"3 \n391\n50\n188",
"3 \n391\n162\n188",
"3 \n19\n67\n188",
"3 \n19\n67\n30",
"3 \n19\n67\n33",
"3 \n19\n126\n25",
"3 \n21\n37\n25",
"3 \n50\n37\n25",
"3 \n11\n42\n25",
"3 \n11\n49\n25",
"3 \n11\n49\n32",
"3 \n11\n69\n32",
"3 \n21\n69\n32",
"3 \n21\n75\n32",
"3 \n21\n47\n32",
"3 \n21\n71\n13",
"3 \n21\n107\n17",
"3 \n21\n107\n32",
"3 \n21\n19\n55",
"3 \n21\n19\n43",
"3 \n7\n19\n43",
"3 \n7\n17\n43",
"3 \n7\n33\n43",
"3 \n5\n33\n43",
"3 \n6\n50\n80",
"3 \n8\n50\n80",
"3 \n8\n50\n159",
"3 \n11\n50\n221",
"3 \n10\n50\n221",
"3 \n10\n50\n408",
"3 \n3\n50\n456",
"3 \n0\n50\n225",
"3 \n0\n93\n225",
"3 \n0\n124\n225",
"3 \n0\n80\n225",
"3 \n0\n49\n293",
"3 \n0\n49\n327",
"3 \n0\n49\n100",
"3 \n0\n49\n110",
"3 \n0\n87\n110",
"3 \n1\n87\n110",
"3 \n1\n87\n111",
"3 \n1200\n500\n392",
"3 \n1200\n703\n242",
"3 \n1224\n360\n255",
"3 \n94\n360\n380",
"3 \n1679\n32\n380",
"3 \n1246\n30\n380",
"3 \n2131\n30\n99",
"3 \n2197\n12\n158",
"3 \n494\n24\n158",
"3 \n391\n77\n158",
"3 \n391\n21\n188",
"3 \n391\n50\n1",
"3 \n555\n87\n188",
"3 \n320\n162\n188",
"3 \n19\n101\n21",
"3 \n10\n67\n33",
"3 \n1\n67\n25",
"3 \n19\n126\n28",
"3 \n19\n37\n40",
"3 \n27\n49\n25",
"3 \n50\n0\n25",
"3 \n71\n9\n25",
"3 \n11\n35\n32",
"3 \n21\n47\n53",
"3 \n21\n107\n51",
"3 \n21\n19\n100",
"3 \n7\n19\n36",
"3 \n5\n33\n49",
"3 \n2\n50\n80",
"3 \n8\n50\n177",
"3 \n9\n63\n221",
"3 \n10\n89\n216",
"3 \n3\n50\n20",
"3 \n0\n124\n286",
"3 \n0\n0\n225",
"3 \n0\n30\n293",
"3 \n0\n1\n327",
"3 \n0\n83\n100",
"3 \n0\n18\n110",
"3 \n1\n117\n110",
"3 \n0\n87\n111",
"3 \n1200\n571\n392",
"3 \n1200\n1258\n242",
"3 \n1224\n331\n255",
"3 \n94\n360\n473"
],
"outputs": [
"12\n5\n7\n",
"12\n5\n7\n",
"12\n5\n4\n",
"12\n11\n7\n",
"12\n10\n7\n",
"12\n4\n7\n",
"12\n3\n7\n",
"12\n3\n8\n",
"12\n3\n5\n",
"12\n2\n5\n",
"12\n4\n5\n",
"9\n4\n5\n",
"9\n6\n5\n",
"9\n6\n8\n",
"9\n1\n8\n",
"9\n4\n8\n",
"4\n4\n8\n",
"4\n4\n3\n",
"4\n4\n5\n",
"4\n5\n3\n",
"3\n5\n3\n",
"1\n5\n3\n",
"2\n5\n3\n",
"2\n7\n3\n",
"2\n7\n4\n",
"2\n5\n4\n",
"3\n5\n4\n",
"3\n4\n4\n",
"3\n6\n4\n",
"3\n4\n3\n",
"3\n3\n3\n",
"3\n3\n4\n",
"3\n4\n2\n",
"3\n4\n6\n",
"2\n4\n6\n",
"2\n3\n6\n",
"2\n5\n6\n",
"1\n5\n6\n",
"2\n1\n4\n",
"3\n1\n4\n",
"3\n1\n5\n",
"2\n1\n5\n",
"1\n1\n5\n",
"1\n1\n7\n",
"2\n1\n7\n",
"0\n1\n5\n",
"0\n7\n5\n",
"0\n5\n5\n",
"0\n4\n5\n",
"0\n7\n9\n",
"0\n7\n7\n",
"0\n7\n1\n",
"0\n7\n2\n",
"0\n6\n2\n",
"1\n6\n2\n",
"1\n6\n3\n",
"12\n5\n9\n",
"12\n9\n7\n",
"16\n5\n4\n",
"7\n5\n7\n",
"22\n4\n7\n",
"18\n3\n7\n",
"25\n3\n8\n",
"28\n2\n5\n",
"11\n4\n5\n",
"9\n5\n5\n",
"9\n3\n8\n",
"9\n1\n1\n",
"7\n6\n8\n",
"5\n4\n8\n",
"4\n2\n3\n",
"1\n4\n5\n",
"1\n4\n3\n",
"4\n5\n5\n",
"4\n5\n4\n",
"4\n7\n3\n",
"1\n0\n3\n",
"4\n3\n3\n",
"2\n4\n4\n",
"3\n6\n3\n",
"3\n3\n2\n",
"3\n4\n1\n",
"2\n4\n5\n",
"1\n5\n7\n",
"1\n1\n4\n",
"3\n1\n6\n",
"3\n4\n5\n",
"1\n7\n5\n",
"2\n1\n2\n",
"0\n5\n8\n",
"0\n0\n5\n",
"0\n3\n9\n",
"0\n1\n7\n",
"0\n6\n1\n",
"0\n4\n2\n",
"1\n4\n2\n",
"0\n6\n3\n",
"12\n9\n9\n",
"12\n16\n7\n",
"16\n7\n4\n",
"7\n5\n9\n"
]
}
|
Consider a currency system in which there are notes of seven denominations, namely, Rs. 1, Rs. 2, Rs. 5, Rs. 10, Rs. 50, Rs. 100. If the sum of Rs. N is input, write a program to computer smallest number of notes that will combine to give Rs. N.
Input
The first line contains an integer T, total number of testcases. Then follow T lines, each line contains an integer N.
Output
Display the smallest number of notes that will combine to give N.
Constraints
1 ≤ T ≤ 1000
1 ≤ N ≤ 1000000
Example
Input
3
1200
500
242
Output
12
5
7
|
{
"inputs": [
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"11\nbabu\nanand\nrani\n`arti\nnandu\nrani\nrani\nap\nanand\nbabu\nnandu\n\nSAMPLE",
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"11\nbabu\nanand\nrani\n`arti\nnandu\nrani\nrani\nap\nadann\nbabu\nnandu\n\nSAMPLE",
"234\nljio\nj\nhfwod\nydgr\nrc\nlzh\nvnhwm\nnyunx\nohjz\nmiyj\nd\ncqk\nzttn\ng\nug\nscw\nmkc\nqa\nmnfj\noiexd\nesez\nwip\npsp\nss\ny\nnimxh\ne\nrtyav\nqhyj\neps\nnvl\na\nd\ngkgb\nnm\nhipsv\nfj\nrzsj\nboxq\noee\nsquak\ne\nl\nkzz\nauk\nwxt\nnsbr\naiyfp\ny\namfb\nwg\npy\noibfa\nbn\nvn\nlp\nmslj\njijt\nbuv\nzkjs\nwcsp\nanky\nk\njgl\nv\ntgfqj\npx\nmy\nf\noiv\nkutxb\nmjy\nvpe\nu\nxh\nodi\nixb\nl\ng\nrs\ntyn\nbosc\nodepm\nssaiu\ncuf\nziok\ni\noyo\ntvpn\nik\nrjjrq\nd\nagafb\nq\ntyn\nmj\ni\nahtnj\nlvrk\nrdcyd\naxa\na\nvsz\nlhdn\nl\nuozq\npj\ncvkr\noju\ndaybm\nkdf\nknh\nvadoi\ndyx\nmpf\ncfww\nhb\nlp\nlb\nldjw\ntdacj\nw\nvicjh\ndkmc\naypd\nvt\niacl\ndh\nx\ndxip\nwtz\ni\nsyv\nrg\nu\nqzys\nuor\ndtpjo\nah\nv\ncy\np\nrqm\ndxs\nyo\nuyzh\nojww\nj\ny\nijzsm\nzg\nuj\ntan\nycxx\nekntm\npvz\nji\nqfkmo\nhkk\nliqw\napjmb\ncb\np\ntijrb\ny\np\njp\npr\nzlony\nfqy\nkucy\ndt\naidg\niklk\nbg\nqpa\na\nqfz\nf\naibr\ntli\nf\nwzuh\nw\nkqnc\nvnop\nq\nk\nnrx\nz\nzrd\neec\nf\nodkk\nhzksk\np\nybyg\nzaw\nkp\nwsh\noclnc\nwbpu\njy\neq\nblh\na\nfulok\ne\nmgrn\nwtpg\nordy\nsql\nyf\nf\nuzth\nr\nrxt\nymmud\nssr\nudqy\nt\nie\nbcmf\ngrxd\nj\nebmal\nzpzf\nvd\nu\nslzi\ntq\ntbrg\nvyogy\nckira",
"74\ngvny\nkd\nvc\nb\nsuvo\nbljl\nh\nnomnb\nzfv\noy\ngqdld\nrgq\nfia\nyhxbj\nyk\ngunj\nnqe\nmopv\nocgq\njwx\no\no\nh\njbsx\nhby\nnq\ndkp\nf\nnu\nnhl\nb\nrki\nefmlq\nlut\nwcem\nzz\niwevs\nwtpr\nvwn\nwwjjw\na\nqjevs\nsumon\nee\nv\nc\nwip\nylr\ny\nfn\nxlgw\njwwcy\nwdh\nx\nh\nurtoq\nlxc\nxc\nltfhu\nslv\nw\nuims\no\nvtx\neya\nwr\nahpr\nir\nrom\nzy\niu\ntxyi\nqj\nbxjwf",
"11\nbabu\nanand\nrani\n`arti\nnandu\nrani\nrnai\nap\nadann\nbabu\nnandu\n\nSAMPLE",
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"74\ngvny\nkd\nvc\nb\nsuvo\nbljl\nh\nnomnb\nzfv\noy\ngqdld\nrgq\nfia\nyhxbj\nyk\ngunj\nnqe\nmopv\nocgq\njwx\no\no\nh\njbsx\nhby\nnq\ndkp\nf\nnu\nnhl\nb\nrki\nefmlq\nlut\nwcem\nzz\niwevs\nwtpr\nvwn\nwwjjw\na\nqjevs\nsumon\nee\nv\nc\nwip\nylr\ny\nfn\nxlgw\njwwcy\nwdh\nx\nh\nurtoq\ncxl\nxc\nltfhu\nslv\nw\nuims\no\nvtx\neya\nwr\nahpr\nir\nrom\nzy\niu\ntxyi\nqj\nbxjwf",
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"11\nbabu\nanand\nsani\n`arti\nnandu\nrani\nrnai\nap\nadann\nbabu\nnandu\n\nELPMAS",
"234\nljio\nj\nhfwod\nydgr\nrc\nlzh\nvnhwm\nxnuyn\nohjz\nmiyj\nd\ncqk\nzttn\ng\nug\nscw\nckm\nqa\nmnfj\noiexd\nesez\nwip\npsp\nss\ny\nnimxh\ne\nrtyav\nqhyj\neps\nnvl\na\nd\ngkgb\nnm\nhipsv\nfj\nrzsj\nboxq\noee\nsquak\ne\nl\nkzz\nauk\nwxt\nnsbr\naiyfp\ny\namfb\nwg\npy\noibfa\nbn\nvn\nlp\nmslj\njijt\nbuv\nzkjs\nwcsp\nanky\nk\njgl\nv\ntgfqj\npx\nmy\nf\noiv\nkutxb\nmjy\nvpe\nu\nxh\nodi\nixb\nl\ng\nrs\ntyn\nbosc\nodepm\nssaiu\ncuf\nziok\ni\noyo\ntvpn\nik\nrjjrq\nd\nagafb\nq\ntyn\nmj\ni\nahtnj\nlvrk\nrdcyd\naxa\na\nvsz\nlhdn\nl\nuozq\npj\ncvkr\noju\ndaybm\nkdf\nknh\nvadoi\ndyx\nmpf\ncfww\nhb\nlp\nlb\nldjw\ntdacj\nw\nvicjh\ndkmc\naypd\nvt\niacl\ndh\nx\ndxip\nwtz\ni\nsyv\nrg\nu\nqzys\nuor\ndtpjo\nah\nv\ncy\np\nrqm\ndxs\nyo\nuyzh\nojww\nj\ny\nijzsm\nzg\nuj\ntan\nycxx\nekntm\npvz\nji\nqfkmo\nhkk\nliqw\napjmb\ncb\np\ntijrb\ny\np\njp\npr\nzlony\nfqy\nkucy\ndt\naidg\niklk\nbg\nqpa\na\nqfz\nf\naibr\ntli\nf\nwzuh\nw\nkqnc\nvnop\nq\nk\nnrx\nz\nzrd\neec\nf\nodkk\nhzksk\np\nybyg\nzaw\nkp\nwsh\noclnc\nwbpu\njy\neq\nblh\na\nfulok\ne\nmgrn\nwtpg\nordy\nsql\nyf\nf\nuzth\nr\nrxt\nymmud\nssr\nudqy\nt\nie\nbcmf\ngrxd\nj\nebmal\nzpzf\nud\nu\nslzi\ntq\ntbrg\nvyogy\nckira",
"74\ngvny\nkd\nvc\nb\nsuvo\nbljl\nh\nnomnb\nzfv\noy\ngqdld\nrgq\nfia\nyhxbj\nyk\ngunj\nnqe\nmopv\nocgq\njwx\no\no\nh\njbsx\nhby\nnq\ndkp\nf\nnu\nnhl\nb\nrki\nefmlq\nlut\nwcem\nzz\niwevs\nwtpr\nvwn\nwwjjw\na\nsvejq\nsumon\nee\nv\nc\nxip\nylr\ny\nfn\nxlgw\njwwcy\nwdh\nx\nh\nurtoq\ncxl\nxc\nltfhu\nslv\nw\nuims\no\nvtx\neya\nwr\nahpr\nir\nrom\nzy\niu\ntxyi\nqj\nbxjwf",
"11\nbabu\nanand\nsani\n`arti\nnandu\nrani\nianr\nap\nadann\nbabu\nnandu\n\nELPMAS",
"234\nljio\nj\nhfwod\nydgr\nrc\nlzh\nvnhwm\nxnuyn\nohjz\nmiyj\nd\ncqk\nzttn\ng\nug\nscw\nckm\nqa\nmnfj\noiexd\nesez\nwip\npsp\nss\ny\nnimxh\ne\nrtyav\nqhyj\neps\nnvl\na\nd\ngkgb\nnm\nhipsv\nfk\nrzsj\nboxq\noee\nsquak\ne\nl\nkzz\nauk\nwxt\nnsbr\naiyfp\ny\namfb\nwg\npy\noibfa\nbn\nvn\nlp\nmslj\njijt\nbuv\nzkjs\nwcsp\nanky\nk\njgl\nv\ntgfqj\npx\nmy\nf\noiv\nkutxb\nmjy\nvpe\nu\nxh\nodi\nixb\nl\ng\nrs\ntyn\nbosc\nodepm\nssaiu\ncuf\nziok\ni\noyo\ntvpn\nik\nrjjrq\nd\nagafb\nq\ntyn\nmj\ni\nahtnj\nlvrk\nrdcyd\naxa\na\nvsz\nlhdn\nl\nuozq\npj\ncvkr\noju\ndaybm\nkdf\nknh\nvadoi\ndyx\nmpf\ncfww\nhb\nlp\nlb\nldjw\ntdacj\nw\nvicjh\ndkmc\naypd\nvt\niacl\ndh\nx\ndxip\nwtz\ni\nsyv\nrg\nu\nqzys\nuor\ndtpjo\nah\nv\ncy\np\nrqm\ndxs\nyo\nuyzh\nojww\nj\ny\nijzsm\nzg\nuj\ntan\nycxx\nekntm\npvz\nji\nqfkmo\nhkk\nliqw\napjmb\ncb\np\ntijrb\ny\np\njp\npr\nzlony\nfqy\nkucy\ndt\naidg\niklk\nbg\nqpa\na\nqfz\nf\naibr\ntli\nf\nwzuh\nw\nkqnc\nvnop\nq\nk\nnrx\nz\nzrd\neec\nf\nodkk\nhzksk\np\nybyg\nzaw\nkp\nwsh\noclnc\nwbpu\njy\neq\nblh\na\nfulok\ne\nmgrn\nwtpg\nordy\nsql\nyf\nf\nuzth\nr\nrxt\nymmud\nssr\nudqy\nt\nie\nbcmf\ngrxd\nj\nebmal\nzpzf\nud\nu\nslzi\ntq\ntbrg\nvyogy\nckira",
"74\ngvny\nkd\nvc\nb\nsuvo\nbljl\nh\nnomnb\nzfv\noy\ngqdld\nrgq\nfia\nyhxbj\nyk\ngunj\nnqe\nmopv\nocgq\njwx\no\no\nh\njbsx\nhby\nnq\ndkp\nf\nnu\nnhl\nb\nrki\nefmlq\nlut\nwcem\nzz\niwevs\nwtpr\nvwn\nwwjjw\na\nsvejq\nsumon\nfe\nv\nc\nxip\nylr\ny\nfn\nxlgw\njwwcy\nwdh\nx\nh\nurtoq\ncxl\nxc\nltfhu\nslv\nw\nuims\no\nvtx\neya\nwr\nahpr\nir\nrom\nzy\niu\ntxyi\nqj\nbxjwf",
"11\nbabu\nanand\nsani\n`arti\nnandu\nrani\nianq\nap\nadann\nbabu\nnandu\n\nELPMAS",
"234\nljio\nj\nhfwod\nydgr\nrc\nlzh\nvnhwm\nxnuyn\nohjz\nmiyj\nd\ncqk\nzttn\ng\nug\nscw\nckm\nqa\nmnfj\noiexd\nesez\nwip\npsp\nss\ny\nnimxh\ne\nrtyav\nqhyj\neps\nnvl\na\nd\ngkgb\nnm\nhipsv\nfk\nrzsj\nboxq\noee\nsquak\ne\nl\nkzz\nauk\nwxt\nnsbr\naiyfp\ny\namfb\nwg\npy\noibfa\nbn\nvn\nlp\nmslj\njijt\nbuv\nzkjs\nwcsp\nanky\nk\njgl\nv\ntgfqj\npx\nmy\nf\noiv\nkutxb\nmjy\nvpe\nu\nxh\nodi\nixb\nl\ng\nrs\ntyn\nbosc\nodepm\nssaiu\ncuf\nziok\ni\noyo\ntvpn\nik\nrjjrq\nd\nagafb\nq\ntyn\nmj\ni\nahtnj\nlvrk\nrdcyd\naxa\na\nvsz\nlhdn\nl\nuozq\npj\ncvkr\noju\ndaybm\nkdf\nknh\nvadoi\ndyx\nmpf\ncfww\nhb\nlp\nlb\nldjw\ntdacj\nw\nvicjh\ndkmc\naypd\nvt\niacl\ndh\nx\ndxip\nwtz\ni\nsyv\nrg\nu\nqzys\nuor\ndtpjo\nah\nv\ncy\np\nrqm\ndxs\nyo\nuyzh\nojww\nj\ny\nijzsm\nzg\nuj\ntan\nycxx\nekntm\npvz\nji\nqfkmo\nhkk\nliqw\napjmb\ncb\np\ntijrb\ny\no\njp\npr\nzlony\nfqy\nkucy\ndt\naidg\niklk\nbg\nqpa\na\nqfz\nf\naibr\ntli\nf\nwzuh\nw\nkqnc\nvnop\nq\nk\nnrx\nz\nzrd\neec\nf\nodkk\nhzksk\np\nybyg\nzaw\nkp\nwsh\noclnc\nwbpu\njy\neq\nblh\na\nfulok\ne\nmgrn\nwtpg\nordy\nsql\nyf\nf\nuzth\nr\nrxt\nymmud\nssr\nudqy\nt\nie\nbcmf\ngrxd\nj\nebmal\nzpzf\nud\nu\nslzi\ntq\ntbrg\nvyogy\nckira",
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"11\nbabu\nnaand\nsani\n`arti\nnandu\nrani\nianq\nap\nadann\nbabu\nnandu\n\nELPMAS",
"234\nljio\nj\nhfwod\nydgr\nrc\nlzh\nvnhwm\nxnuyn\nohjz\nmiyj\nd\ncqk\nzttn\ng\nug\nscw\nckm\nqa\nmnfj\noiexd\nesez\nwip\npsp\nss\ny\nnimxh\ne\nrtyav\nqhyj\neps\nnvl\na\nd\ngkgb\nnm\nhipsv\nfk\nrzsj\nboxq\noee\nsquak\ne\nl\nkzz\nauk\nwxt\nnsbr\naiyfp\ny\namfb\nwg\npy\noibfa\nbn\nvn\nlp\nmslj\njijt\nbuv\nzkjs\nwcsp\nanky\nk\njgl\nv\ntgfqj\npx\nmy\nf\noiv\nkutxb\nmjy\nvpe\nu\nxh\nodi\nixb\nl\ng\nrs\ntyn\nbosc\nodepm\nssaiu\ncuf\nziok\ni\noyo\ntvpn\nik\nrjjrq\nd\nagafb\nq\ntyn\nmj\ni\nahtnj\nlvrk\nrdcyd\naxa\na\nvsz\nlhdn\nl\nuozq\npj\ncvkr\nujo\ndaybm\nkdf\nknh\nvadoi\ndyx\nmpf\ncfww\nhb\nlp\nlb\nldjw\ntdacj\nw\nvicjh\ndkmc\naypd\nvt\niacl\ndh\nx\ndxip\nwtz\ni\nsyv\nrg\nu\nqzys\nuor\ndtpjo\nah\nv\ncy\np\nrqm\ndxs\nyo\nuyzh\nojww\nj\ny\nijzsm\nzg\nuj\ntan\nycxx\nekntm\npvz\nji\nqfkmo\nhkk\nliqw\napjmb\ncb\np\ntijrb\ny\no\njp\npr\nzlony\nfqy\nkucy\ndt\naidg\niklk\nbg\nqpa\na\nqfz\nf\naibr\ntli\nf\nwzuh\nw\nkqnc\nvnop\nq\nk\nnrx\nz\nzrd\neec\nf\nodkk\nhzksk\np\nybyg\nzaw\nkp\nwsh\noclnc\nwbpu\njy\neq\nblh\na\nfulok\ne\nmgrn\nwtpg\nordy\nsql\nyf\nf\nuzth\nr\nrxt\nymmud\nssr\nudqy\nt\nie\nbcmf\ngrxd\nj\nebmal\nzpzf\nud\nu\nslzi\ntq\ntbrg\nvyogy\nckira",
"11\nbabu\nnaand\nsani\n`arti\nnandu\nrani\nianq\nap\nadann\nbabu\nnaudn\n\nELPMAS",
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"11\nbabu\nanand\nrani\nitraa\nnandu\nrani\nrani\nap\nanand\nbabu\nnandu\n\nSAMPLE",
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"11\nbabu\nanand\nrani\nitraa\nnandu\nrani\nrani\naq\nanand\nbabu\nnandu\n\nSAMPLE",
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"11\nbabu\nanand\nrani\nitraa\noandu\nrani\nrani\naq\nanand\nbabu\nnandu\n\nSAMPLE",
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"11\nbabu\nanand\nrani\nitraa\noandu\nrani\nrani\naq\nanand\nbabu\nmandu\n\nSAMPLE",
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"11\nbacu\nanand\nrani\nitraa\noandu\nrani\nrani\naq\nanand\nbabu\nmandu\n\nSAMPLE",
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"11\nbacu\nanand\nrani\nitraa\noandu\nnari\nrani\naq\nanand\nbabu\nmandu\n\nSAMPLE",
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"11\nbacu\nanand\nrani\nitraa\noandu\nnari\nrani\nqa\nanand\nbabu\nmandu\n\nSAMPLE",
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"11\nbacu\nanand\nrani\nitraa\noandu\nnari\nrani\nqa\nanbnd\nbabu\nmandu\n\nSAMPLE",
"234\nljio\nj\nhfwod\nydgr\nrc\nlzh\nvnhwm\nnyunx\nohjz\nmiyj\nd\ncqk\nzttn\ng\nug\nscw\nckm\nqa\nmnfj\noiexd\nesez\nwip\npsp\nss\ny\nnimxh\ne\nrsyav\nqhyj\nspe\nnvl\na\nd\ngkgb\nnm\nhipsv\nfj\nrzsj\nboxq\noee\nsquak\nd\nl\nkzz\nauk\nwxt\nnsbr\naiyfp\ny\namfb\nwg\npy\noibfa\nbn\nvn\nlp\nmslj\njijt\nbuv\nzkjs\nwcsp\nanky\nk\njgl\nv\ntjfqg\npx\nym\nf\noiv\nkutxb\nmjy\nvpe\nu\nxh\nodi\nixb\nl\ng\nrs\ntyn\nbosc\nodepm\nssaiu\ncuf\nziok\ni\noyo\ntvpn\nik\nrjjrq\nd\nagafb\nq\ntyn\nmj\ni\nahtnj\nlvrk\nrdcyd\naxa\na\nvsz\nlhdn\nl\nuozq\npj\ncvkr\noju\ndaybm\nkdf\nknh\nvadoi\ndyw\nmpf\ncfww\nhb\nlp\nlb\nldjw\ntdacj\nw\nvicjh\ndkmc\naypd\nvt\niacl\ndh\nx\ndxip\nwtz\ni\nsyv\nrg\nu\nqzys\nuor\ndtpjo\nah\nv\ncy\np\nrqm\ndxs\nyo\nuyzh\nojww\nj\ny\nmszji\nzg\nuj\ntan\nycxx\nekntm\npvy\nji\nqfkmo\nhkk\nliqw\napjmb\ncc\np\ntijrb\ny\np\njp\npr\nzlony\nfqy\nkucy\ndt\naidg\niklk\nbg\nqpa\na\nzfq\nf\naibr\ntli\nf\nwzuh\nw\nkqnc\nvnop\nq\nk\nnrx\nz\nzrd\neec\nf\nodkk\nhzksk\np\nybyg\nzaw\nkp\nwsh\noclnc\nwbpu\nyj\neq\nblh\na\nfulok\ne\nmgrn\nwtpg\nordy\nsql\nyf\nf\nuzth\nr\nrxt\nymmud\nssr\nudqy\nt\nie\nbcmf\ngrxd\nj\nebmal\nzpzf\nvd\nu\nslzi\ntq\ntbrg\nvyogy\nckira",
"74\ngvny\ndk\nvc\nb\nsuvo\nbljl\nh\nnomnb\nzfv\noy\ngqdld\nrgq\nfia\nyhxbj\nyk\ngunj\nnqe\nmopv\nocgq\njwx\nn\no\nh\njbsx\nhby\nnq\ndkp\nf\nnu\nnhl\nb\nrki\nefmlq\nlut\nwcem\nzz\niwevs\nwtor\nvwn\nwwjjw\na\nqjevs\nsumon\nee\nv\nd\nwip\nylr\ny\nfn\nxlgw\nkwwcy\nhdv\ny\nh\nurtoq\nlxc\nyc\nltfhu\nslv\nw\nuims\no\nvtx\neya\nwr\nahpr\nri\nrom\nyz\niu\ntxyi\nqj\nbxkwf",
"11\nbacu\nanand\nrani\nitsaa\noandu\nnari\nrani\nqa\nanbnd\nbabu\nmandu\n\nSAMPLE",
"234\nljio\nj\nhfwod\nydgr\nrc\nlzh\nvnhwm\nnyunx\nohjz\nmiyj\nd\ncqk\nzttn\ng\nug\nscw\nckm\nqa\nmnfj\noiexd\nesez\nwip\npsp\nss\ny\nnimxh\ne\nrsyav\nqhyj\nspe\nnvl\na\nd\ngkgb\nnm\nhipsv\nfj\nrzsj\nboxq\noee\nsquak\nd\nl\nkzz\nauk\nwxt\nnsbr\naiyfp\ny\namfb\nwg\npy\noibfa\nbn\nvn\nlp\nmslj\njijt\nbuv\nzkjs\nwcsp\nanky\nk\njgl\nv\ntjfqg\npx\nym\nf\noiv\nkutxb\nmjy\nvpe\nu\nxh\nodi\nixb\nl\ng\nrs\ntyn\nbosc\nodepm\nssaiu\ncuf\nziok\ni\noyo\ntvpn\nik\nrjjrq\nd\nagafb\nq\ntyn\nmj\ni\nahtnj\nlvrk\nrdcyd\naxa\na\nvsz\nlhdn\nl\nuozq\npj\ncvkr\noju\ndaybm\nkdf\nknh\nvadoi\ndyw\nmpf\ncfww\nhb\nlp\nlb\nldjw\ntdacj\nw\nvicjh\ndkmc\naypd\nvt\niacl\ndh\nx\ndxip\nwtz\ni\nsyv\nrg\nu\nqzys\nuor\ndtpjo\nah\nv\ncy\np\nrqm\ndxs\nyo\nuyzh\nojww\nj\ny\nmszji\nzg\nuj\ntan\nycxx\nekntm\npvy\nji\nqfkmo\nhjk\nliqw\napjmb\ncc\np\ntijrb\ny\np\njp\npr\nzlony\nfqy\nkucy\ndt\naidg\niklk\nbg\nqpa\na\nzfq\nf\naibr\ntli\nf\nwzuh\nw\nkqnc\nvnop\nq\nk\nnrx\nz\nzrd\neec\nf\nodkk\nhzksk\np\nybyg\nzaw\nkp\nwsh\noclnc\nwbpu\nyj\neq\nblh\na\nfulok\ne\nmgrn\nwtpg\nordy\nsql\nyf\nf\nuzth\nr\nrxt\nymmud\nssr\nudqy\nt\nie\nbcmf\ngrxd\nj\nebmal\nzpzf\nvd\nu\nslzi\ntq\ntbrg\nvyogy\nckira",
"74\ngvny\ndk\nvc\nb\nsuvo\nbljl\nh\nnomnb\nzfv\noy\ngqdld\nrgq\nfia\nyhxbj\nyk\ngunj\nnqe\nmopv\nocgq\njwx\nn\no\nh\njbsx\nhby\nnq\ndkp\nf\nnu\nnhl\nb\nrki\nefmlq\nlut\nwcem\nzz\niwevs\nwtor\nvwn\nwwjjw\na\nqjevs\nsumon\nee\nv\nd\nwip\nylr\ny\nfn\nxlgw\nkwwcy\nhdv\nz\nh\nurtoq\nlxc\nyc\nltfhu\nslv\nw\nuims\no\nvtx\neya\nwr\nahpr\nri\nrom\nyz\niu\ntxyi\nqj\nbxkwf",
"11\nbacu\nanand\nrani\nitsaa\noandu\nnari\nrani\nqa\nanbnd\nb`bu\nmandu\n\nSAMPLE",
"234\nljio\nj\nhfwod\nydgr\nrc\nlzh\nvnhwm\nnyunx\nohjz\nmiyj\nd\ncqk\nzttn\ng\nug\nscw\nckm\nqa\nmnfj\noiexd\nesez\nwip\npsp\nss\ny\nnimxh\ne\nrsyav\nqhyj\nspe\nnvl\na\nd\ngkgb\nnm\nhipsv\nfj\nrzsj\nboxq\noee\nsquak\nd\nl\nkzz\nauk\nwxt\nnsbr\naiyfp\ny\namfb\nwg\npy\noibfa\nbn\nvn\nlp\nmslj\njijt\nbuv\nzkjs\nwcsp\nanky\nk\njgl\nv\ntjfqg\npx\nym\nf\noiv\nkutxb\nmjy\nvpe\nu\nxh\nodi\nixb\nl\ng\nrs\ntyn\nbosc\nodepm\nssaiu\ncuf\nziok\ni\noyo\ntvpn\nik\nrjjrq\nd\nagafb\nq\ntyn\nmj\ni\nahtnj\nlvrk\nrdcyd\naxa\na\nvsz\nlhdn\nl\nuozq\npj\ncvkr\noju\ndaybm\nkdf\nknh\nvadoi\ndyw\nmpf\ncfww\nhb\nlp\nlb\nldjw\ntdacj\nw\nvicjh\ndkmc\naypd\nvt\niacl\ndh\nx\ndxip\nwtz\ni\nsyv\nrg\nu\nqzys\nuor\ndtpjo\nah\nv\ncy\np\nrqm\ndxs\nyo\nuyzh\nojww\nj\ny\nmszji\nzg\nuj\ntan\nycxx\nekntm\npvy\nji\nqfkmo\nhjk\nliqw\napjmb\ncc\np\ntijrb\ny\np\njp\npr\nzlony\nfqy\nkucy\ndt\naidg\niklk\nbg\nqpa\na\nzfq\nf\naibr\ntli\nf\nwzuh\nw\nkqnc\nvnop\nq\nk\nnrx\nz\nzrd\neec\nf\nodkk\nhzksk\np\nybyg\nzaw\nkp\nwsh\noclnc\nwbpu\nyj\neq\nblh\na\nfulok\ne\nmgrn\nwtpg\nordy\nsql\nyf\nf\nuzth\nr\nrxt\nymmud\nssr\nudqy\nt\nie\nbcme\ngrxd\nj\nebmal\nzpzf\nvd\nu\nslzi\ntq\ntbrg\nvyogy\nckira",
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"11\nbacu\nanand\nrani\nitsaa\noandu\nnari\nrani\nqa\ndnbna\nb`bu\nmandu\n\nSAMPLE",
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"11\nbacu\nanand\nrani\natsia\noandu\nnari\nrani\nqa\ndnbna\nb`bu\nmandu\n\nSAMPLE",
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"11\nbacu\nanand\nrani\natsia\noandu\nnari\nrani\nqa\ndnbna\nb`bu\nmandt\n\nSAMPLE",
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"11\nbacu\nanand\nrani\natsia\noandu\nnari\nrani\nqa\ndnbna\nub`b\nmandt\n\nSAMPLF",
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"11\nbacu\nanand\nrani\natsia\noandu\nnari\nranh\nqa\ndnbna\nub`b\nmandt\n\nSAMPLF",
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"11\nbacu\nanand\nrani\natsia\nobndu\nnari\nranh\nqa\ndnbna\nub`b\nmandt\n\nSAMPLF",
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],
"outputs": [
"6\naarti\nanand\nap\nbabu\nnandu\nrani\n",
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"69\na\nahpr\nb\nbljl\nbxkwf\nc\ndk\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nir\niu\niwevs\njbsx\njwwcy\njwx\nltfhu\nlut\nlxc\nmopv\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nv\nvc\nvdh\nvtx\nvwn\nw\nwcem\nwip\nwr\nwtpr\nwwjjw\nx\nxc\nxlgw\ny\nyhxbj\nyk\nylr\nzfv\nzy\nzz\n",
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"6\n`arti\nanand\nap\nbabu\nnandu\nrani\n",
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"69\na\nahpr\nb\nbljl\nbxjwf\nc\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nir\niu\niwevs\njbsx\njwwcy\njwx\nkd\nltfhu\nlut\nlxc\nmopv\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nv\nvc\nvdh\nvtx\nvwn\nw\nwcem\nwip\nwr\nwtpr\nwwjjw\nx\nxc\nxlgw\ny\nyhxbj\nyk\nylr\nzfv\nzy\nzz\n",
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gk\nyglt\nygmmg\nygo\nygp\nygwxf\nygz\nyh\nyhd\nyhft\nyhnc\nyhot\nyhq\nyhrv\nyhsp\nyht\nyhtsv\nyhtte\nyhu\nyhxzx\nyi\nyiaof\nyimr\nyiraw\nyj\nyjicg\nyjlt\nyjmf\nyjo\nyjro\nyk\nykbe\nykbpd\nyke\nykh\nyknv\nykpwt\nykr\nyks\nykx\nykxca\nyky\nyl\nyladj\nylec\nyleg\nylgu\nyloqj\nylvfj\nym\nymb\nymcp\nymdf\nymf\nymfb\nymho\nymhsm\nymihg\nymkhg\nymww\nymy\nymzi\nyn\nynbd\nyndyj\nyngm\nyngqk\nynje\nynleo\nyo\nyob\nyocqz\nyoddd\nyodu\nyolqu\nyoo\nyosqt\nyownn\nyowr\nyowys\nyp\nypgxl\nypin\nypk\nypn\nypsd\nyptfj\nypw\nypy\nyq\nyqe\nyqeuc\nyqf\nyqh\nyqkh\nyqmo\nyqoet\nyqq\nyqsgj\nyqso\nyqw\nyqxrr\nyqyuo\nyr\nyrat\nyrc\nyrijy\nyrot\nyrtn\nys\nysjh\nyslt\nysn\nysp\nysqjr\nysrvz\nyss\nystq\nysvg\nysz\nyszr\nytfy\nytif\nytk\nytkup\nytm\nytmrn\nytpm\nytwqz\nytwz\nytxz\nyty\nytyy\nyu\nyubhr\nyumq\nyumx\nyuog\nyuol\nyuox\nyup\nyuqhk\nyur\nyura\nyusf\nyuxee\nyuxqy\nyuzi\nyuzjk\nyv\nyvfdg\nyvgg\nyvj\nyvjj\nyvjsu\nyvkek\nyvl\nyvomp\nyvoug\nyvr\nyw\nywa\nywhv\nywjkh\nywknb\nywnq\nywojf\nywqyt\nywy\nywyu\nyx\nyxc\nyxcdi\nyxmv\nyxpo\nyxpsn\nyxs\nyxw\nyxxfk\nyybx\nyyeo\nyyk\nyymvo\nyyolt\nyyuv\nyyyt\nyz\nyzac\nyzfdj\nyzkpp\nyzp\nz\nza\nzaf\nzagw\nzah\nzai\nzakx\nzaluc\nzar\nzatlu\nzayt\nzaznq\nzb\nzbcwn\nzbiny\nzbn\nzbnte\nzbpg\nzbspx\nzbt\nzc\nzccy\nzcd\nzceds\nzceoe\nzche\nzcigb\nzcil\nzcj\nzcjgr\nzcm\nzd\nzdapp\nzdbrz\nzdbzt\nzdefn\nzdemd\nzdiw\nzdwv\nzdxa\nzdyr\nze\nzeabp\nzecs\nzefu\nzejtt\nzejx\nzem\nzenxq\nzeph\nzet\nzeuc\nzewqk\nzexfc\nzf\nzfcvj\nzfle\nzfqd\nzfqw\nzfu\nzfvsy\nzfwnf\nzfy\nzfzpc\nzg\nzget\nzgewk\nzghrn\nzghx\nzgk\nzgu\nzgzp\nzh\nzhaso\nzhd\nzhgn\nzhj\nzhpvs\nzhqvv\nzhufy\nzhw\nzhwf\nzi\nzig\nzijim\nzil\nzilbg\nzipa\nzit\nzivhx\nzj\nzjdn\nzjp\nzjuh\nzjy\nzk\nzkdj\nzkf\nzkglp\nzkio\nzkma\nzkmt\nzkoyr\nzkwgp\nzkymj\nzkz\nzkzq\nzl\nzlate\nzleo\nzljfq\nzlk\nzlnsx\nzltbl\nzlv\nzlw\nzlytk\nzm\nzmcj\nzme\nzmebr\nzmee\nzmemu\nzmga\nzmi\nzmjks\nzmr\nzmsg\nzmsy\nzmton\nzmxtn\nzn\nzna\nzngl\nzngnz\nznj\nznjy\nznlis\nznnzh\nznpcp\nzns\nznu\nznv\nznwp\nznz\nzo\nzoa\nzocg\nzohyp\nzoi\nzoo\nzoq\nzot\nzou\nzov\nzowc\nzoxav\nzozaq\nzp\nzpaxn\nzpf\nzpgr\nzphjs\nzpo\nzpor\nzptaj\nzptw\nzpv\nzpva\nzpxkd\nzpzl\nzq\nzqdmh\nzqi\nzqixj\nzqmrd\nzqmy\nzquub\nzqv\nzr\nzrao\nzrdxv\nzrhnk\nzri\nzrjaq\nzrka\nzrlz\nzryx\nzs\nzsca\nzsfu\nzsii\nzskrq\nzslau\nzsn\nzsnyd\nzspqj\nzss\nzswur\nzsxe\nztbd\nztek\nztgj\nzth\nztl\nztlv\nztq\nztud\nztzn\nzu\nzubc\nzuc\nzuj\nzukg\nzupm\nzurq\nzut\nzuusv\nzuxzy\nzv\nzvdf\nzvep\nzvhci\nzvqbf\nzvvek\nzvzo\nzw\nzwbm\nzwc\nzwfj\nzwgi\nzwhn\nzwigl\nzwkb\nzwns\nzwp\nzww\nzwxon\nzx\nzxey\nzxg\nzxmu\nzxwd\nzxzkn\nzy\nzyhia\nzyib\nzyidi\nzylt\nzyo\nzyp\nzyv\nzywh\nzywhg\nzz\nzzc\nzzcym\nzzd\nzzfy\nzzme\nzzpoj\nzzsx\nzzz\n",
"7\n`arti\nadann\nanand\nap\nbabu\nnandu\nrani\n",
"202\na\nagafb\nah\nahtnj\naibr\naidg\naiyfp\namfb\nanky\napjmb\nauk\naxa\naypd\nbcmf\nbg\nblh\nbn\nbosc\nboxq\nbuv\ncb\ncfww\nckira\ncqk\ncuf\ncvkr\ncy\nd\ndaybm\ndh\ndkmc\ndt\ndtpjo\ndxip\ndxs\ndyx\ne\nebmal\neec\nekntm\neps\neq\nesez\nf\nfj\nfqy\nfulok\ng\ngkgb\ngrxd\nhb\nhfwod\nhipsv\nhkk\nhzksk\ni\niacl\nie\nijzsm\nik\niklk\nixb\nj\njgl\nji\njijt\njp\njy\nk\nkdf\nknh\nkp\nkqnc\nkucy\nkutxb\nkzz\nl\nlb\nldjw\nlhdn\nliqw\nljio\nlp\nlvrk\nlzh\nmgrn\nmiyj\nmj\nmjy\nmkc\nmnfj\nmpf\nmslj\nmy\nnimxh\nnm\nnrx\nnsbr\nnvl\nnyunx\noclnc\nodepm\nodi\nodkk\noee\nohjz\noibfa\noiexd\noiv\noju\nojww\nordy\noyo\np\npj\npr\npsp\npvz\npx\npy\nq\nqa\nqfkmo\nqfz\nqhyj\nqpa\nqzys\nr\nrc\nrdcyd\nrg\nrjjrq\nrqm\nrs\nrtyav\nrxt\nrzsj\nscw\nslzi\nsql\nsquak\nss\nssaiu\nssr\nsyv\nt\ntan\ntbrg\ntdacj\ntgfqj\ntijrb\ntli\ntq\ntvpn\ntyn\nu\nudqy\nug\nuj\nuor\nuozq\nuyzh\nuzth\nv\nvadoi\nvd\nvicjh\nvn\nvnhwm\nvnop\nvpe\nvsz\nvt\nvyogy\nw\nwbpu\nwcsp\nwg\nwip\nwsh\nwtpg\nwtz\nwxt\nwzuh\nx\nxh\ny\nybyg\nycxx\nydgr\nyf\nymmud\nyo\nz\nzaw\nzg\nziok\nzkjs\nzlony\nzpzf\nzrd\nzttn\n",
"69\na\nahpr\nb\nbljl\nbxjwf\nc\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nir\niu\niwevs\njbsx\njwwcy\njwx\nkd\nltfhu\nlut\nlxc\nmopv\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwcem\nwdh\nwip\nwr\nwtpr\nwwjjw\nx\nxc\nxlgw\ny\nyhxbj\nyk\nylr\nzfv\nzy\nzz\n",
"8\n`arti\nadann\nanand\nap\nbabu\nnandu\nrani\nrnai\n",
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"69\na\nahpr\nb\nbljl\nbxjwf\nc\ncxl\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nir\niu\niwevs\njbsx\njwwcy\njwx\nkd\nltfhu\nlut\nmopv\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwcem\nwdh\nwip\nwr\nwtpr\nwwjjw\nx\nxc\nxlgw\ny\nyhxbj\nyk\nylr\nzfv\nzy\nzz\n",
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yglt\nygmmg\nygo\nygp\nygwxf\nygz\nyh\nyhd\nyhft\nyhnc\nyhot\nyhq\nyhrv\nyhsp\nyht\nyhtsv\nyhtte\nyhu\nyhxzx\nyi\nyiaof\nyimr\nyiraw\nyj\nyjicg\nyjlt\nyjmf\nyjo\nyjro\nyk\nykbe\nykbpd\nyke\nykh\nyknv\nykpwt\nykr\nyks\nykx\nykxca\nyky\nyl\nyladj\nylec\nyleg\nylgu\nyloqj\nylvfj\nym\nymb\nymcp\nymdf\nymf\nymfb\nymho\nymhsm\nymihg\nymkhg\nymww\nymy\nymzi\nyn\nynbd\nyndyj\nyngm\nyngqk\nynje\nynleo\nyo\nyob\nyocqz\nyoddd\nyodu\nyolqu\nyoo\nyosqt\nyownn\nyowr\nyowys\nyp\nypgxl\nypin\nypk\nypn\nypsd\nyptfj\nypw\nypy\nyq\nyqe\nyqeuc\nyqf\nyqh\nyqkh\nyqmo\nyqoet\nyqq\nyqsgj\nyqso\nyqw\nyqxrr\nyqyuo\nyr\nyrat\nyrc\nyrijy\nyrot\nyrtn\nys\nysjh\nyslt\nysn\nysp\nysqjr\nysrvz\nyss\nystq\nysvg\nysz\nyszr\nytfy\nytif\nytk\nytkup\nytm\nytmrn\nytpm\nytwqz\nytwz\nytxz\nyty\nytyy\nyu\nyubhr\nyumq\nyumx\nyuog\nyuol\nyuox\nyup\nyuqhk\nyur\nyura\nyusf\nyuxee\nyuxqy\nyuzi\nyuzjk\nyv\nyvfdg\nyvgg\nyvj\nyvjj\nyvjsu\nyvkek\nyvl\nyvomp\nyvoug\nyvr\nyw\nywa\nywhv\nywjkh\nywknb\nywnq\nywojf\nywqyt\nywy\nywyu\nyx\nyxc\nyxcdi\nyxmv\nyxpo\nyxpsn\nyxs\nyxw\nyxxfk\nyybx\nyyeo\nyyk\nyymvo\nyyolt\nyyuv\nyyyt\nyz\nyzac\nyzfdj\nyzkpp\nyzp\nz\nza\nzaf\nzagw\nzah\nzai\nzakx\nzaluc\nzar\nzatlu\nzayt\nzaznq\nzb\nzbcwn\nzbiny\nzbn\nzbnte\nzbpg\nzbspx\nzbt\nzc\nzccy\nzcd\nzceds\nzceoe\nzche\nzcigb\nzcil\nzcj\nzcjgr\nzcm\nzd\nzdapp\nzdbrz\nzdbzt\nzdefn\nzdemd\nzdiw\nzdwv\nzdxa\nzdyr\nze\nzeabp\nzecs\nzefu\nzejtt\nzejx\nzem\nzenxq\nzeph\nzet\nzeuc\nzewqk\nzexfc\nzf\nzfcvj\nzfle\nzfqd\nzfqw\nzfu\nzfvsy\nzfwnf\nzfy\nzfzpc\nzg\nzget\nzgewk\nzghrn\nzghx\nzgk\nzgu\nzgzp\nzh\nzhaso\nzhd\nzhgn\nzhj\nzhpvs\nzhqvv\nzhufy\nzhw\nzhwf\nzi\nzig\nzijim\nzil\nzilbg\nzipa\nzit\nzivhx\nzj\nzjdn\nzjp\nzjuh\nzjy\nzk\nzkdj\nzkf\nzkglp\nzkio\nzkma\nzkmt\nzkoyr\nzkwgp\nzkymj\nzkz\nzkzq\nzl\nzlate\nzleo\nzljfq\nzlk\nzlnsx\nzltbl\nzlv\nzlw\nzlytk\nzm\nzmcj\nzme\nzmebr\nzmee\nzmemu\nzmga\nzmi\nzmjks\nzmr\nzmsg\nzmsy\nzmton\nzmxtn\nzn\nzna\nzngl\nzngnz\nznj\nznjy\nznlis\nznnzh\nznpcp\nzns\nznu\nznv\nznwp\nznz\nzo\nzoa\nzocg\nzohyp\nzoi\nzoo\nzoq\nzot\nzou\nzov\nzowc\nzoxav\nzozaq\nzp\nzpaxn\nzpf\nzpgr\nzphjs\nzpo\nzpor\nzptaj\nzptw\nzpv\nzpva\nzpxkd\nzpzl\nzq\nzqdmh\nzqi\nzqixj\nzqmrd\nzqmy\nzquub\nzqv\nzr\nzrao\nzrdxv\nzrhnk\nzri\nzrjaq\nzrka\nzrlz\nzryx\nzs\nzsca\nzsfu\nzsii\nzskrq\nzslau\nzsn\nzsnyd\nzspqj\nzss\nzswur\nzsxe\nztbd\nztfk\nztgj\nzth\nztl\nztlv\nztq\nztud\nztzn\nzu\nzubc\nzuc\nzuj\nzukg\nzupm\nzurq\nzut\nzuusv\nzuxzy\nzv\nzvdf\nzvep\nzvhci\nzvqbf\nzvvek\nzvzo\nzw\nzwbm\nzwc\nzwfj\nzwgi\nzwhn\nzwigl\nzwkb\nzwns\nzwp\nzww\nzwxon\nzx\nzxey\nzxg\nzxmu\nzxwd\nzxzkn\nzy\nzyhia\nzyib\nzyidi\nzylt\nzyo\nzyp\nzyv\nzywh\nzywhg\nzz\nzzc\nzzcym\nzzd\nzzfy\nzzme\nzzpoj\nzzsx\nzzz\n",
"9\n`arti\nadann\nanand\nap\nbabu\nnandu\nrani\nrnai\nsani\n",
"202\na\nagafb\nah\nahtnj\naibr\naidg\naiyfp\namfb\nanky\napjmb\nauk\naxa\naypd\nbcmf\nbg\nblh\nbn\nbosc\nboxq\nbuv\ncb\ncfww\nckira\nckm\ncqk\ncuf\ncvkr\ncy\nd\ndaybm\ndh\ndkmc\ndt\ndtpjo\ndxip\ndxs\ndyx\ne\nebmal\neec\nekntm\neps\neq\nesez\nf\nfj\nfqy\nfulok\ng\ngkgb\ngrxd\nhb\nhfwod\nhipsv\nhkk\nhzksk\ni\niacl\nie\nijzsm\nik\niklk\nixb\nj\njgl\nji\njijt\njp\njy\nk\nkdf\nknh\nkp\nkqnc\nkucy\nkutxb\nkzz\nl\nlb\nldjw\nlhdn\nliqw\nljio\nlp\nlvrk\nlzh\nmgrn\nmiyj\nmj\nmjy\nmnfj\nmpf\nmslj\nmy\nnimxh\nnm\nnrx\nnsbr\nnvl\noclnc\nodepm\nodi\nodkk\noee\nohjz\noibfa\noiexd\noiv\noju\nojww\nordy\noyo\np\npj\npr\npsp\npvz\npx\npy\nq\nqa\nqfkmo\nqfz\nqhyj\nqpa\nqzys\nr\nrc\nrdcyd\nrg\nrjjrq\nrqm\nrs\nrtyav\nrxt\nrzsj\nscw\nslzi\nsql\nsquak\nss\nssaiu\nssr\nsyv\nt\ntan\ntbrg\ntdacj\ntgfqj\ntijrb\ntli\ntq\ntvpn\ntyn\nu\nud\nudqy\nug\nuj\nuor\nuozq\nuyzh\nuzth\nv\nvadoi\nvicjh\nvn\nvnhwm\nvnop\nvpe\nvsz\nvt\nvyogy\nw\nwbpu\nwcsp\nwg\nwip\nwsh\nwtpg\nwtz\nwxt\nwzuh\nx\nxh\nxnuyn\ny\nybyg\nycxx\nydgr\nyf\nymmud\nyo\nz\nzaw\nzg\nziok\nzkjs\nzlony\nzpzf\nzrd\nzttn\n",
"69\na\nahpr\nb\nbljl\nbxjwf\nc\ncxl\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nir\niu\niwevs\njbsx\njwwcy\njwx\nkd\nltfhu\nlut\nmopv\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nrgq\nrki\nrom\nslv\nsumon\nsuvo\nsvejq\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwcem\nwdh\nwr\nwtpr\nwwjjw\nx\nxc\nxip\nxlgw\ny\nyhxbj\nyk\nylr\nzfv\nzy\nzz\n",
"9\n`arti\nadann\nanand\nap\nbabu\nianr\nnandu\nrani\nsani\n",
"202\na\nagafb\nah\nahtnj\naibr\naidg\naiyfp\namfb\nanky\napjmb\nauk\naxa\naypd\nbcmf\nbg\nblh\nbn\nbosc\nboxq\nbuv\ncb\ncfww\nckira\nckm\ncqk\ncuf\ncvkr\ncy\nd\ndaybm\ndh\ndkmc\ndt\ndtpjo\ndxip\ndxs\ndyx\ne\nebmal\neec\nekntm\neps\neq\nesez\nf\nfk\nfqy\nfulok\ng\ngkgb\ngrxd\nhb\nhfwod\nhipsv\nhkk\nhzksk\ni\niacl\nie\nijzsm\nik\niklk\nixb\nj\njgl\nji\njijt\njp\njy\nk\nkdf\nknh\nkp\nkqnc\nkucy\nkutxb\nkzz\nl\nlb\nldjw\nlhdn\nliqw\nljio\nlp\nlvrk\nlzh\nmgrn\nmiyj\nmj\nmjy\nmnfj\nmpf\nmslj\nmy\nnimxh\nnm\nnrx\nnsbr\nnvl\noclnc\nodepm\nodi\nodkk\noee\nohjz\noibfa\noiexd\noiv\noju\nojww\nordy\noyo\np\npj\npr\npsp\npvz\npx\npy\nq\nqa\nqfkmo\nqfz\nqhyj\nqpa\nqzys\nr\nrc\nrdcyd\nrg\nrjjrq\nrqm\nrs\nrtyav\nrxt\nrzsj\nscw\nslzi\nsql\nsquak\nss\nssaiu\nssr\nsyv\nt\ntan\ntbrg\ntdacj\ntgfqj\ntijrb\ntli\ntq\ntvpn\ntyn\nu\nud\nudqy\nug\nuj\nuor\nuozq\nuyzh\nuzth\nv\nvadoi\nvicjh\nvn\nvnhwm\nvnop\nvpe\nvsz\nvt\nvyogy\nw\nwbpu\nwcsp\nwg\nwip\nwsh\nwtpg\nwtz\nwxt\nwzuh\nx\nxh\nxnuyn\ny\nybyg\nycxx\nydgr\nyf\nymmud\nyo\nz\nzaw\nzg\nziok\nzkjs\nzlony\nzpzf\nzrd\nzttn\n",
"69\na\nahpr\nb\nbljl\nbxjwf\nc\ncxl\ndkp\nefmlq\neya\nf\nfe\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nir\niu\niwevs\njbsx\njwwcy\njwx\nkd\nltfhu\nlut\nmopv\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nrgq\nrki\nrom\nslv\nsumon\nsuvo\nsvejq\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwcem\nwdh\nwr\nwtpr\nwwjjw\nx\nxc\nxip\nxlgw\ny\nyhxbj\nyk\nylr\nzfv\nzy\nzz\n",
"9\n`arti\nadann\nanand\nap\nbabu\nianq\nnandu\nrani\nsani\n",
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"70\na\nahpr\nb\nbljl\nbxjwf\nc\ncxl\ndkp\nefmlq\neya\nf\nfe\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\ni\nir\niu\niwevs\njbsx\njwwcy\njwx\nkd\nltfhu\nlut\nmopv\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nrgq\nrki\nrom\nslv\nsumon\nsuvo\nsvejq\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwcem\nwdh\nwr\nwtpr\nwwjjw\nx\nxc\nxip\nxlgw\ny\nyhxbj\nyk\nylr\nzfv\nzy\nzz\n",
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yglt\nygmmg\nygo\nygp\nygwxf\nygz\nyh\nyhd\nyhft\nyhnc\nyhot\nyhq\nyhrv\nyhsp\nyht\nyhtsv\nyhtte\nyhu\nyhxzx\nyi\nyiaof\nyimr\nyiraw\nyj\nyjicg\nyjlt\nyjmf\nyjo\nyjro\nyk\nykbe\nykbpd\nyke\nykh\nyknv\nykpwt\nykr\nyks\nykx\nykxca\nyky\nyl\nyladj\nylec\nyleg\nylgu\nyloqj\nylvfj\nym\nymb\nymcp\nymdf\nymf\nymfb\nymho\nymhsm\nymihg\nymkhg\nymww\nymy\nymzi\nyn\nynbd\nyndyj\nyngm\nyngqk\nynje\nynleo\nyo\nyob\nyocqz\nyoddd\nyodu\nyolqu\nyoo\nyosqt\nyownn\nyowr\nyowys\nyp\nypgxl\nypin\nypk\nypn\nypsd\nyptfj\nypw\nypy\nyq\nyqe\nyqeuc\nyqf\nyqh\nyqkh\nyqmo\nyqoet\nyqq\nyqsgj\nyqso\nyqw\nyqxrr\nyqyuo\nyr\nyrat\nyrc\nyrijy\nyrot\nyrtn\nys\nysjh\nyslt\nysn\nysp\nysqjr\nysrvz\nyss\nystq\nysvg\nysz\nyszr\nyt\nytfy\nytif\nytk\nytkup\nytm\nytmrn\nytpm\nytwqz\nytwz\nytxz\nyty\nytyy\nyu\nyubhr\nyumq\nyumx\nyuog\nyuol\nyuox\nyup\nyuqhk\nyur\nyura\nyusf\nyuxee\nyuxqy\nyuzi\nyuzjk\nyv\nyvfdg\nyvgg\nyvj\nyvjj\nyvjsu\nyvkek\nyvl\nyvomp\nyvoug\nyvr\nyw\nywa\nywhv\nywjkh\nywknb\nywnq\nywojf\nywqyt\nywy\nywyu\nyx\nyxc\nyxcdi\nyxmv\nyxpo\nyxpsn\nyxs\nyxw\nyxxfk\nyybx\nyyeo\nyyk\nyymvo\nyyolt\nyyuv\nyyyt\nyz\nyzac\nyzfdj\nyzkpp\nyzp\nz\nza\nzaf\nzagw\nzah\nzai\nzakx\nzaluc\nzar\nzatlu\nzayt\nzaznq\nzb\nzbcwn\nzbiny\nzbn\nzbnte\nzbpg\nzbspx\nzbt\nzc\nzccy\nzcd\nzceds\nzceoe\nzche\nzcigb\nzcil\nzcj\nzcjgr\nzcm\nzd\nzdapp\nzdbrz\nzdbzt\nzdefn\nzdemd\nzdiw\nzdwv\nzdxa\nzdyr\nze\nzeabp\nzecs\nzefu\nzejtt\nzejx\nzem\nzenxq\nzeph\nzet\nzeuc\nzewqk\nzexfc\nzf\nzfcvj\nzfle\nzfqd\nzfqw\nzfu\nzfvsy\nzfwnf\nzfy\nzfzpc\nzg\nzget\nzgewk\nzghrn\nzghx\nzgk\nzgu\nzgzp\nzh\nzhaso\nzhd\nzhgn\nzhj\nzhpvs\nzhqvv\nzhufy\nzhw\nzhwf\nzi\nzig\nzijim\nzil\nzilbg\nzipa\nzit\nzivhx\nzj\nzjdn\nzjp\nzjuh\nzjy\nzk\nzkdj\nzkf\nzkglp\nzkio\nzkma\nzkmt\nzkoyr\nzkwgp\nzkymj\nzkz\nzkzq\nzl\nzlate\nzleo\nzljfq\nzlk\nzlnsx\nzltbl\nzlv\nzlw\nzlytk\nzm\nzmcj\nzme\nzmebr\nzmee\nzmemu\nzmga\nzmi\nzmjks\nzmr\nzmsg\nzmsy\nzmton\nzmxtn\nzn\nzna\nzngl\nzngnz\nznj\nznjy\nznlis\nznnzh\nznpcp\nzns\nznu\nznv\nznwp\nznz\nzo\nzoa\nzocg\nzohyp\nzoi\nzoo\nzoq\nzot\nzou\nzov\nzowc\nzoxav\nzozaq\nzp\nzpaxn\nzpf\nzpgr\nzphjs\nzpo\nzpor\nzptaj\nzptw\nzpv\nzpva\nzpxkd\nzpzl\nzq\nzqdmh\nzqi\nzqixj\nzqmrd\nzqmy\nzquub\nzqv\nzr\nzrao\nzrdxv\nzrhnk\nzri\nzrjaq\nzrka\nzrlz\nzryx\nzs\nzsca\nzsfu\nzsii\nzskrq\nzslau\nzsn\nzsnyd\nzspqj\nzss\nzswur\nzsxe\nztbd\nztfk\nztgj\nzth\nztl\nztlv\nztq\nztud\nztzn\nzu\nzubc\nzuc\nzuj\nzukg\nzupm\nzurq\nzut\nzuusv\nzuxzy\nzv\nzvdf\nzvep\nzvhci\nzvqbf\nzvvek\nzvzo\nzw\nzwbm\nzwc\nzwfj\nzwgi\nzwhn\nzwigl\nzwkb\nzwns\nzwp\nzww\nzwxon\nzx\nzxey\nzxg\nzxmu\nzxwd\nzxzkn\nzy\nzyhia\nzyib\nzyidi\nzylt\nzyo\nzyp\nzyv\nzywh\nzywhg\nzz\nzzc\nzzcym\nzzd\nzzfy\nzzme\nzzpoj\nzzsx\nzzz\n",
"9\n`arti\nadann\nap\nbabu\nianq\nnaand\nnandu\nrani\nsani\n",
"203\na\nagafb\nah\nahtnj\naibr\naidg\naiyfp\namfb\nanky\napjmb\nauk\naxa\naypd\nbcmf\nbg\nblh\nbn\nbosc\nboxq\nbuv\ncb\ncfww\nckira\nckm\ncqk\ncuf\ncvkr\ncy\nd\ndaybm\ndh\ndkmc\ndt\ndtpjo\ndxip\ndxs\ndyx\ne\nebmal\neec\nekntm\neps\neq\nesez\nf\nfk\nfqy\nfulok\ng\ngkgb\ngrxd\nhb\nhfwod\nhipsv\nhkk\nhzksk\ni\niacl\nie\nijzsm\nik\niklk\nixb\nj\njgl\nji\njijt\njp\njy\nk\nkdf\nknh\nkp\nkqnc\nkucy\nkutxb\nkzz\nl\nlb\nldjw\nlhdn\nliqw\nljio\nlp\nlvrk\nlzh\nmgrn\nmiyj\nmj\nmjy\nmnfj\nmpf\nmslj\nmy\nnimxh\nnm\nnrx\nnsbr\nnvl\no\noclnc\nodepm\nodi\nodkk\noee\nohjz\noibfa\noiexd\noiv\nojww\nordy\noyo\np\npj\npr\npsp\npvz\npx\npy\nq\nqa\nqfkmo\nqfz\nqhyj\nqpa\nqzys\nr\nrc\nrdcyd\nrg\nrjjrq\nrqm\nrs\nrtyav\nrxt\nrzsj\nscw\nslzi\nsql\nsquak\nss\nssaiu\nssr\nsyv\nt\ntan\ntbrg\ntdacj\ntgfqj\ntijrb\ntli\ntq\ntvpn\ntyn\nu\nud\nudqy\nug\nuj\nujo\nuor\nuozq\nuyzh\nuzth\nv\nvadoi\nvicjh\nvn\nvnhwm\nvnop\nvpe\nvsz\nvt\nvyogy\nw\nwbpu\nwcsp\nwg\nwip\nwsh\nwtpg\nwtz\nwxt\nwzuh\nx\nxh\nxnuyn\ny\nybyg\nycxx\nydgr\nyf\nymmud\nyo\nz\nzaw\nzg\nziok\nzkjs\nzlony\nzpzf\nzrd\nzttn\n",
"10\n`arti\nadann\nap\nbabu\nianq\nnaand\nnandu\nnaudn\nrani\nsani\n",
"203\na\nagafb\nah\nahtoj\naibr\naidg\naiyfp\namfb\nanky\napjmb\nauk\naxa\naypd\nbcmf\nbg\nblh\nbn\nbosc\nboxq\nbuv\ncb\ncfww\nckira\nckm\ncqk\ncuf\ncvkr\ncy\nd\ndaybm\ndh\ndkmc\ndt\ndtpjo\ndxip\ndxs\ndyx\ne\nebmal\neec\nekntm\neps\neq\nesez\nf\nfk\nfqy\nfulok\ng\ngkgb\ngrxd\nhb\nhfwod\nhipsv\nhkk\nhzksk\ni\niacl\nie\nijzsm\nik\niklk\nixb\nj\njgl\nji\njijt\njp\njy\nk\nkdf\nknh\nkp\nkqnc\nkucy\nkutxb\nkzz\nl\nlb\nldjw\nlhdn\nliqw\nljio\nlp\nlvrk\nlzh\nmgrn\nmiyj\nmj\nmjy\nmnfj\nmpf\nmslj\nmy\nnimxh\nnm\nnrx\nnsbr\nnvl\no\noclnc\nodepm\nodi\nodkk\noee\nohjz\noibfa\noiexd\noiv\nojww\nordy\noyo\np\npj\npr\npsp\npvz\npx\npy\nq\nqa\nqfkmo\nqfz\nqhyj\nqpa\nqzys\nr\nrc\nrdcyd\nrg\nrjjrq\nrqm\nrs\nrtyav\nrxt\nrzsj\nscw\nslzi\nsql\nsquak\nss\nssaiu\nssr\nsyv\nt\ntan\ntbrg\ntdacj\ntgfqj\ntijrb\ntli\ntq\ntvpn\ntyn\nu\nud\nudqy\nug\nuj\nujo\nuor\nuozq\nuyzh\nuzth\nv\nvadoi\nvicjh\nvn\nvnhwm\nvnop\nvpe\nvsz\nvt\nvyogy\nw\nwbpu\nwcsp\nwg\nwip\nwsh\nwtpg\nwtz\nwxt\nwzuh\nx\nxh\nxnuyn\ny\nybyg\nycxx\nydgr\nyf\nymmud\nyo\nz\nzaw\nzg\nziok\nzkjs\nzlony\nzpzf\nzrd\nzttn\n",
"69\na\nahpr\nb\nbljl\nbxjwf\nc\ncxl\ndkp\nefmlq\neya\nf\nfe\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\ni\nir\niu\niwevs\njbsx\njwwcy\njwx\nkd\nltfhu\nlut\nmopv\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nrgq\nrki\nrom\nslv\nsumon\nsuvo\nsvejq\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwcem\nwdh\nwr\nwtpr\nwwjjw\nx\nxc\nxip\nxlgw\ny\nyhxbj\nyk\nylr\nzfv\nzy\n",
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"6\nanand\nap\nbabu\nitraa\nnandu\nrani\n",
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"6\nanand\naq\nbabu\nitraa\nnandu\nrani\n",
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"7\nanand\naq\nbabu\nitraa\nnandu\noandu\nrani\n",
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"7\nanand\naq\nbabu\nitraa\nmandu\noandu\nrani\n",
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"8\nanand\naq\nbabu\nbacu\nitraa\nmandu\noandu\nrani\n",
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"9\nanand\naq\nbabu\nbacu\nitraa\nmandu\nnari\noandu\nrani\n",
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"9\nanand\nbabu\nbacu\nitraa\nmandu\nnari\noandu\nqa\nrani\n",
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\nygbvt\nygk\nyglt\nygmmg\nygo\nygp\nygwxf\nygz\nyh\nyhd\nyhft\nyhnc\nyhot\nyhq\nyhrv\nyhsp\nyht\nyhtsv\nyhtte\nyhu\nyhxzx\nyi\nyiaof\nyimr\nyiraw\nyj\nyjicg\nyjlt\nyjmf\nyjo\nyjro\nyk\nykbe\nykbpd\nyke\nykh\nyknv\nykpwt\nykr\nyks\nykx\nykxca\nyky\nyl\nyladj\nylec\nyleg\nylgu\nyloqj\nylvfj\nym\nymb\nymcp\nymdf\nymf\nymfb\nymho\nymhsm\nymihg\nymkhg\nymww\nymy\nymzi\nyn\nynbd\nyndyj\nyngm\nyngqk\nynje\nynleo\nyo\nyob\nyocqz\nyoddd\nyodu\nyolqu\nyoo\nyosqt\nyownn\nyowr\nyowys\nyp\nypgxl\nypin\nypk\nypn\nypsd\nyptfj\nypw\nypy\nyq\nyqe\nyqeuc\nyqf\nyqh\nyqkh\nyqmo\nyqoet\nyqq\nyqsgj\nyqso\nyqw\nyqxrr\nyqyuo\nyr\nyrat\nyrc\nyrijy\nyrot\nyrtn\nys\nysjh\nyslt\nysn\nysp\nysqjr\nysrvz\nyss\nystq\nysvg\nysz\nyszr\nytfy\nytif\nytk\nytkup\nytm\nytmrn\nytpm\nytwqz\nytwz\nytxz\nyty\nytyy\nyu\nyubhr\nyumq\nyumx\nyuog\nyuol\nyuox\nyup\nyuqhk\nyur\nyura\nyusf\nyuxee\nyuxqy\nyuzi\nyuzjk\nyv\nyvfdg\nyvgg\nyvj\nyvjj\nyvjsu\nyvkek\nyvl\nyvomp\nyvoug\nyvr\nyw\nywa\nywhv\nywjkh\nywknb\nywnq\nywojf\nywqyt\nywy\nywyu\nyx\nyxc\nyxcdi\nyxmv\nyxpo\nyxpsn\nyxs\nyxw\nyxxfk\nyybx\nyyeo\nyyk\nyymvo\nyyolt\nyyuv\nyyyt\nyz\nyzac\nyzfdj\nyzkpp\nyzp\nz\nza\nzaf\nzagw\nzah\nzai\nzakx\nzaluc\nzar\nzatlu\nzayt\nzaznq\nzb\nzbcwn\nzbiny\nzbn\nzbnte\nzbpg\nzbspx\nzbt\nzc\nzccy\nzcd\nzceds\nzceoe\nzche\nzcigb\nzcil\nzcj\nzcjgr\nzcm\nzd\nzdapp\nzdbrz\nzdbzt\nzdefn\nzdemd\nzdiw\nzdwv\nzdxa\nzdyr\nze\nzeabp\nzecs\nzefu\nzejtt\nzejx\nzem\nzenxq\nzeph\nzet\nzeuc\nzewqk\nzexfc\nzf\nzfcvj\nzfle\nzfqd\nzfqw\nzfu\nzfvsy\nzfwnf\nzfy\nzfzpc\nzg\nzget\nzgewk\nzghrn\nzghx\nzgk\nzgu\nzgzp\nzh\nzhaso\nzhd\nzhgn\nzhj\nzhpvs\nzhqvv\nzhufy\nzhw\nzhwf\nzi\nzig\nzijim\nzil\nzilbg\nzipa\nzit\nzivhx\nzj\nzjdn\nzjp\nzjuh\nzjy\nzk\nzkdj\nzkf\nzkglp\nzkio\nzkma\nzkmt\nzkoyr\nzkwgp\nzkymj\nzkz\nzkzq\nzl\nzlate\nzleo\nzljfq\nzlk\nzlnsx\nzltbl\nzlv\nzlw\nzlytk\nzm\nzmcj\nzme\nzmebr\nzmee\nzmemu\nzmga\nzmi\nzmjks\nzmr\nzmsg\nzmsy\nzmton\nzmxtn\nzn\nzna\nzngl\nzngnz\nznj\nznjy\nznlis\nznnzh\nznpcp\nzns\nznu\nznv\nznwp\nznz\nzo\nzoa\nzocg\nzohyp\nzoi\nzoo\nzoq\nzot\nzou\nzov\nzowc\nzoxav\nzozaq\nzp\nzpaxn\nzpf\nzpgr\nzphjs\nzpo\nzpor\nzptaj\nzptw\nzpv\nzpva\nzpxkd\nzpzl\nzq\nzqdmh\nzqi\nzqixj\nzqmrd\nzqmy\nzquub\nzqv\nzr\nzrao\nzrdxv\nzrhnk\nzri\nzrjaq\nzrka\nzrlz\nzryx\nzs\nzsca\nzsfu\nzsii\nzskrq\nzslau\nzsn\nzsnyd\nzspqj\nzss\nzswur\nzsxe\nztbd\nztek\nztgj\nzth\nztl\nztlv\nztq\nztud\nztzn\nzu\nzubc\nzuc\nzuj\nzukg\nzupm\nzurq\nzut\nzuusv\nzuxzy\nzv\nzvdf\nzvep\nzvhci\nzvqbf\nzvvek\nzvzo\nzw\nzwbm\nzwc\nzwfj\nzwgi\nzwhn\nzwigl\nzwkb\nzwns\nzwp\nzww\nzwxon\nzx\nzxey\nzxg\nzxmu\nzxwd\nzxzkn\nzy\nzyhia\nzyib\nzyidi\nzylt\nzyo\nzyp\nzyv\nzywh\nzywhg\nzz\nzzc\nzzcym\nzzd\nzzfy\nzzme\nzzpoj\nzzsx\nzzz\n",
"10\nanand\nanbnd\nbabu\nbacu\nitraa\nmandu\nnari\noandu\nqa\nrani\n",
"202\na\nagafb\nah\nahtnj\naibr\naidg\naiyfp\namfb\nanky\napjmb\nauk\naxa\naypd\nbcmf\nbg\nblh\nbn\nbosc\nboxq\nbuv\ncc\ncfww\nckira\nckm\ncqk\ncuf\ncvkr\ncy\nd\ndaybm\ndh\ndkmc\ndt\ndtpjo\ndxip\ndxs\ndyw\ne\nebmal\neec\nekntm\neq\nesez\nf\nfj\nfqy\nfulok\ng\ngkgb\ngrxd\nhb\nhfwod\nhipsv\nhkk\nhzksk\ni\niacl\nie\nik\niklk\nixb\nj\njgl\nji\njijt\njp\nk\nkdf\nknh\nkp\nkqnc\nkucy\nkutxb\nkzz\nl\nlb\nldjw\nlhdn\nliqw\nljio\nlp\nlvrk\nlzh\nmgrn\nmiyj\nmj\nmjy\nmnfj\nmpf\nmslj\nmszji\nnimxh\nnm\nnrx\nnsbr\nnvl\nnyunx\noclnc\nodepm\nodi\nodkk\noee\nohjz\noibfa\noiexd\noiv\noju\nojww\nordy\noyo\np\npj\npr\npsp\npvy\npx\npy\nq\nqa\nqfkmo\nqhyj\nqpa\nqzys\nr\nrc\nrdcyd\nrg\nrjjrq\nrqm\nrs\nrsyav\nrxt\nrzsj\nscw\nslzi\nspe\nsql\nsquak\nss\nssaiu\nssr\nsyv\nt\ntan\ntbrg\ntdacj\ntijrb\ntjfqg\ntli\ntq\ntvpn\ntyn\nu\nudqy\nug\nuj\nuor\nuozq\nuyzh\nuzth\nv\nvadoi\nvd\nvicjh\nvn\nvnhwm\nvnop\nvpe\nvsz\nvt\nvyogy\nw\nwbpu\nwcsp\nwg\nwip\nwsh\nwtpg\nwtz\nwxt\nwzuh\nx\nxh\ny\nybyg\nycxx\nydgr\nyf\nyj\nym\nymmud\nyo\nz\nzaw\nzfq\nzg\nziok\nzkjs\nzlony\nzpzf\nzrd\nzttn\n",
"69\na\nahpr\nb\nbljl\nbxkwf\nd\ndk\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nhdv\niu\niwevs\njbsx\njwx\nkwwcy\nltfhu\nlut\nlxc\nmopv\nn\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nri\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwcem\nwip\nwr\nwtor\nwwjjw\nxlgw\ny\nyc\nyhxbj\nyk\nylr\nyz\nzfv\nzz\n",
"10\nanand\nanbnd\nbabu\nbacu\nitsaa\nmandu\nnari\noandu\nqa\nrani\n",
"202\na\nagafb\nah\nahtnj\naibr\naidg\naiyfp\namfb\nanky\napjmb\nauk\naxa\naypd\nbcmf\nbg\nblh\nbn\nbosc\nboxq\nbuv\ncc\ncfww\nckira\nckm\ncqk\ncuf\ncvkr\ncy\nd\ndaybm\ndh\ndkmc\ndt\ndtpjo\ndxip\ndxs\ndyw\ne\nebmal\neec\nekntm\neq\nesez\nf\nfj\nfqy\nfulok\ng\ngkgb\ngrxd\nhb\nhfwod\nhipsv\nhjk\nhzksk\ni\niacl\nie\nik\niklk\nixb\nj\njgl\nji\njijt\njp\nk\nkdf\nknh\nkp\nkqnc\nkucy\nkutxb\nkzz\nl\nlb\nldjw\nlhdn\nliqw\nljio\nlp\nlvrk\nlzh\nmgrn\nmiyj\nmj\nmjy\nmnfj\nmpf\nmslj\nmszji\nnimxh\nnm\nnrx\nnsbr\nnvl\nnyunx\noclnc\nodepm\nodi\nodkk\noee\nohjz\noibfa\noiexd\noiv\noju\nojww\nordy\noyo\np\npj\npr\npsp\npvy\npx\npy\nq\nqa\nqfkmo\nqhyj\nqpa\nqzys\nr\nrc\nrdcyd\nrg\nrjjrq\nrqm\nrs\nrsyav\nrxt\nrzsj\nscw\nslzi\nspe\nsql\nsquak\nss\nssaiu\nssr\nsyv\nt\ntan\ntbrg\ntdacj\ntijrb\ntjfqg\ntli\ntq\ntvpn\ntyn\nu\nudqy\nug\nuj\nuor\nuozq\nuyzh\nuzth\nv\nvadoi\nvd\nvicjh\nvn\nvnhwm\nvnop\nvpe\nvsz\nvt\nvyogy\nw\nwbpu\nwcsp\nwg\nwip\nwsh\nwtpg\nwtz\nwxt\nwzuh\nx\nxh\ny\nybyg\nycxx\nydgr\nyf\nyj\nym\nymmud\nyo\nz\nzaw\nzfq\nzg\nziok\nzkjs\nzlony\nzpzf\nzrd\nzttn\n",
"70\na\nahpr\nb\nbljl\nbxkwf\nd\ndk\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nhdv\niu\niwevs\njbsx\njwx\nkwwcy\nltfhu\nlut\nlxc\nmopv\nn\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nri\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwcem\nwip\nwr\nwtor\nwwjjw\nxlgw\ny\nyc\nyhxbj\nyk\nylr\nyz\nz\nzfv\nzz\n",
"10\nanand\nanbnd\nb`bu\nbacu\nitsaa\nmandu\nnari\noandu\nqa\nrani\n",
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"70\na\nahpr\nb\nbljl\nbxkwf\ncwem\nd\ndk\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nhdv\niu\niwevs\njbsx\njwx\nkwwcy\nltfhu\nlut\nlxc\nmopv\nn\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nri\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nv\nvc\nvtx\nvwn\nw\nwip\nwr\nwtor\nwwjjw\nxlgw\ny\nyc\nyhxbj\nyk\nylr\nyz\nz\nzfv\nzz\n",
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"10\nanand\nb`bu\nbacu\ndnbna\nitsaa\nmandu\nnari\noandu\nqa\nrani\n",
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"70\na\nahpr\nb\nbljl\nbxkwf\ncwem\nd\ndk\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nhdv\niu\niwevs\njbsx\njwx\nkwwcy\nltfhu\nlut\nlxc\nmopv\nn\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nri\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nutx\nv\nvc\nvwn\nw\nwip\nwr\nwtor\nwwjjw\nxlgw\ny\nyc\nyhxbj\nyk\nylr\nyz\nz\nzfv\nzz\n",
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"10\nanand\natsia\nb`bu\nbacu\ndnbna\nmandu\nnari\noandu\nqa\nrani\n",
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"70\na\nahpr\nb\nbljl\nbxkwf\ncwem\nd\ndk\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nhdv\niu\niwevs\njbsx\njwx\nkwwcy\nltfhu\nlut\nlxc\nmopv\nn\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nri\nrki\nrom\nslv\nsumon\nsuvo\ntxyi\nuims\nurtoq\nutx\nv\nvc\nvwn\nw\nwglx\nwip\nwr\nwtor\nwwjjw\ny\nyc\nyhxbj\nyk\nylr\nyz\nz\nzfv\nzz\n",
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"10\nanand\natsia\nb`bu\nbacu\ndnbna\nmandt\nnari\noandu\nqa\nrani\n",
"202\na\nagafb\nah\nahtnj\naibr\naidg\naiyfp\namfb\nanky\napjmb\nauk\nax`\naypd\nbcme\nbg\nblh\nbn\nbosc\nboxq\nbuv\ncc\ncfww\nckira\nckm\ncqk\nct\ncuf\ncvkr\ncy\nd\ndaybm\ndh\ndkmc\ndtpjo\ndxip\ndxs\ndyw\ne\nebmal\neec\nekntm\neq\nesez\nf\nfj\nfqy\nfulok\ng\ngkgb\ngrxd\nhb\nhfwod\nhipsv\nhjk\nhzksk\ni\niacl\nie\nik\niklk\nixb\nj\njgl\nji\njijt\njp\nk\nkdf\nknh\nkp\nkqnc\nkucy\nkutxb\nkzz\nl\nlb\nldjw\nlhdn\nliqw\nljio\nlp\nlvrk\nlzh\nmgrn\nmiyj\nmj\nmjy\nmnfj\nmpf\nmslj\nmszji\nnimxh\nnm\nnrx\nnsbr\nnvl\nnyunx\noclnc\nodepm\nodi\nodkk\noee\nohjz\noibfa\noiexd\noiv\noju\nojww\noyo\np\npj\npr\npsp\npvy\npx\npy\nq\nqa\nqfkmo\nqhyj\nqpa\nqzys\nr\nrc\nrdcyd\nrg\nrjjrq\nrqm\nrs\nrsyav\nrxt\nrzsj\nscw\nslzi\nspe\nsql\nsquak\nss\nssaiu\nssr\nsyv\nt\ntan\ntbrg\ntdacj\ntijrb\ntjfqg\ntli\ntq\ntvpn\ntyn\nu\nudqy\nug\nuj\nuor\nuozq\nuyzh\nuzth\nv\nvadoi\nvd\nvicjh\nvn\nvnhwm\nvnop\nvpe\nvsz\nvt\nvyogy\nw\nwbpu\nwcsp\nwg\nwip\nwsh\nwtpg\nwtz\nwxt\nwzuh\nx\nxh\ny\nybyg\nycxx\nydgr\nydro\nyf\nyj\nym\nymmud\nyo\nz\nzaw\nzfq\nzg\nziok\nzkjs\nzlony\nzpzf\nzrd\nzttn\n",
"70\na\nahpr\nb\nbljl\nbxkwf\ncwem\nd\ndk\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nhdv\niu\niwevs\njbsx\njwx\nkwwcy\nltfhu\nlut\nlxc\nmopv\nn\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqj\nqjevs\nrgq\nri\nrki\nrom\nslv\nsumon\nsuvo\ntxxi\nuims\nurtoq\nutx\nv\nvc\nvwn\nw\nwglx\nwip\nwr\nwtor\nwwjjw\ny\nyc\nyhxbj\nyk\nylr\nyz\nz\nzfv\nzz\n",
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"10\nanand\natsia\nbacu\ndnbna\nmandt\nnari\noandu\nqa\nrani\nub`b\n",
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"70\na\nahpr\nb\nbljl\nbxkwf\ncwem\nd\ndk\ndkp\nee\nefmlq\neya\nf\nfia\nfn\ngqdld\ngunj\ngvny\nh\nhby\nhdv\niu\niwevs\njbsx\njq\njwx\nkwwcy\nltfhu\nlut\nlxc\nmopv\nn\nnhl\nnomnb\nnq\nnqe\nnu\no\nocgq\noy\nqjevs\nrgq\nri\nrik\nrom\nslv\nsumon\nsuvo\ntxxi\nuims\nurtoq\nutx\nv\nvc\nvwn\nw\nwglx\nwip\nwr\nwtor\nwwjjw\ny\nyc\nyhxbj\nyk\nylr\nyz\nz\nzfv\nzz\n",
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"11\nanand\natsia\nbacu\ndnbna\nmandt\nnari\noandu\nqa\nranh\nrani\nub`b\n",
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"11\nanand\natsia\nbacu\ndnbna\nmandt\nnari\nobndu\nqa\nranh\nrani\nub`b\n",
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\nygbvt\nygk\nyglt\nygmmg\nygo\nygp\nygwxf\nygz\nyh\nyhd\nyhft\nyhnc\nyhot\nyhq\nyhrv\nyhsp\nyht\nyhtsv\nyhtte\nyhu\nyhxzx\nyi\nyiaof\nyimr\nyiraw\nyj\nyjicg\nyjlt\nyjmf\nyjo\nyjro\nyk\nykbe\nykbpd\nyke\nykh\nyknv\nykpwt\nykr\nyks\nykx\nykxca\nyky\nyl\nyladj\nylec\nyleg\nylgu\nyloqj\nylvfj\nym\nymb\nymcp\nymdf\nymf\nymfb\nymho\nymhsm\nymihg\nymkhg\nymww\nymy\nymzi\nyn\nynbd\nyndyj\nyngm\nyngqk\nynje\nynleo\nyo\nyob\nyocqz\nyoddd\nyodu\nyolqu\nyoo\nyosqt\nyownn\nyowr\nyowys\nyp\nypgxl\nypin\nypk\nypn\nypsd\nyptfj\nypw\nypy\nyq\nyqe\nyqeuc\nyqf\nyqh\nyqkh\nyqmo\nyqoet\nyqq\nyqsgj\nyqso\nyqw\nyqxrr\nyqyuo\nyr\nyrat\nyrc\nyrijy\nyrot\nyrtn\nys\nysjh\nyslt\nysn\nysp\nysqjr\nysrvz\nyss\nystq\nysvg\nysz\nyszr\nytfy\nytif\nytk\nytkup\nytm\nytmrn\nytpm\nytwqz\nytwz\nytxz\nyty\nytyy\nyu\nyubhr\nyumq\nyumx\nyuog\nyuol\nyuox\nyup\nyuqhk\nyur\nyura\nyusf\nyuxee\nyuxqy\nyuzi\nyuzjk\nyv\nyvfdg\nyvgg\nyvj\nyvjj\nyvjsu\nyvkek\nyvl\nyvomp\nyvoug\nyvr\nyw\nywa\nywhv\nywjkh\nywknb\nywnq\nywojf\nywqyt\nywy\nywyu\nyx\nyxc\nyxcdi\nyxmv\nyxpo\nyxpsn\nyxs\nyxw\nyxxfk\nyybx\nyyeo\nyyk\nyymvo\nyyolt\nyyuv\nyyyt\nyz\nyzac\nyzfdj\nyzkpp\nyzp\nz\nza\nzaf\nzagw\nzah\nzai\nzakx\nzaluc\nzar\nzatlu\nzayt\nzaznq\nzb\nzbcwn\nzbiny\nzbn\nzbnte\nzbpg\nzbspx\nzbt\nzc\nzccy\nzcd\nzceds\nzceoe\nzche\nzcigb\nzcil\nzcj\nzcjgr\nzcm\nzd\nzdapp\nzdbrz\nzdbzt\nzdefn\nzdemd\nzdiw\nzdwv\nzdxa\nzdyr\nze\nzeabp\nzecs\nzefu\nzejtt\nzejx\nzem\nzenxq\nzeph\nzet\nzeuc\nzewqk\nzexfc\nzf\nzfcvj\nzfle\nzfqd\nzfqw\nzfu\nzfvsy\nzfwnf\nzfy\nzfzpc\nzg\nzget\nzgewk\nzghrn\nzghx\nzgk\nzgu\nzgzp\nzh\nzhaso\nzhd\nzhgn\nzhj\nzhpvs\nzhqvv\nzhufy\nzhw\nzhwf\nzi\nzig\nzijim\nzil\nzilbg\nzipa\nzit\nzivhx\nzj\nzjdn\nzjp\nzjuh\nzjy\nzk\nzkdj\nzkf\nzkglp\nzkio\nzkma\nzkmt\nzkoyr\nzkwgp\nzkymj\nzkz\nzkzq\nzl\nzlate\nzleo\nzljfq\nzlk\nzlnsx\nzltbl\nzlv\nzlw\nzlytk\nzm\nzmcj\nzme\nzmebr\nzmee\nzmemu\nzmga\nzmi\nzmjks\nzmr\nzmsg\nzmsy\nzmton\nzmxtn\nzn\nzna\nzngl\nzngnz\nznj\nznjy\nznlis\nznnzh\nznpcp\nzns\nznu\nznv\nznwp\nznz\nzo\nzoa\nzocg\nzohyp\nzoi\nzoo\nzoq\nzot\nzou\nzov\nzowc\nzoxav\nzozaq\nzp\nzpaxn\nzpf\nzpgr\nzphjs\nzpo\nzpor\nzptaj\nzptw\nzpv\nzpva\nzpxkd\nzpzl\nzq\nzqdmh\nzqi\nzqixj\nzqmrd\nzqmy\nzquub\nzqv\nzr\nzrao\nzrdxv\nzrhnk\nzri\nzrjaq\nzrka\nzrlz\nzryx\nzs\nzsca\nzsfu\nzsii\nzskrq\nzslau\nzsn\nzsnyd\nzspqj\nzss\nzswur\nzsxe\nztbd\nztek\nztgj\nzth\nztl\nztlv\nztq\nztud\nztzn\nzu\nzubc\nzuc\nzuj\nzukg\nzupm\nzurq\nzut\nzuusv\nzuxzy\nzv\nzvdf\nzvep\nzvhci\nzvqbf\nzvvek\nzvzo\nzw\nzwbm\nzwc\nzwfj\nzwgi\nzwhn\nzwigl\nzwkb\nzwns\nzwp\nzww\nzwxon\nzx\nzxey\nzxg\nzxmu\nzxwd\nzxzkn\nzy\nzyhia\nzyib\nzyidi\nzylt\nzyo\nzyp\nzyv\nzywh\nzywhg\nzz\nzzc\nzzcym\nzzd\nzzfy\nzzme\nzzpoj\nzzsx\nzzz\n"
]
}
|
Problem :
Chotu's father is the owner of a Vada Pav shop. One Sunday, his father takes him to the shop. Father tells him that at the end of the day, Chotu has to give him a list consisting of the names of all the customers on that day who bought Vada Pav(s) from the shop. The list should not have the names of any of the customers being repeated and it should be such that the lexicographically smallest name comes first, ie., the names should be sorted in dictionary order.
As and when a particular customer buys a Vada Pav, Chotu writes down the name of that particular customer. Chotu's initial list is ready, but, he is confused as to how to make the list Father expects from him. Chotu comes to you for help. Your job now is to create the final list, as Father expects from Chotu.
Input :
First line consists of N, the number of names of customers in Chotu's initial list. The next N lines are such that each line consists of a customer's name.
Output :
On the first line, print the total number of names appearing in Chotu's final list. Then print the list such that every customer's name is printed on a new line.
Constraints :
1 ≤ N ≤ 10^6
1 ≤ Length of names of customers ≤ 5
Customers' names consist only of lower case English alphabets (a-z).
Note : Some test files contain large data. Use scanf/printf instead of cin/cout .
SAMPLE INPUT
11
babu
anand
rani
aarti
nandu
rani
rani
ap
anand
babu
nandu
SAMPLE OUTPUT
6
aarti
anand
ap
babu
nandu
rani
|
{
"inputs": [
"1222",
"3242",
"0290",
"2364",
"1114",
"2005",
"1455",
"1152",
"3246",
"6120",
"2768",
"1183",
"1024",
"1181",
"1785",
"1372",
"1765",
"1280",
"2308",
"1824",
"2162",
"1802",
"1226",
"2412",
"1699",
"4212",
"2632",
"2195",
"1732",
"4915",
"3172",
"1071",
"2193",
"1864",
"2104",
"6793",
"1583",
"3950",
"1842",
"3260",
"3521",
"2533",
"2995",
"2825",
"2225",
"3321",
"2986",
"2296",
"1529",
"1912",
"1347",
"1321",
"2160",
"6234",
"9378",
"2904",
"1213",
"2612",
"3161",
"1284",
"2797",
"1314",
"8265",
"2582",
"3967",
"1295",
"1215",
"2368",
"4113",
"1231",
"2841",
"1758",
"3095",
"2122",
"2326",
"3916",
"6517",
"6188",
"4245",
"5338",
"3387",
"2362",
"3536",
"3297",
"3062",
"1235",
"8739",
"2546",
"2171",
"2049",
"2263",
"1141",
"3611",
"2203",
"1170",
"1675",
"2140",
"5136",
"5321",
"3354",
"1093",
"1798",
"1006"
],
"outputs": [
"1+2+2+2=7",
"3+2+4-2=7",
"0-2+9+0=7",
"2+3+6-4=7\n",
"1+1+1+4=7\n",
"2+0+0+5=7\n",
"1-4+5+5=7\n",
"1-1+5+2=7\n",
"3+2-4+6=7\n",
"6-1+2+0=7\n",
"2+7+6-8=7\n",
"1+1+8-3=7\n",
"1+0+2+4=7\n",
"1-1+8-1=7\n",
"1-7+8+5=7\n",
"1-3+7+2=7\n",
"1+7-6+5=7\n",
"1-2+8+0=7\n",
"2-3+0+8=7\n",
"1+8+2-4=7\n",
"2+1+6-2=7\n",
"1+8+0-2=7\n",
"1+2-2+6=7\n",
"2+4-1+2=7\n",
"1+6+9-9=7\n",
"4+2-1+2=7\n",
"2+6-3+2=7\n",
"2+1+9-5=7\n",
"1+7-3+2=7\n",
"4+9-1-5=7\n",
"3-1+7-2=7\n",
"1+0+7-1=7\n",
"2-1+9-3=7\n",
"1+8-6+4=7\n",
"2+1+0+4=7\n",
"6+7-9+3=7\n",
"1-5+8+3=7\n",
"3+9-5+0=7\n",
"1+8-4+2=7\n",
"3-2+6+0=7\n",
"3+5-2+1=7\n",
"2+5+3-3=7\n",
"2+9-9+5=7\n",
"2+8+2-5=7\n",
"2+2-2+5=7\n",
"3+3+2-1=7\n",
"2-9+8+6=7\n",
"2+2+9-6=7\n",
"1-5+2+9=7\n",
"1+9-1-2=7\n",
"1+3-4+7=7\n",
"1+3+2+1=7\n",
"2-1+6+0=7\n",
"6+2+3-4=7\n",
"9-3-7+8=7\n",
"2+9+0-4=7\n",
"1+2+1+3=7\n",
"2+6+1-2=7\n",
"3-1+6-1=7\n",
"1+2+8-4=7\n",
"2+7-9+7=7\n",
"1+3-1+4=7\n",
"8-2+6-5=7\n",
"2-5+8+2=7\n",
"3-9+6+7=7\n",
"1+2+9-5=7\n",
"1+2-1+5=7\n",
"2+3-6+8=7\n",
"4+1-1+3=7\n",
"1+2+3+1=7\n",
"2+8-4+1=7\n",
"1-7+5+8=7\n",
"3+0+9-5=7\n",
"2+1+2+2=7\n",
"2-3+2+6=7\n",
"3+9+1-6=7\n",
"6-5-1+7=7\n",
"6+1+8-8=7\n",
"4+2-4+5=7\n",
"5-3-3+8=7\n",
"3+3+8-7=7\n",
"2-3+6+2=7\n",
"3-5+3+6=7\n",
"3+2+9-7=7\n",
"3+0+6-2=7\n",
"1-2+3+5=7\n",
"8-7-3+9=7\n",
"2-5+4+6=7\n",
"2-1+7-1=7\n",
"2+0-4+9=7\n",
"2+2+6-3=7\n",
"1+1+4+1=7\n",
"3+6-1-1=7\n",
"2+2+0+3=7\n",
"1-1+7+0=7\n",
"1-6+7+5=7\n",
"2+1+4+0=7\n",
"5-1-3+6=7\n",
"5+3-2+1=7\n",
"3+3+5-4=7\n",
"1+0+9-3=7\n",
"1+7-9+8=7\n",
"1+0+0+6=7\n"
]
}
|
Sitting in a station waiting room, Joisino is gazing at her train ticket.
The ticket is numbered with four digits A, B, C and D in this order, each between 0 and 9 (inclusive).
In the formula A op1 B op2 C op3 D = 7, replace each of the symbols op1, op2 and op3 with `+` or `-` so that the formula holds.
The given input guarantees that there is a solution. If there are multiple solutions, any of them will be accepted.
Constraints
* 0≤A,B,C,D≤9
* All input values are integers.
* It is guaranteed that there is a solution.
Input
Input is given from Standard Input in the following format:
ABCD
Output
Print the formula you made, including the part `=7`.
Use the signs `+` and `-`.
Do not print a space between a digit and a sign.
Examples
Input
1222
Output
1+2+2+2=7
Input
0290
Output
0-2+9+0=7
Input
3242
Output
3+2+4-2=7
|
{
"inputs": [
"2 2 2\n2 1\n1 2\n2 1\n",
"5 3 3\n0 3 0 0 2\n2 4\n3 4\n3 5\n",
"7 6 5\n0 4 5 4 1 0 0\n6 1\n3 6\n3 1\n7 5\n7 1\n7 4\n",
"8 4 6\n0 0 3 0 0 0 0 0\n7 6\n6 2\n6 3\n4 7\n",
"10 11 3\n1 0 0 0 0 0 0 0 2 0\n6 1\n2 10\n7 5\n7 4\n6 4\n8 1\n6 8\n9 10\n7 2\n6 1\n7 10\n",
"7 4 5\n0 0 1 3 5 2 2\n5 6\n2 1\n5 7\n1 3\n",
"40 35 4\n1 1 2 0 0 3 0 0 0 0 0 0 0 4 1 3 0 0 0 0 0 0 2 0 0 0 0 0 0 4 0 2 2 1 0 0 0 4 0 0\n30 34\n38 20\n21 1\n12 32\n14 31\n38 27\n29 7\n13 39\n19 16\n30 24\n4 34\n12 20\n16 1\n5 34\n5 32\n14 23\n18 20\n19 39\n13 29\n5 10\n38 7\n25 4\n5 20\n25 28\n32 35\n21 33\n25 28\n30 20\n3 34\n12 35\n3 1\n25 10\n19 20\n27 26\n32 35\n",
"6 3 4\n0 0 0 0 0 3\n6 5\n6 5\n5 1\n",
"2 2 1\n0 0\n1 2\n1 2\n",
"10 11 3\n0 1 0 0 0 0 0 0 0 2\n10 2\n7 8\n4 9\n4 3\n7 5\n4 9\n9 8\n4 6\n10 2\n7 9\n7 9\n",
"9 12 6\n1 0 0 0 0 5 0 0 1\n5 6\n2 1\n2 3\n4 2\n4 9\n6 8\n8 3\n7 9\n4 2\n5 9\n4 1\n4 3\n",
"100 21 11\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n35 83\n39 54\n10 24\n50 90\n47 49\n49 27\n93 73\n93 52\n97 8\n75 57\n80 72\n98 12\n32 80\n32 23\n42 54\n32 88\n75 99\n98 69\n5 11\n25 86\n60 9\n",
"10 15 4\n4 0 4 0 0 0 0 0 0 0\n1 6\n5 4\n8 10\n6 4\n5 9\n2 4\n3 4\n1 5\n6 9\n5 7\n1 5\n1 6\n5 7\n5 7\n6 2\n",
"7 4 4\n3 0 1 0 2 3 4\n1 4\n6 5\n5 4\n7 2\n",
"3 1 3\n0 0 2\n3 2\n",
"4 3 3\n1 3 2 0\n2 3\n4 3\n4 1\n",
"2 1 3\n2 1\n1 2\n",
"60 20 54\n0 40 50 15 0 54 35 19 12 11 0 48 0 0 21 0 0 25 30 24 14 28 3 0 0 0 26 19 0 38 0 0 0 0 0 0 0 46 0 18 0 51 10 0 2 0 0 17 0 27 29 0 43 31 0 0 0 0 45 0\n13 34\n38 34\n46 24\n20 45\n46 44\n59 15\n14 15\n32 9\n21 29\n16 25\n20 15\n22 45\n30 52\n21 44\n14 18\n12 49\n4 29\n60 8\n20 45\n20 55\n",
"2 4 2\n0 0\n1 2\n1 2\n1 2\n1 2\n",
"9 6 5\n0 2 0 0 0 0 3 5 2\n3 7\n8 9\n3 6\n7 6\n7 6\n9 6\n",
"5 2 5\n0 0 4 0 0\n5 1\n2 5\n",
"5 3 5\n0 4 0 1 0\n2 1\n1 4\n2 5\n",
"5 4 4\n0 0 0 4 0\n5 2\n5 2\n3 1\n4 2\n",
"3 3 3\n0 0 0\n1 2\n2 3\n3 1\n",
"5 1 2\n0 0 0 2 0\n3 5\n",
"4 1 3\n0 0 0 0\n4 2\n",
"9 8 3\n0 0 3 3 0 0 1 3 0\n6 7\n3 1\n6 7\n4 9\n8 7\n1 9\n1 2\n4 5\n",
"5 5 4\n0 0 0 0 0\n1 5\n1 2\n1 3\n4 2\n1 2\n",
"20 31 5\n3 5 0 4 5 0 2 2 0 0 4 5 0 3 4 2 0 1 5 1\n4 16\n2 9\n4 7\n12 20\n5 16\n12 7\n11 1\n5 17\n11 7\n19 18\n2 8\n15 18\n11 10\n1 20\n2 4\n2 16\n4 7\n1 7\n14 7\n1 16\n4 7\n2 15\n6 14\n14 18\n19 20\n2 1\n19 14\n15 8\n12 9\n5 20\n5 11\n",
"20 20 20\n0 0 14 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0\n8 20\n8 3\n8 16\n3 14\n7 2\n19 10\n5 14\n18 20\n8 15\n5 16\n7 10\n13 18\n7 17\n7 17\n7 20\n2 6\n8 18\n16 14\n2 15\n6 11\n",
"6 4 2\n0 0 0 0 0 0\n3 2\n4 2\n5 1\n4 1\n",
"1 0 2\n1\n",
"7 6 5\n0 0 4 3 1 2 0\n7 1\n1 5\n4 5\n7 1\n3 4\n4 1\n",
"10 5 3\n2 3 2 3 1 0 0 3 1 1\n1 10\n8 10\n1 7\n6 7\n8 3\n",
"9 9 6\n0 2 0 0 0 0 1 0 5\n3 1\n3 8\n3 5\n9 5\n3 7\n1 6\n9 2\n3 8\n3 6\n",
"3 4 2\n0 1 0\n2 3\n2 3\n2 3\n2 3\n",
"9 7 4\n4 0 0 0 1 0 1 4 0\n3 4\n2 5\n9 5\n2 7\n1 6\n1 5\n2 9\n",
"5 1 5\n0 3 0 0 0\n1 2\n",
"1 0 1\n0\n",
"10 14 4\n0 0 0 0 0 1 0 2 0 0\n4 9\n10 3\n4 1\n8 2\n9 8\n8 3\n8 7\n8 7\n4 7\n10 1\n5 9\n10 9\n5 8\n10 7\n",
"2 2 2\n0 0\n1 2\n2 1\n",
"3 2 1\n0 0 0\n3 1\n3 1\n",
"7 6 5\n5 2 0 0 4 1 0\n1 4\n3 4\n1 6\n5 6\n5 6\n7 4\n",
"4 5 1\n0 0 0 0\n2 3\n4 2\n2 3\n4 1\n4 2\n",
"6 4 4\n0 0 0 4 2 0\n2 5\n4 2\n6 2\n1 5\n",
"2 5 2\n0 0\n2 1\n2 1\n2 1\n2 1\n2 1\n",
"3 4 3\n0 2 3\n2 3\n2 3\n1 3\n2 3\n",
"5 5 5\n0 0 0 0 0\n2 4\n5 1\n4 1\n3 2\n5 2\n",
"5 3 3\n3 0 1 0 0\n5 3\n1 3\n1 3\n",
"10 12 3\n0 0 0 0 0 0 0 0 0 0\n4 9\n10 8\n3 6\n2 1\n2 7\n5 7\n3 2\n3 2\n5 6\n5 2\n5 2\n3 10\n",
"50 10 30\n0 21 0 30 0 25 28 2 16 0 5 0 0 0 0 8 0 0 0 22 18 0 25 0 0 8 0 0 21 0 0 19 0 0 0 4 0 23 3 0 0 1 0 0 0 3 0 20 28 0\n50 33\n21 12\n50 8\n48 13\n49 1\n38 21\n23 39\n49 17\n19 26\n14 41\n",
"6 3 4\n0 3 0 0 0 0\n2 1\n2 3\n1 3\n",
"70 9 45\n0 44 5 39 3 4 3 2 36 23 0 18 0 37 8 22 34 5 41 13 26 39 7 0 0 11 10 9 15 0 25 28 14 28 5 41 7 24 44 42 0 1 11 18 31 10 20 7 21 19 27 29 10 16 40 43 33 22 35 0 40 37 16 34 0 16 6 27 32 36\n40 43\n41 6\n32 63\n1 12\n20 43\n47 6\n21 26\n58 54\n61 6\n",
"70 20 70\n8 0 0 37 0 0 0 0 59 56 0 26 0 65 0 0 42 46 0 32 0 0 69 0 0 12 51 58 0 0 41 0 36 0 0 0 10 0 0 0 0 70 0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0 5 67 0 19 0 0 0 0 0 0 0 0\n10 68\n11 17\n35 4\n25 38\n18 3\n22 6\n27 61\n54 69\n35 57\n57 49\n20 52\n44 63\n16 33\n24 13\n31 49\n20 67\n35 59\n30 31\n22 1\n25 13\n",
"9 12 6\n0 6 0 5 0 0 2 6 0\n4 3\n6 5\n6 9\n2 3\n1 7\n9 7\n8 3\n8 9\n2 7\n4 5\n4 3\n5 3\n",
"4 5 4\n4 0 0 0\n3 1\n3 2\n2 4\n3 4\n2 4\n",
"3 5 1\n0 0 1\n1 3\n3 2\n1 2\n1 2\n1 2\n",
"10 8 2\n0 0 0 0 0 0 0 0 0 0\n4 10\n6 8\n3 8\n4 7\n4 10\n1 10\n6 8\n5 10\n",
"2 3 2\n0 1\n2 1\n2 1\n2 1\n",
"4 2 4\n2 0 0 0\n1 4\n3 2\n",
"7 4 3\n0 0 0 0 2 0 0\n1 5\n2 6\n7 5\n7 2\n",
"10 10 3\n0 3 0 3 0 0 0 3 0 0\n9 7\n5 9\n9 3\n4 1\n10 3\n2 10\n8 7\n8 3\n4 7\n8 7\n",
"10 10 3\n0 0 0 0 0 1 0 0 0 3\n3 6\n3 8\n9 2\n8 6\n7 6\n7 5\n10 6\n7 1\n1 6\n9 8\n",
"3 1 2\n1 0 0\n3 1\n",
"3 3 2\n1 1 2\n2 1\n3 2\n3 2\n",
"3 4 1\n0 0 0\n3 1\n3 2\n1 2\n3 2\n",
"4 4 1\n0 0 0 1\n2 3\n2 3\n2 3\n3 4\n",
"2 1 2\n0 0\n2 1\n",
"5 3 5\n0 0 2 0 0\n4 3\n1 3\n2 3\n",
"5 1 3\n2 0 0 3 3\n2 5\n",
"7 4 3\n0 0 0 3 0 1 3\n3 1\n3 6\n3 2\n2 6\n",
"2 1 1\n0 0\n2 1\n",
"90 32 45\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 31 0 0 0 0 0 0 0 0 0 23 34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 14 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 37 41\n48 74\n49 19\n32 87\n31 65\n60 50\n12 40\n39 87\n90 36\n79 40\n38 1\n52 50\n29 85\n76 41\n25 35\n72 4\n32 59\n73 79\n15 54\n13 37\n16 68\n78 19\n29 62\n52 41\n43 7\n58 17\n8 16\n81 72\n89 10\n89 84\n73 1\n15 22\n2 66\n",
"6 3 4\n2 3 0 3 0 1\n2 4\n3 4\n3 1\n",
"5 0 6\n0 0 0 0 0\n",
"5 2 4\n2 3 2 0 1\n3 2\n2 1\n",
"6 4 2\n0 0 0 0 0 0\n6 1\n3 2\n6 2\n4 2\n",
"5 4 2\n1 0 0 2 0\n3 5\n2 5\n4 5\n3 5\n",
"6 3 4\n0 2 0 0 0 0\n3 4\n2 6\n3 2\n",
"4 1 2\n0 0 0 0\n1 2\n",
"30 12 2\n1 2 0 0 2 1 0 0 2 2 2 1 0 0 0 2 2 2 0 1 0 1 1 1 1 0 1 0 2 1\n21 12\n14 4\n16 27\n8 25\n2 7\n17 25\n16 24\n16 25\n9 1\n2 13\n28 20\n26 7\n",
"20 7 2\n1 2 0 1 1 1 2 0 1 2 2 2 0 1 2 2 0 0 2 0\n12 5\n7 1\n11 6\n10 3\n12 14\n19 14\n16 9\n",
"2 2 1\n0 0\n1 2\n2 1\n",
"5 1 4\n0 0 0 0 0\n4 2\n",
"7 4 7\n6 3 4 0 0 0 0\n2 5\n4 3\n6 5\n1 5\n",
"5 4 3\n0 0 0 0 0\n5 2\n3 5\n1 2\n4 2\n",
"4 5 2\n0 0 0 0\n3 4\n3 1\n2 3\n3 1\n3 4\n",
"9 7 3\n3 1 0 0 0 1 0 2 0\n8 6\n3 2\n9 3\n7 2\n3 4\n9 4\n1 6\n",
"10 10 5\n0 1 2 5 4 2 0 0 0 0\n5 9\n8 10\n4 1\n5 3\n4 8\n6 2\n8 3\n8 3\n7 2\n4 9\n",
"31 11 26\n0 0 0 0 0 12 24 0 0 24 20 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17\n30 18\n10 9\n15 9\n22 17\n7 30\n7 16\n31 18\n31 28\n25 18\n20 1\n27 26\n",
"7 6 5\n4 3 0 0 1 0 4\n3 6\n2 5\n7 6\n3 4\n3 6\n6 5\n",
"4 2 2\n0 0 0 0\n1 3\n1 3\n",
"3 5 3\n0 0 0\n3 1\n1 2\n1 2\n3 1\n3 1\n",
"5 1 1\n0 0 0 1 0\n5 4\n",
"40 21 3\n0 0 0 3 0 1 2 1 0 3 2 3 0 0 1 0 2 1 2 0 0 3 0 0 0 0 1 2 0 3 0 2 3 0 0 1 3 0 2 0\n5 36\n4 9\n32 6\n5 3\n32 14\n11 9\n33 9\n21 18\n32 18\n39 6\n13 18\n4 2\n29 27\n25 18\n19 27\n31 40\n33 2\n17 15\n12 26\n38 8\n31 27\n",
"6 3 4\n0 0 0 0 0 0\n4 3\n6 3\n5 4\n",
"5 2 3\n0 0 2 0 3\n4 2\n1 3\n",
"9 12 6\n5 4 0 0 3 6 0 0 4\n9 4\n2 5\n1 9\n2 7\n3 9\n6 4\n8 1\n8 9\n1 7\n2 4\n8 4\n6 3\n",
"1 0 1\n1\n",
"3 2 2\n2 2 1\n1 3\n1 3\n",
"10 10 6\n0 0 2 3 4 0 4 0 2 0\n5 2\n10 3\n1 10\n10 3\n8 3\n7 3\n10 9\n4 2\n8 5\n4 3\n",
"5 1 5\n0 0 0 0 0\n2 4\n",
"5 3 2\n0 0 0 1 0\n3 4\n5 3\n5 1\n",
"5 2 2\n0 0 0 0 0\n5 1\n3 4\n",
"1 0 2\n0\n",
"5 3 4\n0 0 0 1 0\n4 1\n4 3\n3 2\n",
"5 4 5\n5 0 5 0 5\n2 5\n3 2\n1 2\n1 2\n",
"9 6 3\n0 0 0 3 3 2 0 2 0\n3 9\n7 2\n1 2\n3 6\n8 9\n1 6\n",
"10 3 4\n2 2 1 2 4 3 3 0 3 1\n4 3\n2 3\n7 10\n",
"10 11 3\n0 0 0 2 0 0 0 0 1 0\n1 2\n10 9\n5 9\n6 2\n4 9\n3 2\n6 2\n8 7\n6 3\n4 7\n6 5\n",
"7 4 3\n3 3 0 2 0 0 2\n3 7\n1 7\n3 4\n4 6\n",
"7 6 5\n3 0 0 5 2 0 5\n4 2\n1 6\n1 6\n7 6\n1 6\n7 1\n",
"4 4 2\n0 2 0 0\n2 3\n1 4\n1 3\n2 4\n",
"9 9 4\n0 0 0 0 2 0 2 3 1\n3 1\n2 4\n2 3\n6 8\n2 5\n5 9\n6 5\n6 8\n6 3\n",
"7 4 3\n0 0 2 3 1 3 2\n6 1\n2 5\n7 5\n7 5\n",
"4 5 3\n0 0 0 0\n1 3\n4 2\n3 2\n3 2\n1 4\n",
"4 4 3\n0 0 0 0\n2 4\n1 3\n2 1\n2 1\n",
"10 13 3\n0 0 0 0 0 0 0 0 0 0\n3 5\n2 6\n10 1\n2 6\n10 9\n1 5\n1 6\n3 8\n10 7\n8 7\n9 6\n2 8\n10 1\n",
"4 3 2\n0 0 0 0\n4 3\n2 3\n1 3\n",
"1 0 200000\n0\n",
"5 5 1\n0 0 0 0 0\n2 1\n5 2\n4 3\n3 2\n4 2\n",
"5 1 4\n0 0 0 0 3\n2 1\n",
"2 5 1\n0 0\n1 2\n1 2\n1 2\n1 2\n1 2\n",
"5 3 1\n1 1 1 0 0\n4 3\n4 3\n1 5\n",
"1 0 200000\n1\n",
"4 3 4\n0 0 0 0\n1 3\n1 3\n1 2\n",
"6 6 4\n0 0 0 0 0 0\n6 2\n3 5\n4 5\n4 2\n3 6\n4 2\n",
"10 15 4\n0 0 0 0 3 0 4 0 4 0\n9 10\n7 10\n7 8\n7 4\n5 2\n5 4\n1 4\n6 10\n10 2\n7 8\n5 1\n7 1\n7 1\n3 5\n8 1\n",
"4 3 1\n1 1 0 1\n1 4\n2 4\n3 2\n",
"3 2 3\n0 0 0\n3 2\n1 2\n",
"3 3 1\n0 0 1\n1 2\n1 3\n1 2\n",
"30 29 10\n2 0 8 9 10 2 0 0 2 0 0 4 6 7 1 0 0 8 2 9 3 0 2 0 0 0 0 0 4 1\n5 14\n18 9\n4 11\n3 2\n28 29\n20 6\n20 9\n5 20\n16 24\n14 6\n4 14\n16 6\n11 26\n14 17\n4 17\n20 10\n18 2\n26 9\n28 8\n2 29\n6 10\n6 15\n28 22\n4 12\n25 3\n27 11\n13 26\n14 8\n27 4\n",
"2 2 2\n0 0\n1 2\n1 2\n",
"80 19 13\n1 0 12 11 0 0 2 0 0 0 13 6 13 0 6 0 0 2 0 0 13 8 10 9 0 9 11 13 3 3 0 0 0 4 12 0 0 0 0 4 0 5 5 0 0 4 5 9 0 0 0 0 0 0 0 11 3 12 0 11 0 7 1 2 1 0 12 13 5 8 2 0 8 11 6 6 9 11 9 0\n11 47\n42 34\n49 40\n13 3\n21 9\n41 37\n61 7\n19 64\n36 38\n74 1\n52 1\n72 45\n28 80\n4 24\n60 45\n11 69\n78 9\n27 30\n23 47\n",
"5 2 1\n0 0 0 1 1\n4 1\n4 1\n",
"4 1 4\n0 2 0 2\n4 3\n",
"2 1 3\n0 0\n1 2\n",
"5 3 5\n0 0 0 0 0\n4 3\n1 3\n2 4\n",
"3 3 1\n0 0 0\n1 2\n2 3\n3 1\n",
"4 2 1\n0 0 0 0\n3 1\n3 4\n",
"8 4 7\n6 0 0 4 0 0 1 4\n8 2\n5 7\n5 4\n3 1\n",
"6 4 2\n0 0 0 0 0 0\n2 6\n5 6\n2 3\n1 4\n",
"3 1 1\n0 0 1\n2 1\n",
"2 4 1\n1 1\n1 2\n1 2\n1 2\n1 2\n",
"6 4 2\n0 0 0 0 0 0\n1 2\n6 2\n4 5\n1 3\n",
"9 10 6\n2 3 0 0 1 0 2 0 4\n8 3\n9 7\n3 6\n1 5\n3 6\n8 5\n3 6\n3 4\n4 5\n2 4\n",
"7 6 5\n0 0 5 1 2 0 3\n3 6\n5 2\n6 1\n5 1\n6 4\n5 1\n",
"4 1 1\n0 0 1 0\n1 3\n",
"3 3 3\n0 0 0\n2 3\n2 1\n3 1\n",
"90 1 49\n0 0 47 0 25 0 0 42 32 39 0 0 47 9 27 11 0 0 29 44 0 11 23 41 23 0 28 0 3 30 0 20 9 19 47 0 3 30 17 48 37 24 0 0 16 0 0 0 0 31 0 24 18 0 20 0 0 0 0 23 0 46 2 0 0 0 6 0 0 0 0 38 0 40 33 0 8 0 0 0 18 39 27 15 0 14 0 0 0 0\n17 80\n",
"5 5 5\n0 0 4 0 0\n3 4\n5 1\n3 4\n5 1\n2 3\n",
"3 5 2\n0 0 0\n1 3\n2 3\n1 3\n2 3\n2 3\n",
"4 2 3\n0 0 0 0\n4 3\n4 1\n",
"2 3 1\n0 0\n2 1\n2 1\n2 1\n",
"3 3 3\n0 1 0\n1 2\n2 3\n3 1\n",
"5 4 1\n0 0 0 0 1\n3 1\n3 1\n3 1\n3 5\n",
"9 6 5\n0 5 0 0 0 4 3 0 4\n6 7\n2 7\n4 8\n7 3\n9 1\n1 8\n",
"4 4 4\n0 0 0 2\n1 3\n1 4\n2 1\n1 3\n",
"5 5 3\n0 0 0 0 0\n1 3\n2 5\n1 3\n4 3\n5 1\n",
"5 5 2\n0 0 0 0 0\n5 3\n2 3\n5 3\n5 2\n4 5\n",
"7 4 7\n5 3 0 2 0 7 4\n6 2\n1 7\n4 5\n4 5\n",
"3 3 2\n0 0 0\n1 2\n2 3\n3 1\n",
"10 11 3\n1 0 0 0 0 0 1 0 2 0\n6 1\n2 10\n7 5\n7 4\n6 4\n8 1\n6 8\n9 10\n7 2\n6 1\n7 10\n",
"10 11 3\n0 1 0 0 0 0 0 0 0 2\n10 3\n7 8\n4 9\n4 3\n7 5\n4 9\n9 8\n4 6\n10 2\n7 9\n7 9\n",
"9 12 6\n1 0 0 0 0 5 0 0 1\n5 6\n2 1\n2 3\n4 2\n4 9\n6 8\n8 3\n7 9\n4 2\n5 9\n4 1\n4 1\n",
"10 15 4\n4 0 4 0 0 0 0 0 0 0\n1 6\n5 8\n8 10\n6 4\n5 9\n2 4\n3 4\n1 5\n6 9\n5 7\n1 5\n1 6\n5 7\n5 7\n6 2\n",
"5 2 5\n1 0 4 0 0\n5 1\n2 5\n",
"5 3 5\n0 4 0 2 0\n2 1\n1 4\n2 5\n",
"5 4 4\n0 1 0 4 0\n5 2\n5 2\n3 1\n4 2\n",
"5 0 2\n0 0 0 2 0\n3 5\n",
"4 1 3\n0 0 0 0\n4 3\n",
"20 31 5\n3 5 0 4 5 0 2 2 0 0 4 5 0 3 4 2 0 1 5 1\n4 16\n2 9\n4 7\n12 20\n5 16\n12 7\n11 1\n5 17\n11 7\n19 18\n2 8\n15 18\n11 10\n1 20\n2 4\n2 16\n4 7\n1 7\n14 7\n1 16\n4 3\n2 15\n6 14\n14 18\n19 20\n2 1\n19 14\n15 8\n12 9\n5 20\n5 11\n",
"20 20 20\n0 0 14 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0\n8 20\n8 3\n8 16\n3 14\n7 2\n19 10\n5 14\n18 20\n8 15\n5 16\n7 10\n13 18\n7 17\n7 17\n7 20\n2 6\n13 18\n16 14\n2 15\n6 11\n",
"10 5 3\n2 3 0 3 1 0 0 3 1 1\n1 10\n8 10\n1 7\n6 7\n8 3\n",
"5 1 5\n0 3 1 0 0\n1 2\n",
"50 10 30\n0 21 0 30 0 25 28 2 16 0 5 0 0 0 0 8 0 0 0 22 18 0 25 1 0 8 0 0 21 0 0 19 0 0 0 4 0 23 3 0 0 1 0 0 0 3 0 20 28 0\n50 33\n21 12\n50 8\n48 13\n49 1\n38 21\n23 39\n49 17\n19 26\n14 41\n",
"70 9 45\n0 44 5 39 3 4 3 2 36 23 0 18 0 37 8 22 34 5 41 13 26 39 7 0 0 11 10 9 15 0 25 28 14 28 5 41 7 24 44 42 0 1 11 18 31 10 20 7 21 19 34 29 10 16 40 43 33 22 35 0 40 37 16 34 0 16 6 27 32 36\n40 43\n41 6\n32 63\n1 12\n20 43\n47 6\n21 26\n58 54\n61 6\n",
"9 12 6\n0 6 0 5 0 0 2 6 0\n7 3\n6 5\n6 9\n2 3\n1 7\n9 7\n8 3\n8 9\n2 7\n4 5\n4 3\n5 3\n",
"4 2 4\n2 0 0 0\n1 4\n3 1\n",
"7 4 3\n0 0 0 0 2 0 0\n1 5\n2 6\n7 5\n3 2\n",
"5 1 3\n2 0 0 3 3\n2 1\n",
"5 2 4\n2 3 4 0 1\n3 2\n2 1\n",
"6 4 2\n1 0 0 0 0 0\n6 1\n3 2\n6 2\n4 2\n",
"6 3 4\n0 2 0 0 0 0\n3 4\n3 6\n3 2\n",
"20 7 2\n1 2 0 1 1 1 2 0 1 2 2 2 0 1 2 2 0 0 2 0\n12 5\n7 1\n11 6\n10 3\n12 14\n19 20\n16 9\n",
"5 1 4\n0 0 0 0 1\n4 2\n",
"9 7 3\n3 1 0 0 0 1 0 2 0\n8 6\n3 2\n9 3\n7 2\n3 4\n9 4\n1 4\n",
"10 10 5\n0 1 2 5 4 0 0 0 0 0\n5 9\n8 10\n4 1\n5 3\n4 8\n6 2\n8 3\n8 3\n7 2\n4 9\n",
"7 6 5\n4 3 0 0 0 0 4\n3 6\n2 5\n7 6\n3 4\n3 6\n6 5\n",
"4 2 2\n0 0 0 0\n1 3\n2 3\n",
"3 5 3\n0 0 0\n3 1\n1 2\n1 2\n3 2\n3 1\n",
"40 21 3\n0 0 0 3 0 1 2 1 0 3 2 3 0 0 1 0 2 1 2 0 0 3 0 0 0 0 1 2 0 3 0 2 3 0 0 1 3 0 2 0\n5 36\n4 9\n32 6\n5 3\n32 14\n11 9\n33 15\n21 18\n32 18\n39 6\n13 18\n4 2\n29 27\n25 18\n19 27\n31 40\n33 2\n17 15\n12 26\n38 8\n31 27\n",
"6 1 4\n0 0 0 0 0 0\n4 3\n6 3\n5 4\n",
"7 4 7\n3 0 1 0 2 3 4\n1 4\n6 5\n5 4\n7 2\n",
"9 8 3\n0 0 3 3 0 0 1 3 0\n6 7\n3 1\n6 7\n4 9\n8 7\n2 9\n1 2\n4 5\n",
"3 4 2\n0 1 0\n2 3\n2 3\n1 3\n2 3\n",
"9 7 4\n4 0 0 0 1 0 1 4 1\n3 4\n2 5\n9 5\n2 7\n1 6\n1 5\n2 9\n",
"10 14 4\n0 0 0 0 0 1 0 2 1 0\n4 9\n10 3\n4 1\n8 2\n9 8\n8 3\n8 7\n8 7\n4 7\n10 1\n5 9\n10 9\n5 8\n10 7\n",
"7 6 1\n5 2 0 0 4 1 0\n1 4\n3 4\n1 6\n5 6\n5 6\n7 4\n",
"10 8 2\n0 0 0 0 1 0 0 0 0 0\n4 10\n6 8\n3 8\n4 7\n4 10\n1 10\n6 8\n5 10\n",
"2 3 2\n0 1\n2 2\n2 1\n2 1\n",
"10 10 3\n0 3 0 3 1 0 0 3 0 0\n9 7\n5 9\n9 3\n4 1\n10 3\n2 10\n8 7\n8 3\n4 7\n8 7\n",
"3 4 1\n0 0 1\n3 1\n3 2\n1 2\n3 2\n",
"4 4 1\n0 0 0 0\n2 3\n2 3\n2 3\n3 4\n",
"2 1 1\n0 1\n2 1\n",
"90 32 45\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 31 0 0 0 0 0 0 0 1 0 23 34 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 14 0 0 0 0 0 32 0 0 0 0 0 0 0 0 0 42 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 37 41\n48 74\n49 19\n32 87\n31 65\n60 50\n12 40\n39 87\n90 36\n79 40\n38 1\n52 50\n29 85\n76 41\n25 35\n72 4\n32 59\n73 79\n15 54\n13 37\n16 68\n78 19\n29 62\n52 41\n43 7\n58 17\n8 16\n81 72\n89 10\n89 84\n73 1\n15 22\n2 66\n",
"4 5 2\n0 0 0 0\n3 4\n4 1\n2 3\n3 1\n3 4\n"
],
"outputs": [
"-1\n",
"3 3 3 1 2 ",
"2 4 5 4 1 3 5\n",
"2 1 3 6 6 4 5 6\n",
"1 2 3 2 2 3 3 2 2 1\n",
"4 5 1 3 5 2 2 ",
"1 1 2 3 4 3 2 4 4 3 4 4 4 4 1 3 4 4 4 3 4 4 2 3 4 2 3 3 3 4 3 2 2 1 1 4 4 4 3 4\n",
"1 4 4 4 2 3\n",
"-1\n",
"3 1 2 3 2 2 3 1 2 2\n",
"1 4 2 6 6 5 6 3 1\n",
"11 11 11 11 11 11 11 3 4 11 5 6 11 11 11 11 11 11 11 11 11 11 7 8 11 11 1 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 9 11 11 10 11 10 11 11 10 11 11 11 11 11 11 11 11 11 11 11 10 11 11 2 10 11 11 11 11 11 11 10 11 11 10 11 11 10 11 10 11 10 11 11 11 11 11 11 11 11 10 11\n",
"4 2 4 1 3 3 2 4 2 3\n",
"3 3 1 1 2 3 4 ",
"3 1 2\n",
"1 3 2 3\n",
"-1\n",
"16 40 50 15 20 54 35 19 12 11 22 48 23 32 21 33 34 25 30 24 14 28 3 9 13 36 26 19 1 38 37 39 41 7 42 44 47 46 49 18 52 51 10 4 2 53 54 17 8 27 29 6 43 31 5 54 54 54 45 54\n",
"2 1\n",
"1 2 4 1 1 1 3 5 2\n",
"1 5 4 2 3\n",
"3 4 5 1 2\n",
"1 2 3 4 4 ",
"-1\n",
"2 2 2 2 1\n",
"2 1 3 3\n",
"2 1 3 3 2 3 1 3 1 ",
"4 1 2 4 3\n",
"3 5 5 4 5 5 2 2 4 3 4 5 5 3 4 2 4 1 5 1\n",
"1 15 14 2 19 10 17 20 3 4 5 6 16 13 7 18 8 11 12 9\n",
"1 1 2 2 2 2 ",
"-1\n",
"2 5 4 3 1 2 5\n",
"2 3 2 3 1 3 1 3 1 1 ",
"5 2 6 6 3 4 1 5 5 ",
"-1\n",
"4 4 4 2 1 3 1 4 3\n",
"5 3 1 2 4\n",
"1\n",
"3 1 1 4 4 1 1 2 3 4 ",
"-1\n",
"-1\n",
"5 2 5 3 4 1 5\n",
"-1\n",
"4 3 1 4 2 4 ",
"1 2\n",
"-1\n",
"1 3 4 2 5\n",
"3 2 1 3 3\n",
"1 2 3 3 3 2 1 1 2 2\n",
"9 21 13 30 14 25 28 2 16 15 5 6 7 17 24 8 10 26 27 22 18 29 25 30 30 8 30 30 21 30 30 19 11 30 30 4 30 23 3 30 12 1 30 30 30 3 30 20 28 30\n",
"2 3 1 4 4 4\n",
"30 44 5 39 3 4 3 2 36 23 12 18 17 37 8 22 34 5 41 13 26 39 7 38 45 11 10 9 15 45 25 28 14 28 5 41 7 24 44 42 45 1 11 18 31 10 20 7 21 19 27 29 10 16 40 43 33 22 35 45 40 37 16 34 45 16 6 27 32 36\n",
"8 17 4 37 18 9 20 21 59 56 43 26 11 65 22 38 42 46 23 32 24 25 69 27 28 12 51 58 29 44 41 30 36 31 39 33 10 13 34 35 45 70 47 48 49 50 52 40 3 53 54 1 55 57 60 61 14 62 5 67 6 19 15 63 64 66 2 7 16 68\n",
"6 6 1 5 3 6 2 6 4\n",
"-1\n",
"-1\n",
"2 2 2 2 2 2 1 1 2 1\n",
"-1\n",
"2 3 4 1\n",
"3 2 3 3 2 1 3\n",
"2 3 1 3 3 3 1 3 2 2 ",
"2 2 3 3 2 1 3 2 3 3\n",
"1 2 2 ",
"-1\n",
"-1\n",
"-1\n",
"1 2\n",
"3 4 2 5 1\n",
"-1\n",
"2 2 3 3 3 1 3 ",
"-1\n",
"8 27 28 5 29 30 9 33 35 1 36 38 39 40 43 11 12 44 13 45 45 10 45 31 45 45 45 45 45 45 45 45 45 23 34 4 15 45 45 6 16 45 45 45 45 45 45 45 45 3 45 45 45 14 45 45 45 45 17 32 45 18 45 45 19 20 45 7 45 42 45 21 45 22 45 45 45 45 24 45 45 45 45 2 25 45 26 45 37 41\n",
"-1\n",
"-1\n",
"-1\n",
"1 1 2 2 2 2 ",
"1 2 2 2 1\n",
"4 2 4 3 4 1\n",
"2 1 2 2\n",
"1 2 2 1 2 1 1 2 2 2 2 1 1 2 2 2 2 2 2 1 2 1 1 1 1 2 1 2 2 1\n",
"1 2 1 1 1 1 2 2 1 2 2 2 2 1 2 2 2 2 2 2\n",
"-1\n",
"2 1 3 4 4\n",
"6 3 4 7 1 5 2\n",
"3 1 3 3 2\n",
"-1\n",
"3 1 2 1 3 1 3 2 3\n",
"4 1 2 5 4 2 5 4 3 3\n",
"6 9 10 11 13 12 24 14 4 24 20 15 16 18 19 2 7 1 21 22 23 25 26 26 26 8 26 3 26 5 17\n",
"4 3 5 4 1 2 4 ",
"2 2 1 2\n",
"2 1 3\n",
"-1\n",
"3 2 2 3 3 1 2 1 1 3 2 3 3 1 1 3 2 1 2 3 3 3 3 3 3 2 1 2 3 3 3 2 3 3 3 1 3 3 2 2\n",
"3 4 1 2 4 4\n",
"3 1 2 3 3 ",
"5 4 5 1 3 6 2 6 4\n",
"1\n",
"2 2 1\n",
"6 1 2 3 4 6 4 6 2 5\n",
"2 3 4 1 5\n",
"-1\n",
"1 2 2 1 2 ",
"-1\n",
"-1\n",
"-1\n",
"3 2 3 3 3 2 3 2 1 ",
"2 2 1 2 4 3 3 4 3 1 ",
"3 1 2 2 2 3 1 3 1 3\n",
"3 3 3 2 3 1 2 ",
"3 4 5 5 2 1 5 ",
"2 2 1 1\n",
"2 4 3 3 2 4 2 3 1 ",
"2 3 2 3 1 3 2 ",
"3 1 2 2\n",
"2 3 1 2 ",
"2 3 3 3 1 1 1 2 2 3 ",
"2 2 1 2\n",
"-1\n",
"-1\n",
"1 2 4 4 3\n",
"-1\n",
"-1\n",
"-1\n",
"4 1 2 3\n",
"4 1 4 4 2 3\n",
"2 2 4 1 3 4 4 3 4 3 ",
"-1\n",
"2 1 3\n",
"-1\n",
"2 7 8 9 10 2 10 6 2 1 8 4 6 7 1 10 6 8 2 9 3 9 2 9 10 5 10 10 4 1\n",
"2 1\n",
"1 13 12 11 13 13 2 13 10 13 13 6 13 13 6 13 13 2 13 13 13 8 10 9 13 9 11 13 3 3 13 13 13 4 12 13 12 12 13 4 13 5 5 13 10 4 5 9 13 13 13 13 13 13 13 11 3 12 13 11 13 7 1 2 1 13 12 13 5 8 2 13 8 11 6 6 9 11 9 12\n",
"-1\n",
"-1\n",
"-1\n",
"3 4 1 2 5\n",
"-1\n",
"-1\n",
"6 2 7 4 5 3 1 4\n",
"2 2 1 1 2 1\n",
"-1\n",
"-1\n",
"2 1 1 2 1 2\n",
"2 3 5 2 1 4 2 6 4 ",
"1 1 5 1 2 4 3\n",
"-1\n",
"1 3 2\n",
"4 5 47 7 25 10 12 42 32 39 13 21 47 9 27 11 22 26 29 44 34 11 23 41 23 35 28 36 3 30 43 20 9 19 47 45 3 30 17 48 37 24 49 49 16 49 49 49 49 31 49 24 18 49 20 49 49 49 49 23 49 46 2 49 49 49 6 49 49 49 49 38 49 40 33 49 8 49 49 1 18 39 27 15 49 14 49 49 49 49\n",
"2 5 4 1 3 ",
"2 2 1\n",
"1 3 2 3 ",
"-1\n",
"-1\n",
"-1\n",
"3 5 1 5 5 4 3 2 4\n",
"3 4 1 2\n",
"-1\n",
"-1\n",
"5 3 6 2 1 7 4\n",
"-1\n",
"-1\n",
"3 1 1 3 2 2 3 1 2 2 \n",
"1 4 2 6 6 5 6 3 1 \n",
"4 2 4 1 3 3 2 2 2 1 \n",
"1 3 4 5 2 \n",
"3 4 5 2 1 \n",
"2 1 3 4 4 \n",
"1 2 2 2 2 \n",
"2 3 1 3 \n",
"3 5 3 4 5 5 2 2 4 3 4 5 5 3 4 2 4 1 5 1 \n",
"9 5 14 10 16 2 11 17 12 6 1 18 19 13 3 15 7 8 20 4 \n",
"2 3 2 3 1 3 1 3 1 1 \n",
"4 3 1 2 5 \n",
"9 21 13 30 14 25 28 2 16 15 5 6 7 17 24 8 10 26 27 22 18 29 25 1 30 8 30 30 21 30 30 19 11 30 30 4 30 23 3 30 12 1 30 30 30 3 30 20 28 30 \n",
"30 44 5 39 3 4 3 2 36 23 12 18 17 37 8 22 34 5 41 13 26 39 7 38 45 11 10 9 15 45 25 28 14 28 5 41 7 24 44 42 45 1 11 18 31 10 20 7 21 19 34 29 10 16 40 43 33 22 35 45 40 37 16 34 45 16 6 27 32 36 \n",
"6 6 1 5 3 6 2 6 4 \n",
"2 3 4 1 \n",
"3 2 3 3 2 1 3 \n",
"2 3 1 3 3 \n",
"2 3 4 4 1 \n",
"1 1 2 2 2 2 \n",
"4 2 4 1 4 3 \n",
"1 2 1 1 1 1 2 2 1 2 2 2 2 1 2 2 2 2 2 1 \n",
"3 2 4 4 1 \n",
"3 1 2 1 3 1 3 2 3 \n",
"4 1 2 5 4 5 5 4 3 3 \n",
"4 3 5 4 1 2 4 \n",
"2 2 1 2 \n",
"2 1 3 \n",
"3 2 2 3 3 1 2 1 1 3 2 3 3 1 1 3 2 1 2 3 3 3 3 3 3 2 1 2 3 3 3 2 3 3 3 1 3 3 2 2 \n",
"2 3 1 4 4 4 \n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n"
]
}
|
There are n military men in the Berland army. Some of them have given orders to other military men by now. Given m pairs (xi, yi), meaning that the military man xi gave the i-th order to another military man yi.
It is time for reform! The Berland Ministry of Defence plans to introduce ranks in the Berland army. Each military man should be assigned a rank — integer number between 1 and k, inclusive. Some of them have been already assigned a rank, but the rest of them should get a rank soon.
Help the ministry to assign ranks to the rest of the army so that:
* for each of m orders it is true that the rank of a person giving the order (military man xi) is strictly greater than the rank of a person receiving the order (military man yi);
* for each rank from 1 to k there is at least one military man with this rank.
Input
The first line contains three integers n, m and k (1 ≤ n ≤ 2·105, 0 ≤ m ≤ 2·105, 1 ≤ k ≤ 2·105) — number of military men in the Berland army, number of orders and number of ranks.
The second line contains n integers r1, r2, ..., rn, where ri > 0 (in this case 1 ≤ ri ≤ k) means that the i-th military man has been already assigned the rank ri; ri = 0 means the i-th military man doesn't have a rank yet.
The following m lines contain orders one per line. Each order is described with a line containing two integers xi, yi (1 ≤ xi, yi ≤ n, xi ≠ yi). This line means that the i-th order was given by the military man xi to the military man yi. For each pair (x, y) of military men there could be several orders from x to y.
Output
Print n integers, where the i-th number is the rank of the i-th military man. If there are many solutions, print any of them.
If there is no solution, print the only number -1.
Examples
Input
5 3 3
0 3 0 0 2
2 4
3 4
3 5
Output
1 3 3 2 2
Input
7 6 5
0 4 5 4 1 0 0
6 1
3 6
3 1
7 5
7 1
7 4
Output
2 4 5 4 1 3 5
Input
2 2 2
2 1
1 2
2 1
Output
-1
|
{
"inputs": [
"6\n3 2 2 2\n0 0 -2 -2 2 2\n3 1 4 1\n0 0 -1 -1 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n0 0 -100 -100 100 0\n",
"1\n83 75 18 67\n-4233924 24412104 -4233956 24412104 -4233832 24412181\n",
"1\n0 0 1 1\n0 0 0 0 0 0\n",
"1\n83 128 18 67\n-4233924 24412104 -4233956 24412104 -4233832 24412181\n",
"1\n0 0 1 1\n1 0 0 0 0 0\n",
"6\n3 2 2 2\n0 0 -2 -2 2 2\n3 1 4 1\n0 0 -1 -1 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n0 0 -66 -100 100 0\n",
"6\n3 2 2 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n-1 0 -66 -100 100 0\n",
"6\n3 2 7 4\n0 1 -2 -1 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 2 1\n1 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n87 128 18 67\n-4233924 24412104 -4233956 24412104 -4233832 24412181\n",
"6\n3 2 2 2\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -1 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n0 0 -66 -100 100 0\n",
"1\n5 128 18 67\n-4233924 24412104 -4233956 24412104 -4233832 24412181\n",
"6\n3 2 2 2\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -1 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n-1 0 -66 -100 100 0\n",
"1\n5 128 18 131\n-4233924 24412104 -4233956 24412104 -4233832 24412181\n",
"6\n3 2 2 2\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n-1 0 -66 -100 100 0\n",
"1\n5 128 18 131\n-4233924 39542966 -4233956 24412104 -4233832 24412181\n",
"1\n5 128 18 131\n-4233924 39542966 -4233956 42559121 -4233832 24412181\n",
"6\n3 2 2 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 100\n1 1 5 1\n-1 0 -66 -100 100 0\n",
"1\n5 128 34 131\n-4233924 39542966 -4233956 42559121 -4233832 24412181\n",
"6\n3 2 2 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 100\n1 1 5 1\n-1 0 -97 -100 100 0\n",
"1\n5 128 34 131\n-4233924 69071404 -4233956 42559121 -4233832 24412181\n",
"6\n3 2 2 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 100\n1 1 5 2\n-1 0 -97 -100 100 0\n",
"1\n5 128 34 131\n-4233924 69071404 -552080 42559121 -4233832 24412181\n",
"6\n3 2 2 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n1 1 5 2\n-1 0 -97 -100 100 0\n",
"1\n5 128 34 131\n-4233924 69071404 -552080 63255464 -4233832 24412181\n",
"6\n3 2 4 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n1 1 5 2\n-1 0 -97 -100 100 0\n",
"1\n5 128 34 131\n-4233924 69071404 -552080 63255464 -4109418 24412181\n",
"6\n3 2 4 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 2\n-1 0 -97 -100 100 0\n",
"1\n5 128 34 131\n-4233924 69071404 -552080 63255464 -6192915 24412181\n",
"6\n3 2 7 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 2\n-1 0 -97 -100 100 0\n",
"1\n5 128 34 131\n-4233924 69071404 -552080 63255464 -7182707 24412181\n",
"6\n3 2 7 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 2\n-1 0 -97 -100 100 0\n",
"1\n5 128 34 131\n-4233924 69071404 -552080 44737010 -7182707 24412181\n",
"6\n3 2 7 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 2\n-1 0 -172 -100 100 0\n",
"1\n2 128 34 131\n-4233924 69071404 -552080 44737010 -7182707 24412181\n",
"6\n3 2 7 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-1 0 -172 -100 100 0\n",
"1\n3 128 34 131\n-4233924 69071404 -552080 44737010 -7182707 24412181\n",
"6\n3 2 7 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 2 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-1 0 -172 -100 100 0\n",
"1\n3 128 34 131\n-4233924 69071404 -552080 55258674 -7182707 24412181\n",
"6\n3 2 7 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 2 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n3 128 34 131\n-4233924 103656085 -552080 55258674 -7182707 24412181\n",
"6\n3 2 7 4\n0 1 -2 -1 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 2 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n1 128 34 131\n-4233924 103656085 -552080 55258674 -7182707 24412181\n",
"1\n1 128 34 131\n-4233924 103656085 -552080 79206947 -7182707 24412181\n",
"6\n3 2 7 4\n-1 1 -2 -1 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 2 1\n1 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n1 128 34 131\n-4233924 103656085 -552080 79206947 -4610608 24412181\n",
"6\n3 2 7 4\n-1 1 -2 -1 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 2\n1 1 1 1 3 1\n1 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n1 128 34 131\n-4536302 103656085 -552080 79206947 -4610608 24412181\n",
"6\n3 2 7 4\n-1 1 -2 -1 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 0\n1 1 1 1 3 1\n1 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n1 128 34 131\n-4536302 147396280 -552080 79206947 -4610608 24412181\n",
"6\n3 2 7 4\n-1 1 -2 -1 2 2\n3 1 4 1\n1 0 -1 -2 1 1\n1 1 1 0\n1 1 1 1 3 1\n1 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n2 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n1 128 5 131\n-4536302 147396280 -552080 79206947 -4610608 24412181\n",
"6\n3 2 7 4\n-1 1 -2 -1 2 2\n3 1 4 1\n1 0 -1 -2 1 1\n1 1 1 0\n1 1 1 1 3 1\n1 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 110\n4 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n1 128 5 131\n-4536302 147396280 -552080 79206947 -4610608 20357158\n",
"6\n3 2 7 4\n-1 1 -2 -1 2 2\n3 1 4 1\n1 0 -1 -2 1 1\n1 1 1 0\n1 1 1 1 3 1\n1 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -52 0 110\n4 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n1 128 0 131\n-4536302 147396280 -552080 79206947 -4610608 20357158\n",
"6\n3 2 7 4\n-1 1 -2 -1 2 2\n3 1 4 1\n1 0 -1 -2 1 1\n1 1 1 0\n1 1 1 1 3 1\n1 0 0 1\n0 0 0 0 0 1\n5 1 0 1\n0 0 -100 -52 0 110\n4 1 5 4\n-2 0 -172 -100 100 0\n",
"1\n1 128 0 131\n-4536302 147396280 -581116 79206947 -4610608 20357158\n",
"1\n0 128 0 131\n-4536302 147396280 -581116 79206947 -4610608 20357158\n",
"1\n0 88 0 131\n-4536302 147396280 -581116 79206947 -4610608 20357158\n",
"1\n0 88 0 131\n-4536302 147396280 -581116 79206947 -954914 20357158\n",
"1\n0 88 0 131\n-4536302 147396280 -581116 79206947 -954914 32316221\n",
"1\n0 88 0 131\n-4536302 147396280 -581116 79206947 -954914 39870902\n",
"1\n0 88 0 131\n-4536302 147396280 -581116 79206947 -954914 37057045\n",
"1\n0 88 0 131\n-4536302 147396280 -581116 79206947 -1609565 37057045\n",
"1\n-1 88 0 131\n-4536302 147396280 -581116 79206947 -1609565 37057045\n",
"1\n-1 88 0 131\n-4536302 147396280 -581116 103236045 -1609565 37057045\n",
"1\n-1 88 0 131\n-4536302 147396280 -581116 128895138 -1609565 37057045\n",
"1\n-1 57 0 131\n-4536302 147396280 -581116 128895138 -1609565 37057045\n",
"1\n-1 57 0 131\n-4536302 147396280 -581116 128895138 -1609565 21536739\n",
"1\n-1 57 0 131\n-4536302 147396280 -581116 138541326 -1609565 21536739\n",
"1\n-1 57 0 131\n-4536302 147396280 -581116 138541326 -1609565 12431293\n",
"1\n-1 57 0 131\n-4536302 147396280 -581116 138541326 -1609565 7448188\n",
"1\n-1 50 0 131\n-4536302 147396280 -581116 138541326 -1609565 7448188\n",
"1\n-1 50 0 131\n-4536302 147396280 -602836 138541326 -1609565 7448188\n",
"1\n-1 50 -1 131\n-4536302 147396280 -602836 138541326 -1609565 7448188\n",
"1\n-1 50 -1 131\n-4536302 32112397 -602836 138541326 -1609565 7448188\n",
"1\n-1 50 -1 131\n-4536302 32112397 -602836 138541326 -2855615 7448188\n",
"1\n-1 50 -1 131\n-4536302 32112397 -602836 199477368 -2855615 7448188\n",
"1\n-1 50 -1 131\n-4536302 32112397 -602836 199477368 -2855615 5325938\n",
"1\n-1 50 -1 131\n-4536302 32112397 -8238 199477368 -2855615 5325938\n",
"1\n-1 50 0 131\n-4536302 32112397 -8238 199477368 -2855615 5325938\n",
"1\n-1 50 0 131\n-4536302 32112397 -8238 199477368 -3482527 5325938\n",
"1\n83 100 18 67\n-4233924 24412104 -4233956 24412104 -4233832 24412181\n",
"1\n1 0 1 1\n0 0 0 0 0 0\n",
"6\n3 2 2 2\n0 0 -2 -2 2 2\n3 1 4 1\n1 0 -1 -1 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n0 0 -100 -100 100 0\n",
"1\n0 0 1 1\n2 0 0 0 0 0\n",
"6\n3 2 2 2\n0 0 -2 -2 2 2\n3 1 4 1\n0 0 -1 -1 0 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n0 0 -66 -100 100 0\n",
"1\n87 128 18 67\n-1549130 24412104 -4233956 24412104 -4233832 24412181\n",
"1\n5 128 18 67\n-4233924 24412104 -6762569 24412104 -4233832 24412181\n",
"6\n3 2 2 2\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -1 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 100\n1 1 6 1\n-1 0 -66 -100 100 0\n",
"1\n5 128 18 131\n-4233924 24412104 -4233956 24412104 -4233832 7832509\n",
"6\n3 2 2 2\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -100 0 000\n1 1 5 1\n-1 0 -66 -100 100 0\n",
"1\n5 128 18 131\n-4233924 39542966 -4233956 2708793 -4233832 24412181\n",
"6\n3 2 2 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n4 1 1 1\n0 0 -100 -100 0 100\n1 1 5 1\n-1 0 -66 -100 100 0\n",
"1\n5 128 18 131\n-8147611 39542966 -4233956 42559121 -4233832 24412181\n",
"6\n3 2 2 4\n0 1 -2 -2 2 2\n3 1 4 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 1 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 100\n1 1 5 1\n-1 0 -66 -100 100 0\n",
"1\n5 128 60 131\n-4233924 39542966 -4233956 42559121 -4233832 24412181\n",
"1\n5 128 34 131\n-4233924 86421988 -4233956 42559121 -4233832 24412181\n",
"6\n3 2 2 4\n0 1 -2 -2 2 2\n3 1 5 1\n0 0 -1 -2 1 1\n1 1 1 1\n1 1 1 1 1 1\n0 0 0 1\n0 0 0 0 0 1\n5 1 1 1\n0 0 -100 -51 0 100\n1 1 5 2\n-1 0 -97 -100 100 0\n",
"1\n5 128 34 131\n-4233924 69071404 -552080 42559121 -549283 24412181\n"
],
"outputs": [
"Yes\nNo\nNo\nYes\nYes\nYes\n",
"Yes\n",
"No\n",
"YES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\nNO\nNO\nYES\nYES\nYES\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"YES\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"YES\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nYES\nYES\nYES\n",
"NO\n",
"NO\nNO\nNO\nNO\nYES\nYES\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\nYES\nYES\nYES\n",
"NO\n"
]
}
|
Alice has a cute cat. To keep her cat fit, Alice wants to design an exercising walk for her cat!
Initially, Alice's cat is located in a cell (x,y) of an infinite grid. According to Alice's theory, cat needs to move:
* exactly a steps left: from (u,v) to (u-1,v);
* exactly b steps right: from (u,v) to (u+1,v);
* exactly c steps down: from (u,v) to (u,v-1);
* exactly d steps up: from (u,v) to (u,v+1).
Note that the moves can be performed in an arbitrary order. For example, if the cat has to move 1 step left, 3 steps right and 2 steps down, then the walk right, down, left, right, right, down is valid.
Alice, however, is worrying that her cat might get lost if it moves far away from her. So she hopes that her cat is always in the area [x_1,x_2]× [y_1,y_2], i.e. for every cat's position (u,v) of a walk x_1 ≤ u ≤ x_2 and y_1 ≤ v ≤ y_2 holds.
Also, note that the cat can visit the same cell multiple times.
Can you help Alice find out if there exists a walk satisfying her wishes?
Formally, the walk should contain exactly a+b+c+d unit moves (a to the left, b to the right, c to the down, d to the up). Alice can do the moves in any order. Her current position (u, v) should always satisfy the constraints: x_1 ≤ u ≤ x_2, y_1 ≤ v ≤ y_2. The staring point is (x, y).
You are required to answer t test cases independently.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^3) — the number of testcases.
The first line of each test case contains four integers a, b, c, d (0 ≤ a,b,c,d ≤ 10^8, a+b+c+d ≥ 1).
The second line of the test case contains six integers x, y, x_1, y_1, x_2, y_2 (-10^8 ≤ x_1≤ x ≤ x_2 ≤ 10^8, -10^8 ≤ y_1 ≤ y ≤ y_2 ≤ 10^8).
Output
For each test case, output "YES" in a separate line, if there exists a walk satisfying her wishes. Otherwise, output "NO" in a separate line.
You can print each letter in any case (upper or lower).
Example
Input
6
3 2 2 2
0 0 -2 -2 2 2
3 1 4 1
0 0 -1 -1 1 1
1 1 1 1
1 1 1 1 1 1
0 0 0 1
0 0 0 0 0 1
5 1 1 1
0 0 -100 -100 0 100
1 1 5 1
0 0 -100 -100 100 0
Output
Yes
No
No
Yes
Yes
Yes
Note
In the first test case, one valid exercising walk is $$$(0,0)→ (-1,0) → (-2,0)→ (-2,1) → (-2,2)→ (-1,2)→(0,2)→ (0,1)→ (0,0) → (-1,0)$$$
|
{
"inputs": [
"4 3 3\n1 1 2 3",
"4 1 4\n3 3 2 2",
"6 2 2\n0 2 2 2 2 0",
"8 7 15\n5 0 9 14 0 4 4 15",
"8 10 18\n2 12 16 14 18 4 17 16",
"4 1 4\n3 2 2 2",
"6 2 2\n1 2 2 2 2 0",
"8 7 15\n5 0 9 14 0 4 0 15",
"8 10 18\n2 12 16 14 18 4 17 10",
"2 1 4\n3 2 2 2",
"8 7 15\n5 0 1 14 0 4 0 15",
"8 10 18\n2 12 16 14 18 6 17 10",
"8 7 15\n5 -1 1 14 0 4 0 15",
"8 10 18\n2 12 5 14 18 6 17 10",
"8 10 18\n2 12 5 14 18 8 17 10",
"8 10 18\n2 12 5 14 18 8 17 0",
"4 3 4\n1 1 2 3",
"6 2 2\n0 2 2 2 0 0",
"8 3 18\n2 12 16 14 18 4 17 16",
"4 1 8\n3 2 2 2",
"6 4 2\n1 2 2 2 2 0",
"8 10 18\n2 12 16 14 18 4 17 11",
"2 1 7\n3 2 2 1",
"8 10 23\n2 12 5 14 18 6 17 10",
"8 19 18\n2 12 5 14 18 8 17 10",
"4 0 4\n1 1 2 3",
"6 1 2\n0 2 2 2 0 0",
"8 7 16\n5 0 5 14 0 4 4 15",
"8 3 18\n2 12 16 14 18 4 17 4",
"6 4 3\n1 2 2 2 2 0",
"8 7 19\n5 0 1 14 0 4 1 15",
"8 10 18\n2 12 18 14 18 4 17 11",
"8 10 23\n2 12 5 14 29 6 17 10",
"8 7 16\n5 0 0 14 0 4 4 15",
"8 3 18\n2 12 16 14 18 4 17 0",
"6 4 3\n1 0 2 2 2 0",
"8 10 18\n2 12 12 14 18 4 17 11",
"8 7 16\n5 -1 1 14 0 4 -1 15",
"8 10 23\n3 12 5 14 29 6 17 10",
"8 3 18\n2 12 16 14 18 4 7 0",
"6 4 3\n1 -1 2 2 2 0",
"8 10 23\n3 12 2 14 29 6 17 10",
"8 5 18\n2 12 16 14 18 4 7 0",
"8 10 18\n2 12 12 4 18 7 17 11",
"8 7 27\n5 -1 1 14 0 8 -1 15",
"8 10 18\n2 12 12 4 18 7 4 11",
"8 10 18\n2 12 12 3 18 7 4 11",
"8 20 18\n2 12 12 3 18 7 4 11",
"2 -1 12\n3 4 2 2",
"8 20 18\n2 12 12 3 18 7 4 8",
"8 20 18\n1 12 12 3 18 7 4 8",
"8 20 22\n1 12 12 3 18 7 4 8",
"8 20 22\n2 12 12 3 18 7 4 8",
"2 -1 22\n1 4 4 2",
"8 20 22\n2 12 12 3 18 7 4 4",
"2 -1 22\n2 4 4 2",
"4 -1 22\n2 4 4 2",
"8 32 22\n2 12 12 3 18 4 4 4",
"4 -1 22\n3 4 4 2",
"8 32 22\n2 12 12 3 17 4 4 4",
"4 -1 22\n6 4 4 2",
"8 17 22\n2 12 12 3 17 4 4 4",
"4 -1 22\n6 5 4 2",
"8 17 22\n2 12 12 3 17 3 4 4",
"4 -1 22\n6 8 4 2",
"4 -1 22\n4 8 4 2",
"8 7 15\n5 0 9 7 0 4 4 15",
"8 10 17\n2 12 16 14 18 4 17 16",
"6 2 2\n1 1 2 2 2 0",
"8 7 15\n5 0 9 14 -1 4 0 15",
"8 10 18\n2 12 5 14 18 6 17 14",
"8 10 18\n2 12 6 14 18 8 17 0",
"8 3 18\n0 12 16 14 18 4 17 16",
"4 1 8\n3 2 2 3",
"8 8 16\n5 0 1 14 0 4 0 15",
"8 10 23\n2 12 0 14 18 6 17 10",
"8 19 18\n2 12 9 14 18 8 17 10",
"8 3 18\n2 12 20 14 18 4 17 4",
"6 7 3\n1 2 2 2 2 0",
"8 8 23\n2 12 5 14 29 6 17 10",
"8 3 18\n4 12 16 14 18 4 17 0",
"4 10 23\n3 12 5 14 29 6 17 10",
"8 5 18\n2 12 16 14 15 4 7 0",
"8 12 18\n2 12 12 4 18 7 17 11",
"8 7 27\n5 -1 1 14 1 8 -1 15",
"8 10 18\n0 12 12 3 18 7 4 11",
"8 20 14\n1 12 12 3 18 7 4 8",
"2 -1 13\n0 4 4 2",
"8 20 22\n0 12 12 3 18 7 4 8",
"8 18 22\n2 12 12 3 18 7 4 8",
"2 -2 22\n1 4 4 2",
"4 -1 22\n2 4 4 4",
"8 32 22\n2 12 12 3 18 4 4 1",
"8 32 22\n2 12 21 3 17 4 4 4",
"8 17 22\n2 12 12 3 17 4 1 4",
"4 -1 22\n6 5 4 0",
"8 17 22\n1 12 12 3 17 3 4 4",
"4 -1 22\n11 8 4 2",
"8 4 15\n5 0 9 7 0 4 4 15",
"8 7 15\n5 0 9 14 -1 1 0 15",
"8 10 18\n2 11 5 14 18 6 17 14",
"8 3 18\n0 12 16 10 18 4 17 16",
"8 9 19\n5 0 1 14 0 4 -1 15",
"8 19 18\n2 12 9 19 18 8 17 10",
"8 8 16\n5 -1 1 12 0 4 0 15"
],
"outputs": [
"9",
"6",
"8",
"189",
"370",
"7\n",
"6\n",
"217\n",
"430\n",
"3\n",
"273\n",
"410\n",
"266\n",
"520\n",
"500\n",
"580\n",
"15\n",
"4\n",
"111\n",
"9\n",
"12\n",
"420\n",
"5\n",
"740\n",
"950\n",
"0\n",
"2\n",
"245\n",
"147\n",
"28\n",
"280\n",
"400\n",
"630\n",
"252\n",
"153\n",
"20\n",
"460\n",
"259\n",
"640\n",
"123\n",
"16\n",
"610\n",
"205\n",
"490\n",
"287\n",
"560\n",
"550\n",
"1100\n",
"-7\n",
"1040\n",
"1020\n",
"1180\n",
"1200\n",
"-5\n",
"1120\n",
"-6\n",
"-12\n",
"1888\n",
"-13\n",
"1856\n",
"-16\n",
"986\n",
"-17\n",
"969\n",
"-20\n",
"-18\n",
"238\n",
"310\n",
"8\n",
"210\n",
"480\n",
"570\n",
"105\n",
"10\n",
"312\n",
"690\n",
"874\n",
"135\n",
"49\n",
"504\n",
"159\n",
"340\n",
"220\n",
"588\n",
"294\n",
"530\n",
"820\n",
"-4\n",
"1160\n",
"1080\n",
"-10\n",
"-14\n",
"1792\n",
"2016\n",
"935\n",
"-15\n",
"952\n",
"-25\n",
"136\n",
"189\n",
"470\n",
"117\n",
"342\n",
"779\n",
"288\n"
]
}
|
In the building of Jewelry Art Gallery (JAG), there is a long corridor in the east-west direction. There is a window on the north side of the corridor, and $N$ windowpanes are attached to this window. The width of each windowpane is $W$, and the height is $H$. The $i$-th windowpane from the west covers the horizontal range between $W\times(i-1)$ and $W\times i$ from the west edge of the window.
<image>
Figure A1. Illustration of the window
You received instructions from the manager of JAG about how to slide the windowpanes. These instructions consist of $N$ integers $x_1, x_2, ..., x_N$, and $x_i \leq W$ is satisfied for all $i$. For the $i$-th windowpane, if $i$ is odd, you have to slide $i$-th windowpane to the east by $x_i$, otherwise, you have to slide $i$-th windowpane to the west by $x_i$.
You can assume that the windowpanes will not collide each other even if you slide windowpanes according to the instructions. In more detail, $N$ windowpanes are alternately mounted on two rails. That is, the $i$-th windowpane is attached to the inner rail of the building if $i$ is odd, otherwise, it is attached to the outer rail of the building.
Before you execute the instructions, you decide to obtain the area where the window is open after the instructions.
Input
The input consists of a single test case in the format below.
$N$ $H$ $W$
$x_1$ ... $x_N$
The first line consists of three integers $N, H,$ and $W$ ($1 \leq N \leq 100, 1 \leq H, W \leq 100$). It is guaranteed that $N$ is even. The following line consists of $N$ integers $x_1, ..., x_N$ while represent the instructions from the manager of JAG. $x_i$ represents the distance to slide the $i$-th windowpane ($0 \leq x_i \leq W$).
Output
Print the area where the window is open after the instructions in one line.
Examples
Input
4 3 3
1 1 2 3
Output
9
Input
8 10 18
2 12 16 14 18 4 17 16
Output
370
Input
6 2 2
0 2 2 2 2 0
Output
8
Input
4 1 4
3 3 2 2
Output
6
Input
8 7 15
5 0 9 14 0 4 4 15
Output
189
|
{
"inputs": [
"3\n3\n1 3 2\n4\n4 1 2 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 2 2 0 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 1 2 0 2 1",
"3\n3\n1 3 2\n4\n4 2 3 1\n6\n1 2 2 2 2 1",
"3\n3\n1 5 2\n4\n4 2 3 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 3\n4\n4 1 3 1\n6\n1 0 2 0 2 1",
"3\n3\n1 3 4\n4\n4 1 1 1\n6\n1 2 2 2 2 1",
"3\n3\n0 5 2\n4\n5 1 3 1\n6\n0 2 0 2 2 1",
"3\n3\n0 5 2\n4\n5 1 3 1\n6\n1 2 0 2 2 2",
"3\n3\n1 3 2\n4\n4 1 3 2\n6\n1 1 2 1 2 1",
"3\n3\n1 3 4\n4\n4 2 1 1\n6\n1 2 2 3 2 1",
"3\n3\n0 5 2\n4\n2 2 3 1\n6\n0 2 2 2 2 1",
"3\n3\n0 2 2\n4\n5 1 3 2\n6\n1 2 0 2 2 2",
"3\n3\n1 0 2\n4\n4 1 2 1\n6\n1 3 2 2 2 2",
"3\n3\n1 3 2\n4\n4 4 0 1\n6\n2 2 2 2 2 1",
"3\n3\n1 3 2\n4\n2 2 3 1\n6\n1 1 2 -1 2 1",
"3\n3\n1 5 3\n4\n2 1 3 0\n6\n2 1 1 -2 2 1",
"3\n3\n1 3 2\n4\n4 4 0 1\n6\n2 2 2 0 2 1",
"3\n3\n1 0 3\n4\n4 2 1 1\n6\n1 2 2 3 2 0",
"3\n3\n1 3 2\n4\n4 1 2 1\n6\n1 3 0 2 2 1",
"3\n3\n2 3 1\n4\n1 2 3 1\n6\n1 2 2 2 2 1",
"3\n3\n1 0 2\n4\n4 1 4 1\n6\n1 3 2 2 2 2",
"3\n3\n0 5 2\n4\n1 2 3 1\n6\n0 2 0 2 2 1",
"3\n3\n1 3 2\n4\n8 2 2 2\n6\n1 2 2 2 0 1",
"3\n3\n0 9 2\n4\n5 1 2 1\n6\n0 1 0 0 0 0",
"3\n3\n3 0 0\n4\n3 2 0 1\n6\n1 0 -1 0 1 0",
"3\n3\n1 0 0\n4\n3 2 0 1\n6\n0 0 -1 0 1 0",
"3\n3\n1 3 2\n4\n4 2 1 1\n6\n2 2 2 2 2 1",
"3\n3\n2 3 2\n4\n2 2 3 1\n6\n1 1 2 -1 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 1 2 0 2 2",
"3\n3\n1 3 2\n4\n4 1 1 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 0 2 0 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 1 2 1 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 1 2 0 2 4",
"3\n3\n1 3 2\n4\n4 2 1 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 1 2 -1 2 1",
"3\n3\n1 3 4\n4\n4 2 1 1\n6\n1 2 2 2 2 1",
"3\n3\n1 5 2\n4\n5 2 3 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 6 1\n6\n1 1 2 -1 2 1",
"3\n3\n0 5 2\n4\n5 2 3 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 6 1\n6\n2 1 2 -1 2 1",
"3\n3\n0 5 2\n4\n5 2 3 1\n6\n0 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 6 0\n6\n2 1 2 -1 2 1",
"3\n3\n0 5 2\n4\n5 1 3 1\n6\n0 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 6 0\n6\n1 1 2 -1 2 1",
"3\n3\n1 3 2\n4\n2 1 6 0\n6\n1 1 2 -1 2 1",
"3\n3\n0 5 2\n4\n5 1 3 1\n6\n1 2 0 2 2 1",
"3\n3\n1 3 3\n4\n2 1 6 0\n6\n1 1 2 -1 2 1",
"3\n3\n1 3 3\n4\n2 1 6 0\n6\n1 1 2 -2 2 1",
"3\n3\n0 5 2\n4\n5 1 3 0\n6\n1 2 0 2 2 2",
"3\n3\n1 3 3\n4\n2 1 6 0\n6\n2 1 2 -2 2 1",
"3\n3\n1 3 2\n4\n4 1 2 1\n6\n1 3 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n0 2 2 2 2 1",
"3\n3\n1 3 1\n4\n4 1 3 1\n6\n1 2 2 0 2 1",
"3\n3\n1 3 2\n4\n4 0 3 1\n6\n1 1 2 0 2 1",
"3\n3\n1 3 2\n4\n4 0 3 1\n6\n1 1 2 0 2 2",
"3\n3\n2 3 2\n4\n4 2 3 1\n6\n1 2 2 2 2 1",
"3\n3\n1 5 2\n4\n4 1 3 1\n6\n1 0 2 0 2 1",
"3\n3\n1 3 2\n4\n4 1 3 0\n6\n1 1 2 0 2 4",
"3\n3\n1 3 2\n4\n4 4 1 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 3\n4\n4 1 3 1\n6\n1 0 2 0 0 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 1 1 -1 2 1",
"3\n3\n1 3 4\n4\n4 1 1 1\n6\n1 2 2 2 2 0",
"3\n3\n1 3 2\n4\n8 1 6 1\n6\n2 1 2 -1 2 1",
"3\n3\n1 3 2\n4\n4 2 6 0\n6\n2 1 2 -1 2 1",
"3\n3\n0 5 3\n4\n5 2 3 1\n6\n0 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 6 0\n6\n1 1 2 -1 2 0",
"3\n3\n0 5 2\n4\n5 1 3 1\n6\n0 2 0 4 2 1",
"3\n3\n1 3 2\n4\n2 2 6 0\n6\n1 1 2 -1 2 1",
"3\n3\n0 5 2\n4\n5 1 3 1\n6\n1 2 1 2 2 1",
"3\n3\n1 3 3\n4\n2 1 6 1\n6\n1 1 2 -1 2 1",
"3\n3\n0 5 2\n4\n5 1 3 2\n6\n1 2 0 2 2 2",
"3\n3\n1 3 3\n4\n2 1 6 0\n6\n1 2 2 -2 2 1",
"3\n3\n0 5 2\n4\n5 1 3 0\n6\n0 2 0 2 2 2",
"3\n3\n1 5 3\n4\n2 1 6 0\n6\n2 1 2 -2 2 1",
"3\n3\n1 0 2\n4\n4 1 2 1\n6\n1 3 2 2 2 1",
"3\n3\n1 3 0\n4\n4 1 3 1\n6\n1 2 2 0 2 1",
"3\n3\n1 3 2\n4\n2 0 3 1\n6\n1 1 2 0 2 1",
"3\n3\n1 3 2\n4\n4 0 3 1\n6\n1 1 2 0 2 0",
"3\n3\n2 3 1\n4\n4 2 3 1\n6\n1 2 2 2 2 1",
"3\n3\n1 5 2\n4\n4 1 3 1\n6\n1 0 2 0 3 1",
"3\n3\n1 3 2\n4\n4 4 0 1\n6\n1 2 2 2 2 1",
"3\n3\n1 3 2\n4\n4 1 3 1\n6\n1 1 1 -1 2 2",
"3\n3\n1 3 3\n4\n4 2 1 1\n6\n1 2 2 3 2 1",
"3\n3\n1 3 4\n4\n4 0 1 1\n6\n1 2 2 2 2 0",
"3\n3\n1 3 2\n4\n8 1 6 1\n6\n2 1 2 -1 2 0",
"3\n3\n1 3 2\n4\n4 2 6 -1\n6\n2 1 2 -1 2 1",
"3\n3\n0 5 3\n4\n8 2 3 1\n6\n0 2 2 2 2 1",
"3\n3\n0 5 2\n4\n5 1 3 1\n6\n0 2 0 4 2 2",
"3\n3\n1 3 2\n4\n2 2 3 0\n6\n1 1 2 -1 2 1",
"3\n3\n0 5 2\n4\n3 1 3 1\n6\n1 2 0 2 2 1",
"3\n3\n1 3 3\n4\n2 1 6 0\n6\n1 1 2 0 2 1",
"3\n3\n1 3 3\n4\n2 1 6 0\n6\n1 2 2 -2 4 1",
"3\n3\n0 5 2\n4\n5 1 3 0\n6\n0 4 0 2 2 2",
"3\n3\n1 5 3\n4\n2 1 6 0\n6\n2 1 1 -2 2 1",
"3\n3\n1 5 0\n4\n4 1 3 1\n6\n1 2 2 0 2 1",
"3\n3\n1 0 2\n4\n2 0 3 1\n6\n1 1 2 0 2 1",
"3\n3\n1 5 2\n4\n4 0 3 1\n6\n1 0 2 0 3 1",
"3\n3\n1 3 2\n4\n4 1 0 1\n6\n1 1 1 -1 2 2",
"3\n3\n1 0 3\n4\n4 2 1 1\n6\n1 2 2 3 2 1"
],
"outputs": [
"4\n5\n9\n",
"4\n4\n9\n",
"4\n4\n7\n",
"4\n4\n6\n",
"4\n5\n9\n",
"3\n5\n9\n",
"3\n4\n6\n",
"3\n4\n9\n",
"3\n4\n7\n",
"3\n4\n8\n",
"4\n5\n6\n",
"3\n5\n8\n",
"3\n6\n9\n",
"4\n5\n8\n",
"3\n5\n10\n",
"4\n4\n10\n",
"4\n6\n6\n",
"3\n5\n6\n",
"4\n4\n8\n",
"3\n5\n7\n",
"4\n5\n7\n",
"4\n6\n9\n",
"3\n4\n10\n",
"3\n6\n7\n",
"4\n6\n8\n",
"3\n4\n12\n",
"4\n4\n12\n",
"4\n4\n13\n",
"4\n5\n10\n",
"3\n6\n6\n",
"4\n4\n7\n",
"4\n4\n9\n",
"4\n4\n6\n",
"4\n4\n6\n",
"4\n4\n6\n",
"4\n5\n9\n",
"4\n4\n6\n",
"3\n5\n9\n",
"3\n5\n9\n",
"4\n4\n6\n",
"3\n5\n9\n",
"4\n4\n6\n",
"3\n5\n9\n",
"4\n4\n6\n",
"3\n4\n9\n",
"4\n4\n6\n",
"4\n4\n6\n",
"3\n4\n7\n",
"3\n4\n6\n",
"3\n4\n6\n",
"3\n4\n8\n",
"3\n4\n6\n",
"4\n5\n9\n",
"4\n4\n9\n",
"3\n4\n7\n",
"4\n4\n6\n",
"4\n4\n7\n",
"3\n5\n9\n",
"3\n4\n6\n",
"4\n4\n6\n",
"4\n4\n9\n",
"3\n4\n7\n",
"4\n4\n6\n",
"3\n4\n9\n",
"4\n4\n6\n",
"4\n4\n6\n",
"3\n5\n9\n",
"4\n4\n6\n",
"3\n4\n6\n",
"4\n5\n6\n",
"3\n4\n9\n",
"3\n4\n6\n",
"3\n5\n8\n",
"3\n4\n7\n",
"3\n4\n8\n",
"3\n4\n6\n",
"3\n5\n9\n",
"3\n4\n7\n",
"4\n4\n6\n",
"4\n4\n6\n",
"4\n5\n9\n",
"3\n4\n6\n",
"4\n4\n9\n",
"4\n4\n7\n",
"3\n5\n8\n",
"3\n4\n9\n",
"4\n4\n6\n",
"4\n4\n6\n",
"3\n5\n9\n",
"3\n4\n7\n",
"4\n5\n6\n",
"3\n4\n7\n",
"3\n4\n6\n",
"3\n4\n7\n",
"3\n4\n8\n",
"3\n4\n6\n",
"3\n4\n7\n",
"3\n4\n6\n",
"3\n4\n6\n",
"4\n4\n7\n",
"3\n5\n8\n"
]
}
|
Chef likes problems involving arrays. Unfortunately, the last one he tried to solve didn't quite get solved.
Chef has an array A of N positive numbers. He wants to find the number of subarrays for which the sum and product of elements are equal.
Please help Chef find this number.
Input
The first line of input contains an integer T denoting the number of test cases. T test cases follow. The first line of each test contains the integer N. The next line contains N integers — A1, A2, ..., AN — denoting the array.
Output
For each test case, output a single line with the answer for the instance.
Constraints
1 ≤ T ≤ 50
1 ≤ n ≤ 50
1 ≤ Ai ≤ 10^9^
A1 * A2 * ... * An ≤ 10^9^
Example
Input:
3
3
1 3 2
4
4 1 2 1
6
1 2 2 2 2 1
Output:
4
5
9
Explanation:
Example case 1. There are 4 such subarrays: A[1..1], A[2..2], A[3..3], A[1..3]. Consider A[1..3], sum = 1 + 3 + 2 = 6, product = 1 * 3 * 2 = 6.
|
{
"inputs": [
"2\n3\n4",
"2\n1\n4",
"2\n2\n4",
"2\n2\n1",
"2\n1\n1",
"2\n4\n4",
"2\n5\n4",
"2\n1\n6",
"2\n-1\n4",
"2\n6\n4",
"2\n4\n1",
"2\n-1\n7",
"2\n6\n2",
"2\n6\n1",
"2\n-1\n8",
"2\n6\n3",
"2\n10\n1",
"2\n4\n3",
"2\n1\n7",
"2\n3\n7",
"2\n3\n3",
"2\n2\n8",
"2\n7\n4",
"2\n2\n7",
"2\n2\n2",
"2\n10\n4",
"2\n12\n4",
"2\n5\n1",
"2\n-1\n2",
"2\n6\n6",
"2\n13\n1",
"2\n2\n3",
"2\n3\n13",
"2\n1\n3",
"2\n7\n1",
"2\n2\n14",
"2\n1\n2",
"2\n12\n7",
"2\n5\n2",
"2\n-1\n3",
"2\n13\n2",
"2\n8\n3",
"2\n3\n5",
"2\n3\n14",
"2\n2\n11",
"2\n2\n6",
"2\n12\n12",
"2\n-1\n1",
"2\n5\n3",
"2\n1\n5",
"2\n2\n22",
"2\n18\n12",
"2\n-2\n2",
"2\n5\n5",
"2\n4\n2",
"2\n1\n22",
"2\n18\n18",
"2\n5\n10",
"2\n18\n15",
"2\n3\n2",
"2\n-1\n-1",
"2\n4\n6",
"2\n5\n6",
"2\n1\n12",
"2\n2\n10",
"2\n-1\n5",
"2\n7\n6",
"2\n9\n-1",
"2\n9\n1",
"2\n3\n1",
"2\n-2\n3",
"2\n-2\n8",
"2\n11\n4",
"2\n9\n4",
"2\n6\n7",
"2\n3\n-1",
"2\n4\n8",
"2\n-3\n3",
"2\n16\n4",
"2\n12\n6",
"2\n8\n4",
"2\n-1\n-2",
"2\n6\n9",
"2\n2\n5",
"2\n4\n13",
"2\n19\n1",
"2\n4\n14",
"2\n4\n7",
"2\n-2\n1",
"2\n-4\n-1",
"2\n2\n-1",
"2\n5\n7",
"2\n8\n6",
"2\n3\n6",
"2\n2\n12",
"2\n2\n9",
"2\n19\n12",
"2\n-3\n6",
"2\n7\n3",
"2\n1\n-1",
"2\n2\n38"
],
"outputs": [
"NO\nYES\n",
"NO\nYES\n",
"YES\nYES\n",
"YES\nNO\n",
"NO\nNO\n",
"YES\nYES\n",
"NO\nYES\n",
"NO\nYES\n",
"NO\nYES\n",
"YES\nYES\n",
"YES\nNO\n",
"NO\nNO\n",
"YES\nYES\n",
"YES\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"NO\nYES\n",
"YES\nNO\n",
"YES\nYES\n",
"NO\nYES\n",
"YES\nYES\n",
"NO\nNO\n",
"NO\nYES\n",
"YES\nYES\n",
"NO\nNO\n",
"YES\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"NO\nYES\n",
"YES\nNO\n",
"NO\nYES\n",
"NO\nNO\n",
"NO\nYES\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"YES\nYES\n",
"YES\nYES\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"NO\nYES\n",
"NO\nYES\n",
"NO\nNO\n",
"YES\nYES\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nYES\n",
"NO\nNO\n",
"YES\nYES\n",
"NO\nYES\n",
"NO\nYES\n",
"YES\nNO\n",
"NO\nNO\n",
"NO\nYES\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nYES\n",
"NO\nYES\n",
"YES\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"NO\nNO\n",
"NO\nYES\n",
"YES\nYES\n",
"NO\nYES\n",
"NO\nNO\n",
"YES\nNO\n",
"YES\nNO\n",
"YES\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"YES\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nNO\n",
"NO\nNO\n",
"NO\nYES\n",
"NO\nYES\n",
"YES\nYES\n",
"YES\nNO\n",
"NO\nYES\n",
"NO\nYES\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nNO\n"
]
}
|
Asmany strings are strings of '0's and '1's that have as many 00 as 11. A string such as 00110001 consists of 3 "00" and
1 "11". Of course this is not an Asmany string. 0011, 1100, 000111000111 are Asmany strings. An L'th Asmany number is the number of
Asmany strings of length L for all positive integers L.
For esoteric purposes Chef had an oracle (a device) that was capable of answering whether a number that he entered was an Asmany number.
The problem is that his oracle takes too long for large numbers. Him being Chef, he wants to ask the oracle very
large numbers! You tell him that you can give him a better oracle (a program) that will tell him what he wants to know in the blink of
an eye.
Input
The first Line contains a single number T, the number of test cases.
Each test case contains 1 positive integer N, with not more than 1000 digits.
Output
Print YES if N is an Asmany number, NO otherwise.
Constraints
1 ≤ T ≤ 100
1 ≤ Number of digits in N ≤ 1000
Sample Input
2
3
4
Sample Output
NO
YES
Explanation
4 is an Asmany number. To be precise, it is the 4th Asmany number: There are 4 Asmany strings of length 4. 0011, 1100, 0101, 1010.
|
{
"inputs": [
"3\n3 1\n4 108\n1 10",
"3\n3 2\n4 108\n1 10",
"3\n3 0\n4 108\n1 10",
"3\n3 1\n4 98\n1 10",
"3\n1 1\n4 108\n1 10",
"3\n3 1\n4 108\n1 2",
"3\n3 1\n2 98\n1 10",
"3\n3 1\n4 50\n1 2",
"3\n3 2\n2 98\n1 10",
"3\n3 1\n4 75\n1 2",
"3\n3 2\n2 98\n1 9",
"3\n3 1\n4 75\n1 0",
"3\n6 2\n4 108\n1 10",
"3\n3 0\n4 108\n2 10",
"3\n1 1\n4 108\n1 11",
"3\n5 1\n2 98\n1 10",
"3\n3 1\n4 4\n1 2",
"3\n3 1\n4 124\n1 2",
"3\n3 0\n2 108\n2 10",
"3\n1 1\n8 108\n1 11",
"3\n5 1\n2 10\n1 10",
"3\n3 1\n4 64\n1 2",
"3\n1 1\n6 108\n1 11",
"3\n5 2\n2 10\n1 10",
"3\n3 1\n4 37\n1 2",
"3\n1 1\n6 108\n1 22",
"3\n5 2\n1 10\n1 10",
"3\n1 1\n6 108\n1 18",
"3\n1 2\n6 108\n1 18",
"3\n1 2\n6 25\n1 18",
"3\n1 2\n6 25\n1 13",
"3\n1 2\n6 25\n1 11",
"3\n3 1\n4 108\n2 10",
"3\n3 2\n4 26\n1 10",
"3\n6 1\n4 98\n1 10",
"3\n3 1\n4 89\n1 2",
"3\n3 1\n4 50\n2 2",
"3\n3 2\n2 98\n1 4",
"3\n3 0\n4 75\n1 2",
"3\n3 2\n4 98\n1 9",
"3\n3 1\n4 108\n2 13",
"3\n1 1\n4 108\n1 8",
"3\n5 1\n2 98\n1 6",
"3\n4 1\n4 124\n1 2",
"3\n6 0\n2 108\n2 10",
"3\n1 1\n8 50\n1 11",
"3\n8 1\n2 10\n1 10",
"3\n3 1\n8 64\n1 2",
"3\n5 2\n2 7\n1 10",
"3\n3 1\n4 52\n1 2",
"3\n1 1\n6 108\n1 31",
"3\n5 2\n1 15\n1 10",
"3\n1 0\n6 108\n1 18",
"3\n1 2\n6 108\n1 31",
"3\n1 1\n6 25\n1 18",
"3\n1 2\n6 25\n1 9",
"3\n1 1\n6 25\n1 11",
"3\n4 1\n4 108\n2 10",
"3\n3 2\n4 8\n1 10",
"3\n6 2\n4 98\n1 10",
"3\n4 1\n4 89\n1 2",
"3\n3 1\n4 50\n2 1",
"3\n3 2\n2 98\n2 4",
"3\n3 1\n4 98\n1 9",
"3\n1 1\n4 108\n1 1",
"3\n5 1\n1 98\n1 6",
"3\n4 1\n4 87\n1 2",
"3\n1 2\n8 50\n1 11",
"3\n10 1\n2 10\n1 10",
"3\n3 0\n8 64\n1 2",
"3\n10 2\n2 7\n1 10",
"3\n5 2\n1 28\n1 10",
"3\n2 0\n6 108\n1 18",
"3\n1 1\n6 25\n1 32",
"3\n1 3\n6 25\n1 9",
"3\n1 1\n4 108\n2 10",
"3\n3 2\n2 8\n1 10",
"3\n6 2\n4 95\n1 10",
"3\n6 1\n4 89\n1 2",
"3\n3 1\n4 61\n2 1",
"3\n3 2\n2 43\n2 4",
"3\n1 1\n4 124\n1 1",
"3\n4 1\n3 87\n1 2",
"3\n1 2\n5 50\n1 11",
"3\n2 1\n2 10\n1 10",
"3\n1 0\n8 64\n1 2",
"3\n10 2\n3 7\n1 10",
"3\n5 2\n1 28\n1 14",
"3\n2 0\n6 108\n1 4",
"3\n1 1\n12 25\n1 32",
"3\n1 3\n6 27\n1 9",
"3\n1 1\n6 108\n2 10",
"3\n1 2\n2 8\n1 10",
"3\n2 2\n4 95\n1 10",
"3\n6 1\n4 89\n1 4",
"3\n2 1\n4 61\n2 1",
"3\n3 2\n2 69\n2 4",
"3\n4 2\n3 87\n1 2",
"3\n1 2\n5 50\n2 11",
"3\n2 2\n2 10\n1 10",
"3\n1 1\n8 64\n1 2"
],
"outputs": [
"255\n400\n10",
"256\n400\n10\n",
"254\n400\n10\n",
"255\n410\n10\n",
"1\n400\n10\n",
"255\n400\n2\n",
"255\n156\n10\n",
"255\n458\n2\n",
"256\n156\n10\n",
"255\n433\n2\n",
"256\n156\n9\n",
"255\n433\n0\n",
"760\n400\n10\n",
"254\n400\n244\n",
"1\n400\n11\n",
"509\n156\n10\n",
"255\n504\n2\n",
"255\n384\n2\n",
"254\n146\n244\n",
"1\n908\n11\n",
"509\n244\n10\n",
"255\n444\n2\n",
"1\n654\n11\n",
"510\n244\n10\n",
"255\n471\n2\n",
"1\n654\n22\n",
"510\n10\n10\n",
"1\n654\n18\n",
"2\n654\n18\n",
"2\n737\n18\n",
"2\n737\n13\n",
"2\n737\n11\n",
"255\n400\n244\n",
"256\n482\n10\n",
"761\n410\n10\n",
"255\n419\n2\n",
"255\n458\n252\n",
"256\n156\n4\n",
"254\n433\n2\n",
"256\n410\n9\n",
"255\n400\n241\n",
"1\n400\n8\n",
"509\n156\n6\n",
"507\n384\n2\n",
"762\n146\n244\n",
"1\n966\n11\n",
"1015\n244\n10\n",
"255\n952\n2\n",
"510\n247\n10\n",
"255\n456\n2\n",
"1\n654\n31\n",
"510\n15\n10\n",
"0\n654\n18\n",
"2\n654\n31\n",
"1\n737\n18\n",
"2\n737\n9\n",
"1\n737\n11\n",
"507\n400\n244\n",
"256\n500\n10\n",
"760\n410\n10\n",
"507\n419\n2\n",
"255\n458\n253\n",
"256\n156\n250\n",
"255\n410\n9\n",
"1\n400\n1\n",
"509\n98\n6\n",
"507\n421\n2\n",
"2\n966\n11\n",
"1269\n244\n10\n",
"254\n952\n2\n",
"1268\n247\n10\n",
"510\n28\n10\n",
"254\n654\n18\n",
"1\n737\n32\n",
"3\n737\n9\n",
"1\n400\n244\n",
"256\n246\n10\n",
"760\n413\n10\n",
"761\n419\n2\n",
"255\n447\n253\n",
"256\n211\n250\n",
"1\n384\n1\n",
"507\n341\n2\n",
"2\n558\n11\n",
"253\n244\n10\n",
"0\n952\n2\n",
"1268\n261\n10\n",
"510\n28\n14\n",
"254\n654\n4\n",
"1\n1499\n32\n",
"3\n735\n9\n",
"1\n654\n244\n",
"2\n246\n10\n",
"252\n413\n10\n",
"761\n419\n4\n",
"253\n447\n253\n",
"256\n185\n250\n",
"506\n341\n2\n",
"2\n558\n243\n",
"252\n244\n10\n",
"1\n952\n2\n"
]
}
|
A professor invented Cookie Breeding Machine for his students who like cookies very much.
When one cookie with the taste of x is put into the machine and a non-negative integer y less than or equal to 127 is input on the machine, it consumes the cookie and generates two cookies with the taste of y and (x XOR y).
Here, XOR represents Bitwise Exclusive OR.
At first, there is only one cookie and the taste of it is D .
Find the maximum value of the sum of the taste of the exactly N cookies generated after the following operation is conducted N-1 times.
1. Put one of the cookies into the machine.
2. Input a non-negative integer less than or equal to 127 on the machine.
Constraints
* 1 \leq T \leq 1000
* 1 \leq N_t \leq 1000 (1 \leq t \leq T)
* 1 \leq D_t \leq 127 (1 \leq t \leq T)
Input
The input is given from Standard Input in the following format:
T
N_1 D_1
:
N_T D_T
The input consists of multiple test cases. An Integer T that represents the number of test cases is given on line 1.
Each test case is given on the next T lines.
In the t-th test case ( 1 \leq t \leq T ), N_t that represents the number of cookies generated through the operations and D_t that represents the taste of the initial cookie are given separated by space.
Output
For each test case, print the maximum value of the sum of the taste of the N cookies generated through the operations on one line.
Example
Input
3
3 1
4 108
1 10
Output
255
400
10
|
{
"inputs": [
"red blue\n3 4\nred",
"red blue\n5 5\nblue",
"red blue\n3 2\nred",
"red blte\n3 0\nred",
"red blue\n5 0\nred",
"red blue\n7 0\nred",
"red blue\n5 1\nred",
"red blue\n0 0\nred",
"red blte\n3 4\nred",
"red blue\n1 0\nred",
"red blue\n11 0\nred",
"red blue\n-1 0\nred",
"red blue\n11 -1\nred",
"red bkfu\n8 0\nred",
"red blue\n11 -2\nred",
"red bkfu\n16 0\nred",
"red ufkb\n22 0\nred",
"red blue\n3 3\nred",
"red blue\n2 0\nred",
"red bule\n7 -1\nred",
"red blte\n9 0\nred",
"red blue\n7 1\nred",
"red bleu\n12 0\nred",
"red blue\n0 1\nred",
"red bmte\n6 0\nred",
"red blue\n-1 1\nred",
"red bkfu\n26 0\nred",
"red bule\n7 -2\nred",
"red bkfu\n4 0\nred",
"red blve\n3 6\nred",
"red blte\n3 -1\nred",
"red bule\n7 -3\nred",
"red beul\n4 1\nred",
"red bleu\n17 0\nred",
"red ctle\n1 1\nred",
"red blve\n3 1\nred",
"red elbt\n-2 0\nred",
"red elbt\n0 -1\nred",
"red elbt\n0 -2\nred",
"red blue\n5 2\nred",
"red blue\n2 -1\nred",
"red bkfu\n14 0\nred",
"red blue\n3 5\nred",
"red blve\n2 2\nred",
"red blue\n2 1\nred",
"red bule\n1 -1\nred",
"red bleu\n12 -1\nred",
"red blue\n0 2\nred",
"red blve\n0 4\nred",
"red bule\n1 -2\nred",
"red lueb\n9 1\nred",
"red bulf\n-2 -1\nred",
"red lbue\n-1 2\nred",
"red clue\n-1 4\nred",
"red laeu\n9 2\nred",
"red blue\n11 1\nred",
"red blue\n-1 -1\nred",
"red bkfu\n8 -1\nred",
"red blue\n12 -2\nred",
"red beul\n4 2\nred",
"red bleu\n10 0\nred",
"red blue\n3 8\nred",
"red blve\n1 4\nred",
"red beul\n6 1\nred",
"red blve\n3 9\nred",
"red vkeb\n9 -1\nred",
"red blue\n14 1\nred",
"red bulf\n-3 0\nred",
"red bule\n-1 -2\nred",
"red lbue\n-1 3\nred",
"red laeu\n18 1\nred",
"red luec\n-2 4\nred",
"red etlb\n4 4\nred",
"red bldu\n18 0\nred",
"red blue\n10 1\nred",
"red tmbe\n3 -2\nred",
"red blue\n3 15\nred",
"red beul\n6 2\nred",
"red bule\n-2 -2\nred",
"red lbeu\n7 2\nred",
"red alue\n12 -3\nred",
"red alve\n6 9\nred",
"red blue\n-4 -1\nred",
"red alve\n7 9\nred",
"red akve\n7 12\nred",
"red bltf\n5 -1\nred",
"red bkfu\n8 1\nred",
"red blue\n11 -3\nred",
"red ufkb\n22 1\nred",
"red blve\n1 2\nred",
"red blue\n13 1\nred",
"red bleu\n12 1\nred",
"red blue\n-2 1\nred",
"red blve\n0 6\nred",
"red blue\n3 7\nred",
"red buel\n2 -2\nred",
"red uelb\n10 -1\nred",
"red eulb\n0 8\nred",
"red vkeb\n9 -2\nred",
"red lbte\n0 3\nred",
"red bule\n-3 -2\nred",
"red lbeu\n7 3\nred"
],
"outputs": [
"2 4",
"5 4",
"2 2\n",
"2 0\n",
"4 0\n",
"6 0\n",
"4 1\n",
"-1 0\n",
"2 4\n",
"0 0\n",
"10 0\n",
"-2 0\n",
"10 -1\n",
"7 0\n",
"10 -2\n",
"15 0\n",
"21 0\n",
"2 3\n",
"1 0\n",
"6 -1\n",
"8 0\n",
"6 1\n",
"11 0\n",
"-1 1\n",
"5 0\n",
"-2 1\n",
"25 0\n",
"6 -2\n",
"3 0\n",
"2 6\n",
"2 -1\n",
"6 -3\n",
"3 1\n",
"16 0\n",
"0 1\n",
"2 1\n",
"-3 0\n",
"-1 -1\n",
"-1 -2\n",
"4 2\n",
"1 -1\n",
"13 0\n",
"2 5\n",
"1 2\n",
"1 1\n",
"0 -1\n",
"11 -1\n",
"-1 2\n",
"-1 4\n",
"0 -2\n",
"8 1\n",
"-3 -1\n",
"-2 2\n",
"-2 4\n",
"8 2\n",
"10 1\n",
"-2 -1\n",
"7 -1\n",
"11 -2\n",
"3 2\n",
"9 0\n",
"2 8\n",
"0 4\n",
"5 1\n",
"2 9\n",
"8 -1\n",
"13 1\n",
"-4 0\n",
"-2 -2\n",
"-2 3\n",
"17 1\n",
"-3 4\n",
"3 4\n",
"17 0\n",
"9 1\n",
"2 -2\n",
"2 15\n",
"5 2\n",
"-3 -2\n",
"6 2\n",
"11 -3\n",
"5 9\n",
"-5 -1\n",
"6 9\n",
"6 12\n",
"4 -1\n",
"7 1\n",
"10 -3\n",
"21 1\n",
"0 2\n",
"12 1\n",
"11 1\n",
"-3 1\n",
"-1 6\n",
"2 7\n",
"1 -2\n",
"9 -1\n",
"-1 8\n",
"8 -2\n",
"-1 3\n",
"-4 -2\n",
"6 3\n"
]
}
|
We have A balls with the string S written on each of them and B balls with the string T written on each of them.
From these balls, Takahashi chooses one with the string U written on it and throws it away.
Find the number of balls with the string S and balls with the string T that we have now.
Constraints
* S, T, and U are strings consisting of lowercase English letters.
* The lengths of S and T are each between 1 and 10 (inclusive).
* S \not= T
* S=U or T=U.
* 1 \leq A,B \leq 10
* A and B are integers.
Input
Input is given from Standard Input in the following format:
S T
A B
U
Output
Print the answer, with space in between.
Examples
Input
red blue
3 4
red
Output
2 4
Input
red blue
5 5
blue
Output
5 4
|
{
"inputs": [
"2 1 3\n9 5\n1\n2 8 5\n",
"1 1 1\n3\n5\n4\n",
"10 1 1\n11 7 20 15 19 14 2 4 13 14\n8\n11\n",
"2 2 2\n3 10\n6 9\n10 9\n",
"9 4 7\n17 19 19 9 20 6 1 14 11\n15 12 10 20\n15 10 3 20 1 16 7\n",
"16 26 8\n44 13 2 24 56 74 72 4 87 98 43 4 17 30 82 8\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 37 82 36 67 86 81 6\n",
"1 3 6\n2\n8 6 7\n5 2 4 1 10 4\n",
"2 2 2\n3 10\n6 13\n10 9\n",
"9 4 7\n17 19 19 9 20 6 1 14 11\n15 12 10 20\n15 10 3 31 1 16 7\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 8\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 37 82 36 67 86 81 6\n",
"1 3 6\n2\n8 6 10\n5 2 4 1 10 4\n",
"2 1 3\n9 9\n1\n2 8 5\n",
"1 1 1\n6\n5\n4\n",
"2 2 2\n3 10\n6 13\n12 9\n",
"9 4 7\n17 19 19 9 20 6 1 14 11\n15 19 10 20\n15 10 3 31 1 16 7\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 8\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 37 82 21 67 86 81 6\n",
"2 1 3\n16 9\n1\n2 8 5\n",
"2 2 2\n3 10\n6 13\n12 17\n",
"9 4 7\n17 19 19 9 20 6 1 14 11\n19 19 10 20\n15 10 3 31 1 16 7\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 37 82 21 67 86 81 6\n",
"2 2 2\n3 10\n5 13\n12 17\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 61 82 21 67 86 81 6\n",
"2 2 2\n0 10\n5 13\n12 17\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"2 2 2\n0 10\n5 13\n12 18\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 89 33 100 76 1 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 2 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 89 33 100 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 2 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 13 33 100 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 13 33 100 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 13 33 101 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 76 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 19 64 44 55 18 67 72 75 10 24 47 23 27 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 64 44 55 18 67 72 75 10 24 47 23 27 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 64 44 55 18 67 72 65 10 24 47 23 27 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 64 44 55 18 67 72 65 10 24 47 23 27 101 129 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 64 44 55 18 67 12 65 10 24 47 23 27 101 129 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 64 44 55 18 67 12 65 10 24 83 23 27 101 129 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 12\n31 6 76 15 88 37 22 64 44 55 18 67 12 65 10 24 83 23 27 101 129 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 12\n31 6 76 15 88 37 22 64 44 55 18 67 12 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 88 4 172 98 43 4 6 30 82 12\n31 6 76 15 88 37 22 64 44 55 18 67 12 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 88 4 172 98 43 4 6 30 82 12\n31 6 76 15 88 37 22 64 44 55 18 67 18 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 25 0 24 56 74 88 4 172 98 43 4 6 30 82 12\n31 6 76 15 88 37 22 64 44 55 18 67 18 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 25 0 24 56 74 88 4 172 98 43 4 6 30 82 3\n31 6 76 15 88 37 22 64 44 55 18 67 18 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 25 0 24 56 74 88 4 172 98 43 4 6 30 82 3\n31 6 76 15 88 37 22 64 44 55 18 67 18 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 92 6\n",
"16 26 8\n13 25 0 24 56 74 88 4 172 98 43 4 6 30 82 3\n31 6 76 15 88 37 22 64 44 55 18 67 18 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 77 6\n",
"16 26 8\n13 25 0 24 56 74 88 4 172 98 43 4 3 30 82 3\n31 6 76 15 88 37 22 64 44 55 18 67 18 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 77 6\n",
"16 26 8\n13 25 0 24 56 74 88 4 172 98 43 4 3 30 82 3\n31 6 76 15 88 37 22 64 13 55 18 67 18 65 10 24 83 23 27 101 198 2 58 59 34 38\n31 61 138 21 67 86 77 6\n",
"2 2 2\n3 10\n6 9\n10 14\n",
"9 4 7\n17 19 19 9 20 6 1 14 11\n28 12 10 20\n15 10 3 20 1 16 7\n",
"16 26 8\n44 13 2 24 56 74 72 4 87 98 43 4 17 30 82 8\n31 6 76 32 88 37 19 64 44 106 18 67 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 37 82 36 67 86 81 6\n",
"1 3 6\n2\n6 6 7\n5 2 4 1 10 4\n",
"2 1 3\n9 5\n1\n2 8 4\n",
"1 1 1\n3\n0\n4\n",
"10 1 1\n11 7 20 15 19 14 2 5 13 14\n8\n11\n",
"2 2 2\n3 10\n6 19\n10 9\n",
"9 4 7\n2 19 19 9 20 6 1 14 11\n15 12 10 20\n15 10 3 31 1 16 7\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 8\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 45 47 89 33 100 76 1 58 38 24 38\n31 37 82 36 67 86 81 6\n",
"1 3 6\n2\n8 6 10\n5 2 4 1 10 5\n",
"2 2 2\n3 10\n3 13\n12 9\n",
"9 4 7\n17 19 19 9 20 6 2 14 11\n15 19 10 20\n15 10 3 31 1 16 7\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 8\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 45 45 89 33 100 76 1 58 38 34 38\n31 37 82 21 67 86 81 6\n",
"2 1 3\n16 17\n1\n2 8 5\n",
"9 4 7\n4 19 19 9 20 6 1 14 11\n19 19 10 20\n15 10 3 31 1 16 7\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 109 37 19 64 44 55 18 67 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 37 82 21 67 86 81 6\n",
"2 2 2\n3 10\n5 21\n12 17\n",
"2 2 2\n0 10\n5 13\n12 6\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 43 72 75 10 45 47 89 33 100 76 1 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"2 2 2\n0 5\n5 13\n12 18\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 89 33 100 76 1 58 38 34 38\n31 61 82 21 67 73 63 6\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 31 75 10 24 47 89 33 100 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 2 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 111 10 24 47 89 33 100 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 2 24 56 74 72 4 172 98 43 4 17 10 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 13 33 100 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 13 33 100 76 2 58 38 34 38\n31 61 82 21 14 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 38 47 13 33 101 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 34 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 24 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 76 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 129 2 58 38 34 38\n31 61 138 21 67 20 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 100 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 4 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 19 64 44 55 18 67 72 75 10 24 47 23 33 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 7 82 7\n31 6 76 15 88 37 19 64 44 55 18 67 72 75 10 24 47 23 27 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 65 44 55 18 67 72 75 10 24 47 23 27 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 0 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 64 44 55 18 67 72 65 10 24 47 23 27 101 129 2 58 38 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 64 44 55 18 67 72 65 10 24 47 23 27 101 129 2 58 59 34 38\n31 61 138 21 43 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 64 44 55 18 67 12 65 10 24 47 23 27 101 129 2 58 59 34 38\n31 61 138 12 67 86 63 6\n",
"16 26 8\n13 13 0 24 56 74 72 4 172 98 43 4 6 30 82 7\n31 6 76 15 88 37 22 56 44 55 18 67 12 65 10 24 83 23 27 101 129 2 58 59 34 38\n31 61 138 21 67 86 63 6\n",
"16 26 8\n13 13 2 24 56 74 72 4 87 98 43 4 17 30 82 7\n31 6 76 32 88 37 19 64 44 55 18 67 72 75 10 24 47 89 33 100 76 2 58 38 34 38\n31 61 82 21 67 86 63 6\n"
],
"outputs": [
"99\n",
"20\n",
"372\n",
"199\n",
"1863\n",
"73851\n",
"147\n",
"238\n",
"2083\n",
"72588\n",
"172\n",
"119\n",
"30\n",
"264\n",
"2190\n",
"71977\n",
"175\n",
"359\n",
"2255\n",
"71945\n",
"356\n",
"73232\n",
"341\n",
"71972\n",
"354\n",
"71614\n",
"79993\n",
"76441\n",
"76421\n",
"76593\n",
"76641\n",
"83605\n",
"89163\n",
"88821\n",
"88713\n",
"88635\n",
"88653\n",
"87893\n",
"88902\n",
"86611\n",
"89200\n",
"89315\n",
"101183\n",
"102319\n",
"102343\n",
"102686\n",
"102497\n",
"104453\n",
"103376\n",
"103314\n",
"102651\n",
"248\n",
"2116\n",
"77798\n",
"132\n",
"94\n",
"12\n",
"372\n",
"298\n",
"1946\n",
"72512\n",
"178\n",
"255\n",
"2191\n",
"71903\n",
"218\n",
"2130\n",
"73870\n",
"492\n",
"216\n",
"70615\n",
"294\n",
"70579\n",
"69599\n",
"84107\n",
"75741\n",
"74023\n",
"76772\n",
"76793\n",
"83867\n",
"85583\n",
"85243\n",
"88465\n",
"87862\n",
"88720\n",
"74347\n",
"87523\n",
"86339\n",
"88680\n",
"71614\n"
]
}
|
You are given three multisets of pairs of colored sticks:
* R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R;
* G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G;
* B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B;
You are constructing rectangles from these pairs of sticks with the following process:
1. take a pair of sticks of one color;
2. take a pair of sticks of another color different from the first one;
3. add the area of the resulting rectangle to the total area.
Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.
Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.
What is the maximum area you can achieve?
Input
The first line contains three integers R, G, B (1 ≤ R, G, B ≤ 200) — the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.
The second line contains R integers r_1, r_2, ..., r_R (1 ≤ r_i ≤ 2000) — the lengths of sticks in each pair of red sticks.
The third line contains G integers g_1, g_2, ..., g_G (1 ≤ g_i ≤ 2000) — the lengths of sticks in each pair of green sticks.
The fourth line contains B integers b_1, b_2, ..., b_B (1 ≤ b_i ≤ 2000) — the lengths of sticks in each pair of blue sticks.
Output
Print the maximum possible total area of the constructed rectangles.
Examples
Input
1 1 1
3
5
4
Output
20
Input
2 1 3
9 5
1
2 8 5
Output
99
Input
10 1 1
11 7 20 15 19 14 2 4 13 14
8
11
Output
372
Note
In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 × 5 = 20.
In the second example the best rectangles are: red/blue 9 × 8, red/blue 5 × 5, green/blue 2 × 1. So the total area is 72 + 25 + 2 = 99.
In the third example the best rectangles are: red/green 19 × 8 and red/blue 20 × 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.
|
{
"inputs": [
"1 1 5\n1 1\n1 1\n1 1\n1 1\n1 1\n",
"3 3 7\n1 2\n2 3\n1 3\n3 2\n3 3\n2 1\n2 1\n",
"2000 2000 1\n1387 936\n",
"9 9 55\n5 1\n8 3\n1 6\n5 6\n5 9\n6 5\n9 8\n6 6\n5 5\n7 7\n7 2\n1 6\n3 8\n4 3\n1 8\n8 5\n5 4\n6 1\n2 7\n2 6\n2 8\n7 7\n7 3\n6 9\n2 7\n9 3\n3 5\n7 9\n6 8\n4 6\n5 2\n9 2\n4 3\n9 5\n3 2\n2 2\n7 3\n3 8\n3 4\n5 9\n4 2\n7 9\n1 8\n8 8\n9 9\n7 1\n6 6\n4 8\n9 4\n8 8\n3 5\n6 8\n1 6\n7 5\n5 3\n",
"2000 2000 2\n804 1037\n1788 295\n",
"4 4 88\n2 1\n3 3\n1 1\n4 3\n3 3\n2 1\n1 1\n3 2\n4 3\n1 1\n2 1\n4 4\n2 1\n2 2\n2 4\n2 3\n2 1\n2 4\n3 4\n4 4\n1 2\n1 2\n1 4\n4 4\n1 2\n1 1\n1 2\n4 2\n4 3\n4 4\n4 1\n2 4\n3 4\n3 3\n1 3\n1 1\n4 4\n1 3\n1 2\n3 4\n4 1\n3 1\n3 1\n4 3\n2 3\n1 1\n1 1\n1 1\n3 2\n3 1\n3 3\n1 1\n1 4\n2 2\n3 1\n3 2\n4 2\n2 4\n4 1\n2 3\n3 3\n1 1\n2 3\n2 3\n4 1\n4 1\n3 1\n4 1\n1 4\n3 2\n1 3\n4 4\n4 2\n3 1\n4 3\n3 3\n4 1\n1 1\n2 2\n2 1\n4 1\n1 2\n1 2\n2 1\n4 1\n3 2\n3 1\n2 1\n",
"1 1 0\n",
"2000 1377 1\n1387 936\n",
"9 9 55\n5 1\n8 3\n1 6\n5 6\n5 9\n6 5\n9 8\n6 6\n5 5\n7 7\n7 2\n1 6\n3 8\n4 3\n1 3\n8 5\n5 4\n6 1\n2 7\n2 6\n2 8\n7 7\n7 3\n6 9\n2 7\n9 3\n3 5\n7 9\n6 8\n4 6\n5 2\n9 2\n4 3\n9 5\n3 2\n2 2\n7 3\n3 8\n3 4\n5 9\n4 2\n7 9\n1 8\n8 8\n9 9\n7 1\n6 6\n4 8\n9 4\n8 8\n3 5\n6 8\n1 6\n7 5\n5 3\n",
"4 4 88\n2 1\n3 3\n1 1\n4 3\n3 3\n2 1\n1 1\n3 2\n4 3\n1 1\n2 1\n4 4\n2 1\n2 2\n2 4\n2 3\n2 1\n2 4\n3 4\n4 4\n1 2\n1 2\n1 4\n4 4\n1 2\n1 1\n1 2\n4 2\n4 3\n4 4\n4 1\n2 4\n3 4\n3 3\n1 3\n1 1\n4 4\n1 3\n1 2\n3 4\n4 1\n3 1\n3 1\n4 3\n2 3\n1 1\n1 1\n1 1\n3 2\n3 1\n3 3\n1 1\n1 4\n2 2\n3 1\n3 2\n4 2\n2 4\n4 1\n2 3\n3 4\n1 1\n2 3\n2 3\n4 1\n4 1\n3 1\n4 1\n1 4\n3 2\n1 3\n4 4\n4 2\n3 1\n4 3\n3 3\n4 1\n1 1\n2 2\n2 1\n4 1\n1 2\n1 2\n2 1\n4 1\n3 2\n3 1\n2 1\n",
"2000 1741 2\n804 1037\n1788 295\n",
"0 1 0\n",
"2000 1377 1\n1638 936\n",
"2000 1741 2\n804 118\n1788 295\n",
"2000 1377 1\n1638 748\n",
"2000 1377 1\n1638 1106\n",
"2000 1377 0\n1638 1106\n",
"2000 1377 0\n1638 1666\n",
"2000 2000 0\n1387 936\n",
"2000 1377 1\n1387 288\n",
"0 2 0\n",
"2094 1377 1\n1638 936\n",
"2000 1741 2\n804 118\n1195 295\n",
"2000 1377 1\n1371 748\n",
"2000 1377 0\n2565 1106\n",
"1149 1377 0\n1638 1666\n",
"9 9 55\n5 1\n8 3\n1 6\n5 6\n5 9\n6 5\n9 8\n6 6\n5 7\n7 7\n7 2\n1 6\n3 8\n4 3\n1 3\n8 5\n5 4\n6 1\n2 7\n2 6\n2 8\n7 7\n7 3\n6 9\n2 7\n9 3\n3 5\n7 9\n6 8\n4 6\n5 2\n9 2\n4 3\n9 5\n3 2\n2 2\n7 3\n3 8\n3 4\n5 9\n4 2\n7 9\n1 8\n8 8\n9 9\n7 1\n6 6\n4 8\n9 4\n8 8\n3 5\n6 8\n1 6\n7 5\n5 3\n",
"1715 1377 1\n1387 288\n",
"-1 2 0\n",
"2000 570 2\n804 118\n1195 295\n",
"2000 1377 0\n1371 748\n",
"1421 1377 0\n2565 1106\n",
"1149 1377 0\n572 1666\n",
"9 9 55\n5 1\n8 3\n1 6\n5 6\n5 9\n6 5\n9 8\n6 6\n5 7\n7 7\n7 2\n1 6\n3 8\n4 3\n1 3\n8 5\n5 4\n6 1\n2 7\n2 6\n2 8\n7 7\n7 3\n6 9\n2 7\n9 3\n3 5\n7 9\n6 8\n4 6\n5 2\n9 2\n4 3\n9 5\n3 2\n2 2\n7 3\n3 8\n3 4\n5 9\n4 2\n7 9\n1 8\n8 8\n9 9\n7 1\n6 6\n4 8\n9 4\n8 8\n3 5\n6 6\n1 6\n7 5\n5 3\n",
"1715 1163 1\n1387 288\n",
"2000 570 2\n321 118\n1195 295\n",
"2000 1377 0\n1037 748\n",
"682 1377 0\n2565 1106\n",
"2112 1377 0\n572 1666\n",
"1715 1112 1\n1387 288\n"
],
"outputs": [
"0 \n1 1 \n2 1 2 \n3 1 2 3 \n4 1 2 3 4 \n5 1 2 3 4 5 \n",
"0\n3 3 4 6\n6 1 3 4 5 6 7\n",
"0 \n",
"0 \n9 1 3 7 10 14 16 24 36 39 \n18 1 2 3 7 10 11 14 15 16 17 18 19 24 27 30 36 39 45 \n27 1 2 3 5 6 7 10 11 12 14 15 16 17 18 19 24 25 27 30 33 35 36 39 44 45 46 49 \n",
"0 \n",
"0 \n4 1 4 19 21 \n8 1 3 4 9 15 19 21 86 \n12 1 2 3 4 6 9 12 15 19 21 22 86 \n16 1 2 3 4 5 6 8 9 11 12 15 19 20 21 22 25 \n20 1 2 3 4 5 6 8 9 11 12 13 15 19 20 21 22 24 25 27 76 \n24 1 2 3 4 5 6 8 9 11 12 13 15 17 19 20 21 22 24 25 27 28 33 34 35 \n28 1 2 3 4 5 6 8 9 11 12 13 15 17 18 19 20 21 22 24 25 27 28 29 33 34 35 39 42 \n32 1 2 3 4 5 6 8 9 11 12 13 14 15 17 18 19 20 21 22 24 25 27 28 29 30 33 34 35 38 39 42 43 \n36 1 2 3 4 5 6 8 9 11 12 13 14 15 16 17 18 19 20 21 22 24 25 27 28 29 30 31 33 34 35 38 39 40 42 43 82 \n40 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 24 25 27 28 29 30 31 33 34 35 37 38 39 40 42 43 45 49 82 \n44 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 45 49 51 82 83 \n48 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 54 82 83 \n52 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 54 55 57 58 71 82 83 \n56 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 53 54 55 56 57 58 59 60 71 82 83 \n60 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 53 54 55 56 57 58 59 60 61 65 69 71 79 82 83 \n64 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 53 54 55 56 57 58 59 60 61 63 65 69 70 71 72 79 82 83 \n",
"0 \n",
"0\n",
"0\n9 1 3 7 10 14 16 24 36 39\n18 1 2 3 7 10 11 14 16 17 18 19 24 27 30 36 39 43 45\n27 1 2 3 5 6 7 10 11 12 14 16 17 18 19 24 25 27 30 33 35 36 39 43 44 45 46 49\n",
"0\n4 1 4 19 21\n8 1 3 4 9 15 19 21 86\n12 1 2 3 4 6 9 12 15 19 21 22 86\n16 1 2 3 4 5 6 8 9 11 12 15 19 20 21 22 25\n20 1 2 3 4 5 6 8 9 11 12 13 15 19 20 21 22 24 25 27 76\n24 1 2 3 4 5 6 8 9 11 12 13 15 17 19 20 21 22 24 25 27 28 33 34 35\n28 1 2 3 4 5 6 8 9 11 12 13 15 17 18 19 20 21 22 24 25 27 28 29 33 34 35 39 42\n32 1 2 3 4 5 6 8 9 11 12 13 14 15 17 18 19 20 21 22 24 25 27 28 29 30 33 34 35 38 39 42 43\n36 1 2 3 4 5 6 8 9 11 12 13 14 15 16 17 18 19 20 21 22 24 25 27 28 29 30 31 33 34 35 38 39 40 42 43 82\n40 1 2 3 4 5 6 8 9 11 12 13 14 15 16 17 18 19 20 21 22 24 25 27 28 29 30 31 33 34 35 37 38 39 40 42 43 50 54 71 82\n44 1 2 3 4 5 6 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 33 34 35 37 38 39 40 41 42 43 45 49 50 54 71 82\n48 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 54 56 71 82\n52 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 54 56 57 58 71 82\n56 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 54 56 57 58 59 60 61 71 82 83\n60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 53 54 56 57 58 59 60 61 63 65 70 71 82 83\n64 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 53 54 56 57 58 59 60 61 63 65 66 69 70 71 76 79 82 83\n68 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 42 43 44 45 49 50 51 53 54 56 57 58 59 60 61 63 64 65 66 69 70 71 72 76 79 82 83 86\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n9 1 3 7 10 14 16 24 36 39\n18 1 2 3 7 10 11 14 16 17 18 19 24 27 30 36 39 43 45\n27 1 2 3 5 6 7 10 11 12 14 16 17 18 19 24 25 27 30 33 35 36 39 43 44 45 46 49\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n9 1 3 7 10 14 16 24 36 39\n18 1 2 3 7 10 11 14 16 17 18 19 24 27 30 36 39 43 45\n27 1 2 3 5 6 7 10 11 12 14 16 17 18 19 24 25 27 30 33 35 36 39 43 44 45 46 49\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
}
|
You are given a bipartite graph G = (U, V, E), U is the set of vertices of the first part, V is the set of vertices of the second part and E is the set of edges. There might be multiple edges.
Let's call some subset of its edges <image> k-covering iff the graph <image> has each of its vertices incident to at least k edges. Minimal k-covering is such a k-covering that the size of the subset <image> is minimal possible.
Your task is to find minimal k-covering for each <image>, where minDegree is the minimal degree of any vertex in graph G.
Input
The first line contains three integers n1, n2 and m (1 ≤ n1, n2 ≤ 2000, 0 ≤ m ≤ 2000) — the number of vertices in the first part, the number of vertices in the second part and the number of edges, respectively.
The i-th of the next m lines contain two integers ui and vi (1 ≤ ui ≤ n1, 1 ≤ vi ≤ n2) — the description of the i-th edge, ui is the index of the vertex in the first part and vi is the index of the vertex in the second part.
Output
For each <image> print the subset of edges (minimal k-covering) in separate line.
The first integer cntk of the k-th line is the number of edges in minimal k-covering of the graph. Then cntk integers follow — original indices of the edges which belong to the minimal k-covering, these indices should be pairwise distinct. Edges are numbered 1 through m in order they are given in the input.
Examples
Input
3 3 7
1 2
2 3
1 3
3 2
3 3
2 1
2 1
Output
0
3 3 7 4
6 1 3 6 7 4 5
Input
1 1 5
1 1
1 1
1 1
1 1
1 1
Output
0
1 5
2 4 5
3 3 4 5
4 2 3 4 5
5 1 2 3 4 5
|
{
"inputs": [
"ABC\nabc\n",
"AbC\nDCbA\n",
"abacaba\nAbaCaBA\n",
"r\nqA\n",
"CdAbD\ndecbde\n",
"a\nB\n",
"Adc\neadeabcad\n",
"DBAdeb\ndeeabcddadaa\n",
"CCAE\ndcecc\n",
"l\nFPbAVjsMpPDTLkfwNYFmBDHPTDSWSOUlrBHYJHPM\n",
"Dccb\nbeeeb\n",
"EDCED\neebeacdba\n",
"DpiNBmCRFWxpdbfGOzvvOcemjructoAdEwegTvbVbfWWRPGyEAxGdDRWVlqNyGWMWHMrHAIZpyxvgaflrsVZhhZRouvpxrKXFZam\nwwPLFtNfPtJXvMLuHjKfYyaRhreNSWSzOvDpqHCGcqllACNPGHxReeFUCmAqIKXYytsSQwIxJzNiiUtgebVuwRmWpRALLyKAzyDPvgIGxALSaeeTIqm\n",
"abcdefghijklmnopqrstuvwxyz\nqrsimtabuvzhnwcdefgjklxyop\n",
"zzzzz\nZZZZZ\n",
"zzzZZZ\nZZZzzZ\n",
"ncMeXssLHS\nuwyeMcaFatpInZVdEYpwJQSnVxLK\n",
"abcdefghijklmnopqrstuvwxyz\nABCDEFGHIJKLMNOPQRSTUVWXYZ\n",
"r\nAq\n",
"CbAdD\ndecbde\n",
"Adc\neadeabcac\n",
"DBAdeb\ndeaabcddadea\n",
"l\nMPHJYHBrlUOSWSDTPHDBmFYNwfkLTDPpMsjVAbPF\n",
"Dccb\nbedeb\n",
"EDCED\nabdcaebee\n",
"maZFXKrxpvuoRZhhZVsrlfagvxypZIAHrMHWMWGyNqlVWRDdGxAEyGPRWWfbVbvTgewEdAotcurjmecOvvzOGfbdpxWFRCmBNipD\nwwPLFtNfPtJXvMLuHjKfYyaRhreNSWSzOvDpqHCGcqllACNPGHxReeFUCmAqIKXYytsSQwIxJzNiiUtgebVuwRmWpRALLyKAzyDPvgIGxALSaeeTIqm\n",
"abcdefghiiklmnopqrstuvwxyz\nqrsimtabuvzhnwcdefgjklxyop\n",
"ndMeXssLHS\nuwyeMcaFatpInZVdEYpwJQSnVxLK\n",
"abcdefghijklmnopqrstuvwxyz\nABCDEFGHIJKLMONPQRSTUVWXYZ\n",
"AAC\nabc\n",
"AaC\nDCbA\n",
"bbacaba\nAbaCaBA\n",
"EDCED\nabdcaebed\n",
"maZFXKrxpvuoRZhhZVsrlfagvxypZIAHrMHXMWGyNqlVWRDdGxAEyGPRWWfbVbvTgewEdAotcurjmecOvvzOGfbdpxWFRCmBNipD\nwwPLFtNfPtJXvMLuHjKfYyaRhreNSWSzOvDpqHCGcqllACNPGHxReeFUCmAqIKXYytsSQwIxJzNiiUtgebVuwRmWpRALLyKAzyDPvgIGxALSaeeTIqm\n",
"abcdefghijklmnppqrstuvwxyz\nABCDEFGHIJKLMONPQRSTUVWXYZ\n",
"DdAbC\ndeccde\n",
"maZFXKrxpvuoRZhhZVsrlfagvxypZIAHrMHXMWGyNqlVWRDdGxAEyGPRWWfbVbvTgewEcAotcurjmecOvvzOGfbdpxWFRCmBNipD\nwwPLFtNfPtJXvMLuHjKfYyaRhreNSWSzOvDpqHCGcqllACNPGHxReeFUCmAqIKXYytsSQwIxJzNiiUtgebVuwRmWpRALLyKAzyDPvgIGxALSaeeTIqm\n",
"abcdefghiiklmnopqrstuuwxyz\npoyxlkjgfedcwnhzvubatmisrq\n",
"abcdefghijklnnppqrstuvwxyz\nABCDEFGHIJKLMONPQRSTUVWXYZ\n",
"abcdefghiiklmnopqrstuuwxyz\npoyxlkjgfedcwnhyvubatmisrq\n",
"CAA\ndba\n",
"bacdefghiiklmnopqrssuuwxyz\npoyxlkjgfedcwnhyvubatmisrq\n",
"zyxwvutsrqppnnlkjihgfedcba\nABCDEFGTIJKMMONPQRSHUVWXYZ\n",
"bacdefghiiklmnopqrssuuwxyz\npoyxmkjgfedcwnhyvubatmisrq\n",
"a\nC\n",
"s\nAq\n",
"DdAbC\ndecbde\n",
"Adb\neadeabcac\n",
"DBAbed\ndeaabcddadea\n",
"k\nFPbAVjsMpPDTLkfwNYFmBDHPTDSWSOUlrBHYJHPM\n",
"bccD\nbedeb\n",
"abcdefghiiklmnopqrstuvwxyz\npoyxlkjgfedcwnhzvubatmisrq\n",
"ndMeXssLHS\nuwzeMcaFatpInZVdEYpwJQSnVxLK\n",
"CAA\nabc\n",
"AaC\nDDbA\n",
"s\nqA\n",
"Bdb\neadeabcac\n",
"DBAbed\ndeacbaddadea\n",
"k\nFPbAVjsMpPDDLkfwNYFmBDHPTTSWSOUlrBHYJHPM\n",
"bccD\nbedea\n",
"ECCED\nabdcaebed\n",
"SHLssXeMdn\nuwzeMcaFatpInZVdEYpwJQSnVxLK\n",
"CAA\ncba\n",
"s\nAp\n",
"DdAbC\nedcced\n",
"bdB\neadeabcac\n",
"bBADed\ndeacbaddadea\n",
"k\nFPWAVjsMpPDDLkfwNYFmBDHPTTSbSOUlrBHYJHPM\n",
"bccD\ndebea\n",
"ECCED\ndebeacdba\n",
"maZFXKrxpvuoPZhhZVsrlfagvxypZIAHrMHXMWGyNqlVWRDdGxAEyGRRWWfbVbvTgewEcAotcurjmecOvvzOGfbdpxWFRCmBNipD\nwwPLFtNfPtJXvMLuHjKfYyaRhreNSWSzOvDpqHCGcqllACNPGHxReeFUCmAqIKXYytsSQwIxJzNiiUtgebVuwRmWpRALLyKAzyDPvgIGxALSaeeTIqm\n",
"SHLssWeMdn\nuwzeMcaFatpInZVdEYpwJQSnVxLK\n",
"zyxwvutsrqppnnlkjihgfedcba\nABCDEFGHIJKLMONPQRSTUVWXYZ\n",
"s\npA\n",
"CbAdD\nedcced\n",
"bdB\nbadeaecac\n",
"bBADed\naedaddabcaed\n",
"k\nFPWAVjsMpPDDLkfwNYFmSDHPTTBbSOUlrBHYJHPM\n",
"bccD\ndebeb\n",
"CECED\ndebeacdba\n",
"DpiNBmCRFWxpdbfGOzvvOcemjructoAcEwegTvbVbfWWRRGyEAxGdDRWVlqNyGWMXHMrHAIZpyxvgaflrsVZhhZPouvpxrKXFZam\nwwPLFtNfPtJXvMLuHjKfYyaRhreNSWSzOvDpqHCGcqllACNPGHxReeFUCmAqIKXYytsSQwIxJzNiiUtgebVuwRmWpRALLyKAzyDPvgIGxALSaeeTIqm\n",
"bacdefghiiklmnopqrstuuwxyz\npoyxlkjgfedcwnhyvubatmisrq\n",
"SHLssWeMdn\nuwzeMcaFatpInYVdEZpwJQSnVxLK\n",
"zyxwvutsrqppnnlkjihgfedcba\nABCDEFGTIJKLMONPQRSHUVWXYZ\n",
"BAA\ndba\n",
"t\nAp\n",
"CbAdD\nedcded\n",
"bdC\nbadeaecac\n",
"l\nFPWAVjsMpPDDLkfwNYFmSDHPTTBbSOUlrBHYJHPM\n",
"Dccb\ndebeb\n",
"CECDE\ndebeacdba\n",
"DpiNBmCRFWxpdbfGOzvvOcemjructoAcEwegTvbVbfWWRRGyEAxGdDRWVlqNyGWMXHMrHAIZpyxvgaflrsVZhhZPpuvoxrKXFZam\nwwPLFtNfPtJXvMLuHjKfYyaRhreNSWSzOvDpqHCGcqllACNPGHxReeFUCmAqIKXYytsSQwIxJzNiiUtgebVuwRmWpRALLyKAzyDPvgIGxALSaeeTIqm\n",
"SHKssWeMdn\nuwzeMcaFatpInYVdEZpwJQSnVxLK\n",
"AAB\ndba\n",
"u\nAp\n",
"DdAbC\nedcded\n",
"Cdb\nbadeaecac\n",
"l\nFPWAVjsMpPDDLkfwNYFmSDHPTTBbSOUlrBHYJHPN\n",
"Dccb\ndbbee\n",
"EDCEC\ndebeacdba\n",
"maZFXKrxovupPZhhZVsrlfagvxypZIAHrMHXMWGyNqlVWRDdGxAEyGRRWWfbVbvTgewEcAotcurjmecOvvzOGfbdpxWFRCmBNipD\nwwPLFtNfPtJXvMLuHjKfYyaRhreNSWSzOvDpqHCGcqllACNPGHxReeFUCmAqIKXYytsSQwIxJzNiiUtgebVuwRmWpRALLyKAzyDPvgIGxALSaeeTIqm\n",
"ndMeWssKHS\nuwzeMcaFatpInYVdEZpwJQSnVxLK\n",
"zyxwvutsrqppnnlkjihgfedcba\nABCDEFGTIJLMMONPQRSHUVWXYZ\n",
"AAB\nbda\n",
"t\npA\n",
"DdAbC\neccded\n",
"bdC\nbadeaacec\n",
"l\nFPWAVjsMpPDDLkfwNYFmSDHPTTBcSOUlrBHYJHPN\n",
"Dccb\ndabee\n",
"EECDC\ndebeacdba\n",
"DpiNBmCRFWxpdbfGOzvvOcemjructoAcEwegTvbVbfWWRRGyEAxGdDRWVlqNyGWMXHMrHAIZpyxvgaflrsVZhhZPpuvoxrKXFZam\nmqITeeaSLAxGIgvPDyzAKyLLARpWmRwuVbegtUiiNzJxIwQSstyYXKIqAmCUFeeRxHGPNCAllqcGCHqpDvOzSWSNerhRayYfKjHuLMvXJtPfNtFLPww\n",
"bacdefghiiklmnopqrssuuwxyz\npoyxmkjgfedcwnhyvubasmisrq\n"
],
"outputs": [
"0 3\n",
"3 0\n",
"3 4\n",
"0 0\n",
"2 2\n",
"0 0\n",
"2 1\n",
"3 2\n",
"0 3\n",
"1 0\n",
"1 0\n",
"0 4\n",
"66 12\n",
"26 0\n",
"0 5\n",
"5 1\n",
"6 1\n",
"0 26\n",
"0 0\n",
"2 2\n",
"2 1\n",
"3 2\n",
"1 0\n",
"1 1\n",
"0 4\n",
"66 12\n",
"25 0\n",
"6 1\n",
"0 26\n",
"0 2\n",
"2 0\n",
"3 3\n",
"0 5\n",
"67 11\n",
"0 25\n",
"1 2\n",
"67 12\n",
"24 0\n",
"0 24\n",
"23 0\n",
"0 1\n",
"22 0\n",
"0 23\n",
"21 0\n",
"0 0\n",
"0 0\n",
"2 2\n",
"2 1\n",
"3 2\n",
"1 0\n",
"1 1\n",
"25 0\n",
"6 1\n",
"0 2\n",
"1 0\n",
"0 0\n",
"2 0\n",
"3 2\n",
"1 0\n",
"1 1\n",
"0 4\n",
"6 1\n",
"0 2\n",
"0 0\n",
"1 2\n",
"2 0\n",
"3 2\n",
"1 0\n",
"1 1\n",
"0 4\n",
"67 12\n",
"6 1\n",
"0 24\n",
"0 0\n",
"1 2\n",
"2 0\n",
"3 2\n",
"1 0\n",
"1 1\n",
"0 4\n",
"67 12\n",
"23 0\n",
"6 1\n",
"0 24\n",
"0 2\n",
"0 0\n",
"1 2\n",
"2 1\n",
"1 0\n",
"1 1\n",
"0 4\n",
"67 12\n",
"6 1\n",
"0 2\n",
"0 0\n",
"1 2\n",
"2 1\n",
"1 0\n",
"1 1\n",
"0 4\n",
"67 12\n",
"6 1\n",
"0 23\n",
"0 2\n",
"0 0\n",
"1 2\n",
"2 1\n",
"1 0\n",
"1 1\n",
"0 4\n",
"67 12\n",
"22 0\n"
]
}
|
Little Tanya decided to present her dad a postcard on his Birthday. She has already created a message — string s of length n, consisting of uppercase and lowercase English letters. Tanya can't write yet, so she found a newspaper and decided to cut out the letters and glue them into the postcard to achieve string s. The newspaper contains string t, consisting of uppercase and lowercase English letters. We know that the length of string t greater or equal to the length of the string s.
The newspaper may possibly have too few of some letters needed to make the text and too many of some other letters. That's why Tanya wants to cut some n letters out of the newspaper and make a message of length exactly n, so that it looked as much as possible like s. If the letter in some position has correct value and correct letter case (in the string s and in the string that Tanya will make), then she shouts joyfully "YAY!", and if the letter in the given position has only the correct value but it is in the wrong case, then the girl says "WHOOPS".
Tanya wants to make such message that lets her shout "YAY!" as much as possible. If there are multiple ways to do this, then her second priority is to maximize the number of times she says "WHOOPS". Your task is to help Tanya make the message.
Input
The first line contains line s (1 ≤ |s| ≤ 2·105), consisting of uppercase and lowercase English letters — the text of Tanya's message.
The second line contains line t (|s| ≤ |t| ≤ 2·105), consisting of uppercase and lowercase English letters — the text written in the newspaper.
Here |a| means the length of the string a.
Output
Print two integers separated by a space:
* the first number is the number of times Tanya shouts "YAY!" while making the message,
* the second number is the number of times Tanya says "WHOOPS" while making the message.
Examples
Input
AbC
DCbA
Output
3 0
Input
ABC
abc
Output
0 3
Input
abacaba
AbaCaBA
Output
3 4
|
{
"inputs": [
"4 2 2 2\n3\n3 2\n5 3\n2 4",
"1 1 6 5\n3\n3 2\n5 3\n2 4",
"3 5 6 4\n3\n3 2\n5 3\n2 4",
"4 2 2 2\n3\n3 0\n5 3\n2 4",
"0 1 6 5\n3\n3 2\n5 3\n2 4",
"3 5 6 5\n3\n3 2\n5 3\n2 4",
"0 1 6 8\n3\n3 2\n5 3\n2 4",
"3 1 6 5\n3\n3 4\n5 3\n2 4",
"4 2 2 2\n3\n3 2\n5 3\n0 4",
"1 1 6 5\n3\n3 2\n5 3\n2 5",
"4 0 2 2\n3\n3 0\n5 3\n2 4",
"0 1 6 6\n3\n3 2\n5 3\n2 4",
"0 1 6 8\n3\n3 2\n9 3\n2 4",
"0 1 1 8\n3\n1 2\n5 3\n2 4",
"0 2 6 8\n3\n1 1\n5 3\n2 4",
"3 5 2 5\n3\n3 2\n10 3\n2 4",
"0 1 6 6\n3\n3 2\n9 3\n2 4",
"0 2 3 8\n3\n1 1\n5 3\n2 4",
"3 5 6 4\n3\n3 2\n5 3\n2 3",
"0 1 1 8\n3\n2 2\n5 1\n2 4",
"4 1 6 5\n3\n3 7\n5 3\n2 2",
"3 4 2 5\n3\n6 2\n10 3\n2 4",
"1 1 6 6\n3\n3 3\n9 3\n2 4",
"4 0 2 1\n3\n3 1\n10 1\n2 4",
"1 1 6 0\n3\n3 3\n9 1\n2 4",
"5 1 6 5\n3\n8 7\n9 3\n3 2",
"10 0 2 4\n3\n-1 3\n10 2\n2 4",
"5 1 3 4\n3\n-1 0\n10 2\n3 4",
"0 2 2 14\n3\n3 2\n5 2\n0 3",
"0 1 2 14\n3\n3 2\n5 2\n0 3",
"0 1 2 22\n3\n3 2\n5 0\n0 3",
"1 1 2 22\n3\n3 2\n5 0\n0 3",
"1 1 2 17\n3\n3 2\n5 0\n0 4",
"1 1 2 13\n3\n3 1\n5 -1\n-1 7",
"4 2 1 2\n3\n3 2\n5 3\n2 4",
"3 8 6 4\n3\n3 2\n5 3\n2 4",
"0 1 8 8\n3\n1 2\n5 3\n2 4",
"0 4 6 4\n3\n3 2\n5 3\n2 4",
"3 1 6 4\n3\n3 2\n5 3\n2 3",
"5 1 3 4\n3\n-1 0\n4 2\n3 4",
"-1 1 2 14\n3\n3 2\n5 1\n0 3",
"0 0 6 5\n3\n3 2\n5 3\n2 0",
"0 0 8 8\n3\n1 2\n5 3\n2 4",
"3 5 3 5\n3\n5 4\n3 2\n2 6",
"2 4 2 5\n3\n12 3\n12 3\n2 4",
"10 0 2 2\n3\n-1 3\n8 3\n2 4",
"0 1 2 17\n3\n3 3\n5 0\n0 4",
"0 1 2 17\n3\n3 2\n8 -1\n-1 4",
"1 2 6 5\n3\n3 2\n5 0\n3 4",
"0 1 1 8\n3\n0 1\n5 1\n0 4",
"14 1 2 1\n3\n1 3\n10 1\n2 4",
"9 0 2 2\n3\n-1 3\n8 3\n2 4",
"1 1 1 22\n3\n3 2\n5 0\n0 5",
"2 1 3 22\n3\n3 4\n5 0\n0 4",
"0 0 6 8\n3\n2 1\n5 0\n2 5",
"3 0 6 4\n3\n3 2\n4 3\n0 3",
"1 1 1 9\n3\n1 2\n5 2\n2 4",
"6 1 2 5\n3\n3 5\n5 1\n4 2",
"3 1 3 22\n3\n3 4\n5 0\n0 4",
"1 1 2 26\n3\n6 1\n9 -1\n0 7",
"0 1 1 11\n3\n-1 1\n5 2\n2 5",
"0 1 0 5\n3\n3 7\n5 1\n0 2",
"3 8 11 4\n3\n3 2\n4 3\n0 3",
"9 0 4 0\n3\n-1 0\n11 1\n4 0",
"1 1 1 26\n3\n6 1\n9 -1\n-1 7",
"0 1 1 9\n3\n1 1\n5 2\n1 4",
"14 1 1 5\n3\n8 7\n14 2\n4 0",
"0 2 1 22\n3\n3 2\n3 0\n0 2",
"0 2 3 16\n3\n1 1\n0 2\n3 10",
"0 1 0 15\n3\n0 1\n5 3\n2 2",
"4 2 2 2\n3\n3 0\n5 5\n2 4",
"3 5 6 5\n3\n3 4\n5 3\n2 4",
"0 1 6 8\n3\n1 2\n5 3\n2 4",
"0 1 6 8\n3\n1 1\n5 3\n2 4",
"3 4 6 4\n3\n3 2\n5 3\n2 4",
"3 5 6 5\n3\n3 2\n10 3\n2 4",
"3 5 6 5\n3\n5 4\n5 3\n2 4",
"3 1 6 5\n3\n3 7\n5 3\n2 4",
"4 2 2 2\n3\n4 2\n5 3\n0 4",
"3 4 6 4\n3\n3 2\n5 3\n2 3",
"4 0 2 2\n3\n3 0\n5 1\n2 4",
"0 1 6 6\n3\n3 2\n5 3\n0 4",
"3 5 6 5\n3\n5 4\n5 2\n2 4",
"0 1 1 8\n3\n1 2\n5 1\n2 4",
"3 1 6 5\n3\n3 7\n5 3\n2 2",
"4 2 2 2\n3\n4 2\n1 3\n0 4",
"4 0 2 2\n3\n3 0\n10 1\n2 4",
"0 1 6 6\n3\n3 2\n9 3\n0 4",
"3 5 2 5\n3\n6 2\n10 3\n2 4",
"0 1 6 6\n3\n3 3\n9 3\n2 4",
"3 5 6 5\n3\n5 4\n3 2\n2 4",
"0 2 2 8\n3\n1 1\n5 3\n2 4",
"4 2 2 2\n3\n0 2\n1 3\n0 4",
"4 0 2 2\n3\n3 1\n10 1\n2 4",
"0 1 6 6\n3\n5 2\n9 3\n0 4",
"0 1 1 8\n3\n2 1\n5 1\n2 4",
"6 1 6 5\n3\n3 7\n5 3\n2 2",
"0 2 2 8\n3\n1 1\n5 3\n3 4",
"4 2 2 0\n3\n0 2\n1 3\n0 4",
"0 1 6 6\n3\n5 2\n9 3\n0 5",
"3 4 2 5\n3\n6 3\n10 3\n2 4",
"1 1 6 6\n3\n3 3\n9 1\n2 4",
"0 1 1 8\n3\n0 1\n5 1\n2 4"
],
"outputs": [
"211.415926535897938",
"891.415926535897938",
"400.000000000000000",
"200.000000000000\n",
"991.415926535898\n",
"300.000000000000\n",
"1291.415926535898\n",
"695.707963267949\n",
"211.415926535898\n",
"891.415926535898\n",
"395.707963267949\n",
"1091.415926535898\n",
"1295.707963267949\n",
"795.707963267949\n",
"1195.707963267949\n",
"100.000000000000\n",
"1095.707963267949\n",
"895.707963267949\n",
"400.000000000000\n",
"800.000000000000\n",
"595.707963267949\n",
"195.707963267949\n",
"995.707963267949\n",
"295.707963267949\n",
"600.000000000000\n",
"500.000000000000\n",
"1191.415926535898\n",
"495.707963267949\n",
"1395.707963267949\n",
"1495.707963267949\n",
"2295.707963267949\n",
"2200.000000000000\n",
"1700.000000000000\n",
"1300.000000000000\n",
"311.415926535898\n",
"700.000000000000\n",
"1491.415926535898\n",
"611.415926535898\n",
"591.415926535898\n",
"491.415926535898\n",
"1595.707963267949\n",
"1087.123889803847\n",
"1591.415926535898\n",
"0.000000000000\n",
"111.415926535898\n",
"1000.000000000000\n",
"1795.707963267949\n",
"1800.000000000000\n",
"791.415926535898\n",
"807.123889803847\n",
"1211.415926535898\n",
"900.000000000000\n",
"2100.000000000000\n",
"2195.707963267949\n",
"1391.415926535898\n",
"691.415926535898\n",
"811.415926535898\n",
"787.123889803847\n",
"2111.415926535898\n",
"2600.000000000000\n",
"1100.000000000000\n",
"411.415926535898\n",
"1200.000000000000\n",
"511.415926535898\n",
"2500.000000000000\n",
"907.123889803847\n",
"1695.707963267949\n",
"2095.707963267949\n",
"1691.415926535898\n",
"1411.415926535898\n",
"200.000000000000\n",
"300.000000000000\n",
"1291.415926535898\n",
"1291.415926535898\n",
"300.000000000000\n",
"300.000000000000\n",
"300.000000000000\n",
"695.707963267949\n",
"211.415926535898\n",
"300.000000000000\n",
"395.707963267949\n",
"1091.415926535898\n",
"300.000000000000\n",
"795.707963267949\n",
"695.707963267949\n",
"211.415926535898\n",
"395.707963267949\n",
"1095.707963267949\n",
"100.000000000000\n",
"1095.707963267949\n",
"300.000000000000\n",
"795.707963267949\n",
"200.000000000000\n",
"395.707963267949\n",
"1095.707963267949\n",
"800.000000000000\n",
"400.000000000000\n",
"800.000000000000\n",
"400.000000000000\n",
"1095.707963267949\n",
"195.707963267949\n",
"995.707963267949\n",
"795.707963267949\n"
]
}
|
In the city of Nevermore, there are 10^8 streets and 10^8 avenues, both numbered from 0 to 10^8-1. All streets run straight from west to east, and all avenues run straight from south to north. The distance between neighboring streets and between neighboring avenues is exactly 100 meters.
Every street intersects every avenue. Every intersection can be described by pair (x, y), where x is avenue ID and y is street ID.
There are N fountains in the city, situated at intersections (X_i, Y_i). Unlike normal intersections, there's a circle with radius 10 meters centered at the intersection, and there are no road parts inside this circle.
The picture below shows an example of how a part of the city with roads and fountains may look like.
1f931bf0c98ec6f07e612b0282cdb094.png
City governors don't like encountering more than one fountain while moving along the same road. Therefore, every street contains at most one fountain on it, as well as every avenue.
Citizens can move along streets, avenues and fountain perimeters. What is the shortest distance one needs to cover in order to get from intersection (x_1, y_1) to intersection (x_2, y_2)?
Constraints
* 0 \leq x_1, y_1, x_2, y_2 < 10^8
* 1 \leq N \leq 200,000
* 0 \leq X_i, Y_i < 10^8
* X_i \neq X_j for i \neq j
* Y_i \neq Y_j for i \neq j
* Intersections (x_1, y_1) and (x_2, y_2) are different and don't contain fountains.
* All input values are integers.
Input
Input is given from Standard Input in the following format:
x_1 y_1 x_2 y_2
N
X_1 Y_1
X_2 Y_2
:
X_N Y_N
Output
Print the shortest possible distance one needs to cover in order to get from intersection (x_1, y_1) to intersection (x_2, y_2), in meters. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^{-11}.
Examples
Input
1 1 6 5
3
3 2
5 3
2 4
Output
891.415926535897938
Input
3 5 6 4
3
3 2
5 3
2 4
Output
400.000000000000000
Input
4 2 2 2
3
3 2
5 3
2 4
Output
211.415926535897938
|
{
"inputs": [
"1\n3 3\n\nSAMPLE",
"10\n97654 99999\n97655 99998\n97656 99997\n97657 99996\n97658 99995\n97659 99994\n97660 99993\n97661 99992\n97662 99991\n97663 99990",
"10\n23 100000\n24 99999\n25 99998\n26 99997\n27 99996\n28 99995\n29 99994\n30 99993\n31 99992\n32 99991",
"10\n23 100000\n24 99999\n25 99998\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 99992\n32 99991",
"10\n23 100000\n24 99999\n25 99998\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 114698\n32 99991",
"10\n23 100000\n24 99999\n25 81271\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 114698\n32 99991",
"10\n23 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 114698\n32 99991",
"10\n23 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 99993\n31 114698\n32 99991",
"10\n23 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 99993\n31 114698\n41 99991",
"10\n23 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 196529\n31 114698\n41 99991",
"10\n16 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 196529\n31 114698\n41 99991",
"10\n16 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n16 100000\n24 99999\n25 81271\n10 10221\n27 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n12 100000\n24 99999\n25 81271\n10 10221\n27 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n12 100000\n24 99999\n25 81271\n10 10221\n36 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n10 10221\n36 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n10 10221\n36 175149\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n10 10221\n36 175149\n28 99995\n29 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n10 10221\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n14 10221\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 127272\n25 81271\n14 10221\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 127272\n50 81271\n14 10221\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 29296\n50 81271\n14 10221\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 29296\n50 81271\n14 864\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 29296\n50 81271\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 29296\n50 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 46482\n50 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 46482\n50 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 39787\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 114408\n14 864\n36 175149\n55 99995\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 114408\n14 864\n36 175149\n55 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n111 114408\n14 864\n36 175149\n55 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n111 114408\n14 864\n20 175149\n55 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n35 100000\n24 46482\n111 114408\n14 864\n20 175149\n55 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n35 100000\n24 46482\n111 135348\n14 864\n20 175149\n55 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n35 100000\n32 46482\n111 135348\n14 864\n20 175149\n55 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n97654 99999\n81840 99998\n97656 99997\n97657 99996\n97658 99995\n97659 99994\n97660 99993\n97661 99992\n97662 99991\n97663 99990",
"10\n23 100000\n24 99999\n25 99998\n26 99997\n27 99996\n28 99995\n29 99994\n30 99993\n31 99992\n10 99991",
"1\n3 3\n\nSAMPLF",
"10\n9 100000\n24 99999\n25 99998\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 99992\n32 99991",
"10\n36 100000\n24 99999\n25 99998\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 114698\n32 99991",
"10\n23 100000\n24 99999\n25 81271\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 114698\n32 7763",
"10\n23 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 31400\n32 99991",
"10\n23 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 99993\n31 114698\n19 99991",
"10\n23 100000\n24 99999\n25 9083\n10 99997\n27 99996\n28 99995\n29 13560\n59 99993\n31 114698\n41 99991",
"10\n23 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 10919\n31 114698\n41 99991",
"10\n16 100000\n24 99999\n29 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 196529\n31 114698\n41 99991",
"10\n16 100010\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n16 100000\n24 99999\n25 81271\n10 14738\n27 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n12 100000\n24 99999\n25 81271\n10 7539\n27 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n12 100000\n24 99999\n25 81271\n10 10221\n36 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 147661",
"10\n19 100000\n24 99999\n25 81271\n10 10221\n36 99996\n39 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n1 100000\n24 99999\n25 81271\n10 10221\n36 175149\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 150137\n25 81271\n10 10221\n36 175149\n28 99995\n29 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n10 11688\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n14 10221\n36 175149\n28 99995\n19 14854\n59 196529\n11 114698\n41 99991",
"10\n19 100000\n24 127272\n25 81271\n14 10221\n36 175149\n28 99995\n19 16219\n59 196529\n21 114698\n41 99991",
"10\n19 110000\n24 127272\n50 81271\n14 10221\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 24418\n50 81271\n14 10221\n36 175149\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 29296\n50 81271\n14 864\n36 175149\n28 99995\n19 14854\n59 196529\n21 48010\n41 99991",
"10\n19 100000\n24 29296\n50 81271\n14 864\n36 175149\n55 99995\n19 14854\n59 87794\n21 114698\n41 99991",
"10\n19 100000\n24 29296\n50 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n41 13382",
"10\n19 100000\n24 46482\n50 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n8 99991",
"10\n19 100000\n24 46482\n76 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 114408\n14 1143\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 114408\n14 864\n36 175149\n73 99995\n19 14854\n59 39787\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n49 114408\n14 864\n36 175149\n55 99995\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 114408\n5 864\n36 175149\n55 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n19 100000\n24 3032\n111 114408\n14 864\n36 175149\n55 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n111 114408\n14 864\n20 175149\n55 16259\n19 16485\n92 39787\n21 114698\n2 99991",
"10\n35 100000\n24 46482\n111 114408\n14 864\n20 175149\n55 16259\n19 14854\n148 39787\n21 114698\n2 99991",
"10\n35 100000\n24 46482\n111 135348\n14 864\n20 175149\n21 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n35 100000\n32 46482\n111 135348\n14 864\n20 175149\n65 16259\n19 14854\n92 39787\n21 114698\n2 99991",
"10\n23 100000\n24 99999\n14 99998\n26 99997\n27 99996\n28 99995\n29 99994\n30 99993\n31 99992\n10 99991",
"10\n9 100000\n24 99999\n25 99998\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n23 99992\n32 99991",
"10\n36 100000\n24 99999\n25 99998\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 114698\n9 99991",
"10\n23 100000\n24 99999\n25 81271\n26 99997\n27 99996\n28 99995\n29 99994\n59 99993\n51 114698\n32 7763",
"10\n23 100000\n24 99999\n31 81271\n10 99997\n27 99996\n28 99995\n29 99994\n59 99993\n31 31400\n32 99991",
"10\n23 100000\n24 99999\n25 81271\n10 99997\n27 99996\n28 182806\n29 13560\n59 99993\n31 114698\n19 99991",
"10\n23 100000\n24 99999\n25 9083\n10 99997\n27 99996\n28 99995\n29 13560\n59 99993\n31 114698\n23 99991",
"10\n23 100000\n24 99999\n25 81271\n17 99997\n27 99996\n28 99995\n29 13560\n59 10919\n31 114698\n41 99991",
"10\n16 100000\n1 99999\n29 81271\n10 99997\n27 99996\n28 99995\n29 13560\n59 196529\n31 114698\n41 99991",
"10\n16 100010\n24 99999\n25 81271\n10 99997\n27 99996\n28 99995\n29 13560\n107 196529\n21 114698\n41 99991",
"10\n16 100000\n24 99999\n25 81271\n10 14738\n27 99996\n28 99995\n29 22121\n59 196529\n21 114698\n41 99991",
"10\n12 100000\n24 99999\n25 81271\n10 7539\n27 194052\n28 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n12 100001\n24 99999\n25 81271\n10 10221\n36 99996\n28 99995\n29 13560\n59 196529\n21 114698\n41 147661",
"10\n19 100000\n48 99999\n25 81271\n10 10221\n36 99996\n39 99995\n29 13560\n59 196529\n21 114698\n41 99991",
"10\n1 100000\n24 99999\n25 81271\n10 10221\n36 175149\n28 99995\n29 13560\n59 72528\n21 114698\n41 99991",
"10\n19 100000\n24 150137\n25 81271\n10 10221\n36 175149\n28 99995\n29 14854\n72 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n10 11688\n36 175149\n28 99995\n24 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 99999\n25 81271\n14 10221\n36 175149\n35 99995\n19 14854\n59 196529\n11 114698\n41 99991",
"10\n19 100000\n24 127272\n25 81271\n14 2068\n36 175149\n28 99995\n19 16219\n59 196529\n21 114698\n41 99991",
"10\n19 110000\n24 127272\n50 81271\n14 10221\n36 224681\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 24418\n50 81271\n14 10221\n36 182662\n28 99995\n19 14854\n59 196529\n21 114698\n41 99991",
"10\n19 100000\n24 29296\n50 81271\n14 864\n36 189203\n28 99995\n19 14854\n59 196529\n21 48010\n41 99991",
"10\n19 100000\n24 1112\n50 81271\n14 864\n36 175149\n55 99995\n19 14854\n59 87794\n21 114698\n41 99991",
"10\n19 100000\n24 29296\n50 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n41 24943",
"10\n29 100000\n24 46482\n50 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n8 99991",
"10\n19 100000\n9 46482\n76 114408\n14 864\n36 175149\n55 99995\n19 14854\n59 196529\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 114408\n14 1143\n36 175149\n55 68609\n19 14854\n59 196529\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n67 11655\n14 864\n36 175149\n73 99995\n19 14854\n59 39787\n21 114698\n2 99991",
"10\n19 100000\n24 46482\n49 114408\n14 864\n36 298252\n55 99995\n19 14854\n92 39787\n21 114698\n2 99991"
],
"outputs": [
"6\n",
"991879483\n601526804\n436424908\n382445914\n829121437\n542869638\n229051652\n421432812\n703201416\n235932927\n",
"813663176\n831992858\n962669731\n308395250\n306816746\n762324486\n627450826\n158487841\n781054085\n287928459\n",
"813663176\n831992858\n962669731\n308395250\n306816746\n762324486\n627450826\n750605912\n781054085\n287928459\n",
"813663176\n831992858\n962669731\n308395250\n306816746\n762324486\n627450826\n750605912\n625473937\n287928459\n",
"813663176\n831992858\n250242083\n308395250\n306816746\n762324486\n627450826\n750605912\n625473937\n287928459\n",
"813663176\n831992858\n250242083\n182391403\n306816746\n762324486\n627450826\n750605912\n625473937\n287928459\n",
"813663176\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n750605912\n625473937\n287928459\n",
"813663176\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n750605912\n625473937\n449945554\n",
"813663176\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n177132007\n625473937\n449945554\n",
"957765120\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n177132007\n625473937\n449945554\n",
"957765120\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"957765120\n831992858\n250242083\n406350719\n306816746\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"734275823\n831992858\n250242083\n406350719\n306816746\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"734275823\n831992858\n250242083\n406350719\n193713672\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n406350719\n193713672\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n406350719\n287423269\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n406350719\n287423269\n762324486\n453890912\n177132007\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n406350719\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n715807755\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n685398573\n250242083\n715807755\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n685398573\n890619901\n715807755\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n923373374\n890619901\n715807755\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n923373374\n890619901\n989973817\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n923373374\n890619901\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n923373374\n190779901\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n218082519\n190779901\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n218082519\n190779901\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n998100027\n",
"21793049\n218082519\n541091229\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n998100027\n",
"21793049\n218082519\n541091229\n989973817\n287423269\n287933742\n144169489\n578850063\n781226525\n998100027\n",
"21793049\n218082519\n541091229\n989973817\n287423269\n287933742\n144169489\n436822706\n781226525\n998100027\n",
"21793049\n218082519\n541091229\n989973817\n287423269\n48195483\n144169489\n436822706\n781226525\n998100027\n",
"21793049\n218082519\n108171788\n989973817\n287423269\n48195483\n144169489\n436822706\n781226525\n998100027\n",
"21793049\n218082519\n108171788\n989973817\n497917156\n48195483\n144169489\n436822706\n781226525\n998100027\n",
"484035074\n218082519\n108171788\n989973817\n497917156\n48195483\n144169489\n436822706\n781226525\n998100027\n",
"484035074\n218082519\n529628327\n989973817\n497917156\n48195483\n144169489\n436822706\n781226525\n998100027\n",
"484035074\n940846617\n529628327\n989973817\n497917156\n48195483\n144169489\n436822706\n781226525\n998100027\n",
"991879483\n792858873\n436424908\n382445914\n829121437\n542869638\n229051652\n421432812\n703201416\n235932927\n",
"813663176\n831992858\n962669731\n308395250\n306816746\n762324486\n627450826\n158487841\n781054085\n13609499\n",
"6\n",
"743510330\n831992858\n962669731\n308395250\n306816746\n762324486\n627450826\n750605912\n781054085\n287928459\n",
"565833708\n831992858\n962669731\n308395250\n306816746\n762324486\n627450826\n750605912\n625473937\n287928459\n",
"813663176\n831992858\n250242083\n308395250\n306816746\n762324486\n627450826\n750605912\n625473937\n419907908\n",
"813663176\n831992858\n250242083\n182391403\n306816746\n762324486\n627450826\n750605912\n3603610\n287928459\n",
"813663176\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n750605912\n625473937\n886567671\n",
"813663176\n831992858\n242904177\n182391403\n306816746\n762324486\n248496097\n750605912\n625473937\n449945554\n",
"813663176\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n359117451\n625473937\n449945554\n",
"957765120\n831992858\n267604944\n182391403\n306816746\n762324486\n248496097\n177132007\n625473937\n449945554\n",
"286056228\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"957765120\n831992858\n250242083\n288139493\n306816746\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"734275823\n831992858\n250242083\n807516848\n306816746\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"734275823\n831992858\n250242083\n406350719\n193713672\n762324486\n248496097\n177132007\n781226525\n522442741\n",
"21793049\n831992858\n250242083\n406350719\n193713672\n731752356\n248496097\n177132007\n781226525\n449945554\n",
"100000\n831992858\n250242083\n406350719\n287423269\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"21793049\n55532596\n250242083\n406350719\n287423269\n762324486\n453890912\n177132007\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n505735753\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n715807755\n287423269\n762324486\n144169489\n177132007\n938376785\n449945554\n",
"21793049\n685398573\n250242083\n715807755\n287423269\n762324486\n688366939\n177132007\n781226525\n449945554\n",
"838688401\n685398573\n890619901\n715807755\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n48183371\n890619901\n715807755\n287423269\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n923373374\n890619901\n989973817\n287423269\n762324486\n144169489\n177132007\n148608976\n449945554\n",
"21793049\n923373374\n890619901\n989973817\n287423269\n287933742\n144169489\n166014432\n781226525\n449945554\n",
"21793049\n923373374\n190779901\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n155554271\n",
"21793049\n218082519\n190779901\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n496192600\n",
"21793049\n218082519\n437843524\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n998100027\n",
"21793049\n218082519\n541091229\n569411597\n287423269\n287933742\n144169489\n177132007\n781226525\n998100027\n",
"21793049\n218082519\n541091229\n989973817\n287423269\n766474353\n144169489\n578850063\n781226525\n998100027\n",
"21793049\n218082519\n52433047\n989973817\n287423269\n287933742\n144169489\n436822706\n781226525\n998100027\n",
"21793049\n218082519\n541091229\n394829207\n287423269\n48195483\n144169489\n436822706\n781226525\n998100027\n",
"21793049\n132631432\n108171788\n989973817\n287423269\n48195483\n144169489\n436822706\n781226525\n998100027\n",
"21793049\n218082519\n108171788\n989973817\n497917156\n48195483\n117529624\n436822706\n781226525\n998100027\n",
"484035074\n218082519\n108171788\n989973817\n497917156\n48195483\n144169489\n934488207\n781226525\n998100027\n",
"484035074\n218082519\n529628327\n989973817\n497917156\n864467496\n144169489\n436822706\n781226525\n998100027\n",
"484035074\n940846617\n529628327\n989973817\n497917156\n404321882\n144169489\n436822706\n781226525\n998100027\n",
"813663176\n831992858\n148786273\n308395250\n306816746\n762324486\n627450826\n158487841\n781054085\n13609499\n",
"743510330\n831992858\n962669731\n308395250\n306816746\n762324486\n627450826\n750605912\n417252835\n287928459\n",
"565833708\n831992858\n962669731\n308395250\n306816746\n762324486\n627450826\n750605912\n625473937\n824378530\n",
"813663176\n831992858\n250242083\n308395250\n306816746\n762324486\n627450826\n750605912\n815289969\n419907908\n",
"813663176\n831992858\n699967988\n182391403\n306816746\n762324486\n627450826\n750605912\n3603610\n287928459\n",
"813663176\n831992858\n250242083\n182391403\n306816746\n252173652\n248496097\n750605912\n625473937\n886567671\n",
"813663176\n831992858\n242904177\n182391403\n306816746\n762324486\n248496097\n750605912\n625473937\n643284951\n",
"813663176\n831992858\n250242083\n822044232\n306816746\n762324486\n248496097\n359117451\n625473937\n449945554\n",
"957765120\n99999\n267604944\n182391403\n306816746\n762324486\n248496097\n177132007\n625473937\n449945554\n",
"286056228\n831992858\n250242083\n182391403\n306816746\n762324486\n248496097\n389654388\n781226525\n449945554\n",
"957765120\n831992858\n250242083\n288139493\n306816746\n762324486\n893054051\n177132007\n781226525\n449945554\n",
"734275823\n831992858\n250242083\n807516848\n261732766\n762324486\n248496097\n177132007\n781226525\n449945554\n",
"771418022\n831992858\n250242083\n406350719\n193713672\n762324486\n248496097\n177132007\n781226525\n522442741\n",
"21793049\n285678575\n250242083\n406350719\n193713672\n731752356\n248496097\n177132007\n781226525\n449945554\n",
"100000\n831992858\n250242083\n406350719\n287423269\n762324486\n248496097\n731124773\n781226525\n449945554\n",
"21793049\n55532596\n250242083\n406350719\n287423269\n762324486\n453890912\n457201690\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n505735753\n287423269\n762324486\n320503495\n177132007\n781226525\n449945554\n",
"21793049\n831992858\n250242083\n715807755\n287423269\n579745131\n144169489\n177132007\n938376785\n449945554\n",
"21793049\n685398573\n250242083\n893150592\n287423269\n762324486\n688366939\n177132007\n781226525\n449945554\n",
"838688401\n685398573\n890619901\n715807755\n159902848\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n48183371\n890619901\n715807755\n616221654\n762324486\n144169489\n177132007\n781226525\n449945554\n",
"21793049\n923373374\n890619901\n989973817\n146600552\n762324486\n144169489\n177132007\n148608976\n449945554\n",
"21793049\n694134173\n890619901\n989973817\n287423269\n287933742\n144169489\n166014432\n781226525\n449945554\n",
"21793049\n923373374\n190779901\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n924064943\n",
"77681661\n218082519\n190779901\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n496192600\n",
"21793049\n41408195\n437843524\n989973817\n287423269\n287933742\n144169489\n177132007\n781226525\n998100027\n",
"21793049\n218082519\n541091229\n569411597\n287423269\n325252630\n144169489\n177132007\n781226525\n998100027\n",
"21793049\n218082519\n63819366\n989973817\n287423269\n766474353\n144169489\n578850063\n781226525\n998100027\n",
"21793049\n218082519\n52433047\n989973817\n683789423\n287933742\n144169489\n436822706\n781226525\n998100027\n"
]
}
|
Our Friend Monk has finally found the Temple of Programming secrets. However, the door of the temple is firmly locked. Now, as per the rules of the temple, Monk needs to enter a Secret Password in a special language to unlock the door. This language, unlike English consists of K alphabets. The properties of this secret password are:
It has a length of N characters.
It is composed only of the K characters belonging to the Special language.
Each character belonging to the special language has been used at max once in the secret code.
Now, Monk has no idea about what the ideal password may be and needs you help. You need to help Monk find the total number of distinct candidate Strings for it Modulo 10^9+7.
Input Format:
The first line contains a single integer T denoting the number of test cases. Each of the next T lines contain two integers N and K denoting the length of the Secret Password and the number of characters of the Special language to be used respectively.
Output Format:
For each test case, output the number of possible distinct secret passwords Modulo 10^9+7.
Constraints:
1 ≤ T ≤ 10
1 ≤ N ≤ K ≤ 10^5
Note:
You need to print the value of each element and not their weight.
SAMPLE INPUT
1
3 3
SAMPLE OUTPUT
6
Explanation
Let's number the characters of the special language to be 1 , 2 and 3 respectively. So, all possible candidate Strings are:
123
132
213
231
312
321
So, here we have 6 possible passwords. So, the answer = 6 \% (10^9+7) =6
|
{
"inputs": [
"5\n-1 -1 1 1\n-4 0 0 4\n0 0 4 4\n-4 -4 0 0\n0 -4 4 0\n",
"4\n0 0 4 4\n-4 -4 0 0\n0 -4 4 0\n-2 -4 2 4\n",
"5\n-1 0 2 4\n1 4 4 5\n2 3 5 4\n-5 3 1 5\n0 -4 2 3\n",
"10\n-39 29 10 85\n-44 69 83 71\n-35 33 31 74\n-68 66 47 86\n77 -49 96 89\n-24 25 7 93\n-24 -35 47 -12\n85 -91 95 33\n-94 15 -70 29\n-9 28 49 54\n",
"10\n89 -10 95 -1\n9 -44 47 -10\n24 72 73 82\n-66 -19 72 34\n0 -31 14 56\n29 -66 87 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 34 77\n24 -30 48 28\n",
"5\n2 2 3 5\n-1 -2 5 -1\n-5 0 4 2\n-1 0 4 4\n-4 3 4 5\n",
"5\n-3 4 -2 5\n3 1 5 4\n-5 -3 1 2\n-1 4 4 5\n2 4 5 5\n",
"10\n17 -64 34 46\n63 27 71 32\n-20 16 95 38\n24 -96 85 46\n-86 -13 60 82\n-23 -61 88 -9\n98 -97 100 24\n-83 -47 82 54\n-8 -63 15 -39\n50 -97 53 39\n",
"8\n2 0 3 1\n3 1 4 2\n3 2 4 3\n2 0 4 3\n0 3 6 6\n-1 3 7 4\n-1 4 7 5\n-1 5 7 6\n",
"10\n1 2 3 4\n3 -4 5 0\n-1 -2 4 3\n2 2 5 4\n-2 -2 -1 -1\n-3 -5 5 -2\n-3 -5 3 -2\n4 -2 5 5\n-5 -1 2 5\n4 3 5 5\n",
"5\n-1 -3 3 5\n4 -4 5 -3\n-4 4 0 5\n4 2 5 3\n-1 0 2 2\n",
"4\n0 0 3 3\n-1 0 4 1\n-1 1 4 2\n-1 2 4 3\n",
"5\n1 -2 3 1\n2 -4 4 5\n1 -5 3 -3\n-1 1 2 3\n-3 2 -2 4\n",
"5\n-1 1 2 4\n1 4 4 5\n2 3 5 4\n-5 3 1 5\n0 -4 2 3\n",
"10\n-11 29 10 85\n-44 69 83 71\n-35 33 31 74\n-68 66 47 86\n77 -49 96 89\n-24 25 7 93\n-24 -35 47 -12\n85 -91 95 33\n-94 15 -70 29\n-9 28 49 54\n",
"10\n89 -10 95 -1\n9 -44 47 -10\n24 72 73 82\n-66 -19 72 34\n0 -31 14 56\n29 -66 87 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 34 77\n24 -22 48 28\n",
"5\n2 2 3 5\n-1 -2 2 -1\n-5 0 4 2\n-1 0 4 4\n-4 3 4 5\n",
"4\n0 0 3 3\n-1 -1 4 1\n-1 1 4 2\n-1 2 4 3\n",
"5\n-3 4 -2 5\n3 1 5 4\n-5 -3 1 2\n-1 4 4 5\n2 1 5 5\n",
"8\n2 0 3 1\n3 1 6 2\n3 2 4 3\n2 0 4 3\n0 3 6 6\n-1 3 7 4\n-1 4 7 5\n-1 5 7 6\n",
"5\n-1 -3 3 5\n4 -4 5 -3\n-1 4 0 5\n4 2 5 3\n-1 0 2 2\n",
"5\n1 -2 3 1\n2 -4 4 5\n1 -5 3 -3\n-1 1 2 3\n-3 0 -2 4\n",
"5\n-1 -1 1 1\n-4 0 0 4\n0 1 4 4\n-4 -4 0 0\n0 -4 4 0\n",
"4\n0 0 4 4\n-4 -4 0 0\n0 -4 6 0\n-2 -4 2 4\n",
"5\n-1 1 2 4\n0 4 4 5\n2 3 5 4\n-5 3 1 5\n0 -4 2 3\n",
"10\n89 -4 95 -1\n9 -44 47 -10\n24 72 73 82\n-66 -19 72 34\n0 -31 14 56\n29 -66 87 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 34 77\n24 -22 48 28\n",
"5\n2 2 5 5\n-1 -2 2 -1\n-5 0 4 2\n-1 0 4 4\n-4 3 4 5\n",
"5\n-3 4 -2 5\n3 1 5 4\n-5 -3 1 2\n-1 4 2 5\n2 1 5 5\n",
"4\n0 0 6 3\n-1 -1 4 1\n-1 1 4 2\n-1 2 4 3\n",
"5\n1 -2 3 1\n2 -4 4 4\n1 -5 3 -3\n-1 1 2 3\n-3 0 -2 4\n",
"5\n-1 -2 1 1\n-4 0 0 4\n0 1 4 4\n-4 -4 0 0\n0 -4 4 0\n",
"4\n0 0 4 4\n-4 -4 0 0\n0 -4 8 0\n-2 -4 2 4\n",
"10\n89 -4 95 -1\n9 -44 47 -10\n24 72 73 82\n-66 -19 72 34\n0 -31 14 56\n29 -66 87 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 34 77\n24 -22 61 28\n",
"5\n2 2 5 5\n-1 -2 2 -1\n-5 0 4 4\n-1 0 4 4\n-4 3 4 5\n",
"5\n-3 4 -2 5\n3 1 5 4\n-5 0 1 2\n-1 4 2 5\n2 1 5 5\n",
"4\n0 0 6 3\n-1 -1 1 1\n-1 1 4 2\n-1 2 4 3\n",
"5\n-1 -2 1 1\n-4 0 0 4\n0 0 4 4\n-4 -4 0 0\n0 -4 4 0\n",
"4\n0 0 4 4\n-3 -4 0 0\n0 -4 8 0\n-2 -4 2 4\n",
"10\n89 -4 95 -1\n9 -44 47 -10\n24 67 73 82\n-66 -19 72 34\n0 -31 14 56\n29 -66 87 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 34 77\n24 -22 61 28\n",
"5\n2 2 5 5\n-1 -2 2 -1\n-5 0 3 4\n-1 0 4 4\n-4 3 4 5\n",
"4\n0 0 6 3\n-1 0 1 1\n-1 1 4 2\n-1 2 4 3\n",
"5\n-1 -2 1 1\n-4 -1 0 4\n0 0 4 4\n-4 -4 0 0\n0 -4 4 0\n",
"10\n89 -4 95 -1\n9 -44 39 -10\n24 67 73 82\n-66 -19 72 34\n0 -31 14 56\n29 -66 87 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 34 77\n24 -22 61 28\n",
"5\n2 2 5 5\n-1 -2 0 -1\n-5 0 3 4\n-1 0 4 4\n-4 3 4 5\n",
"4\n0 0 6 3\n-1 0 1 1\n-1 0 4 2\n-1 2 4 3\n",
"5\n-1 -1 1 1\n-4 -1 0 4\n0 0 4 4\n-4 -4 0 0\n0 -4 4 0\n",
"10\n89 -4 95 -1\n9 -44 39 -10\n24 67 73 82\n-66 -19 72 34\n0 -31 14 56\n29 -66 87 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 21 77\n24 -22 61 28\n",
"4\n1 0 6 3\n-1 0 1 1\n-1 0 4 2\n-1 2 4 3\n",
"5\n-1 -1 1 1\n-4 -1 0 4\n0 0 4 4\n-4 -4 0 0\n0 -4 4 -1\n",
"10\n89 -4 95 -1\n9 -44 39 -10\n24 67 73 82\n-66 -19 34 34\n0 -31 14 56\n29 -66 87 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 21 77\n24 -22 61 28\n",
"5\n-1 -1 1 1\n-4 -1 0 4\n0 0 4 4\n-4 -4 0 0\n0 -7 4 -1\n",
"10\n89 -4 95 -1\n9 -44 39 -10\n24 67 73 82\n-66 -19 34 34\n0 -31 14 56\n29 -66 52 -11\n-63 -14 84 70\n-3 31 51 82\n5 28 21 77\n24 -22 61 28\n"
],
"outputs": [
"5",
"5",
"6",
"11",
"11",
"5",
"6",
"10",
"5",
"9",
"6",
"4",
"6",
"6\n",
"10\n",
"11\n",
"5\n",
"4\n",
"5\n",
"6\n",
"6\n",
"6\n",
"6\n",
"5\n",
"6\n",
"11\n",
"6\n",
"5\n",
"5\n",
"6\n",
"6\n",
"5\n",
"11\n",
"6\n",
"5\n",
"5\n",
"5\n",
"5\n",
"11\n",
"6\n",
"5\n",
"5\n",
"11\n",
"6\n",
"4\n",
"5\n",
"11\n",
"4\n",
"6\n",
"11\n",
"6\n",
"11\n"
]
}
|
Arkady has got an infinite plane painted in color 0. Then he draws n rectangles filled with paint with sides parallel to the Cartesian coordinate axes, one after another. The color of the i-th rectangle is i (rectangles are enumerated from 1 to n in the order he draws them). It is possible that new rectangles cover some of the previous ones completely or partially.
Count the number of different colors on the plane after Arkady draws all the rectangles.
Input
The first line contains a single integer n (1 ≤ n ≤ 100 000) — the number of rectangles.
The i-th of the next n lines contains 4 integers x_1, y_1, x_2 and y_2 (-10^9 ≤ x_1 < x_2 ≤ 10^9, -10^9 ≤ y_1 < y_2 ≤ 10^9) — the coordinates of corners of the i-th rectangle.
Output
In the single line print the number of different colors in the plane, including color 0.
Examples
Input
5
-1 -1 1 1
-4 0 0 4
0 0 4 4
-4 -4 0 0
0 -4 4 0
Output
5
Input
4
0 0 4 4
-4 -4 0 0
0 -4 4 0
-2 -4 2 4
Output
5
Note
<image> That's how the plane looks in the first sample
<image> That's how the plane looks in the second sample
0 = white, 1 = cyan, 2 = blue, 3 = purple, 4 = yellow, 5 = red.
|
{
"inputs": [
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"5\n1 2\n2 3\n3 4\n3 5\n1 2 1 2 1\n11\nQ 1\nQ 4\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 1",
"5\n1 2\n2 3\n3 4\n2 5\n1 2 1 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 1 1\nQ 1\nU 5 2\nQ 1\nQ 2\nU 5 6\nQ 2",
"5\n1 2\n2 3\n3 4\n2 5\n1 2 1 2 3\n3\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 2 2\nQ 1\nQ 2\nU 5 4\nQ 1",
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"5\n1 2\n2 3\n3 4\n2 5\n1 2 1 3 6\n11\nQ 1\nQ 2\nQ 3\nQ 7\nU 5 2\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 2",
"5\n1 2\n2 4\n3 4\n4 5\n2 2 1 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 2\nQ 2\nU 2 4\nQ 1",
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"5\n1 2\n2 4\n3 4\n3 5\n1 2 1 2 3\n9\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 4 2\nQ 1\nQ 2\nU 2 4\nQ 1",
"5\n1 2\n2 3\n3 4\n2 5\n1 4 1 2 5\n11\nQ 1\nQ 2\nQ 3\nQ 8\nU 1 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 2\nQ 2",
"5\n1 2\n2 3\n3 4\n2 5\n1 4 1 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 1 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 1\nQ 2",
"5\n1 2\n2 4\n3 4\n3 5\n1 2 1 2 3\n9\nQ 2\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 2 2\nQ 1\nQ 2\nV 2 4\nQ 1",
"5\n1 2\n2 5\n3 4\n3 5\n1 2 2 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 2 4\nQ 1",
"5\n1 2\n2 5\n3 4\n3 5\n2 2 1 2 1\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 2\nQ 2\nU 5 4\nQ 1",
"5\n1 2\n2 3\n3 4\n2 5\n1 2 2 2 6\n11\nQ 1\nQ 2\nQ 3\nQ 7\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 3",
"5\n1 2\n2 3\n2 4\n4 5\n2 2 1 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 2\nQ 3\nU 2 1\nQ 1",
"5\n1 2\n2 3\n3 4\n3 5\n2 2 1 2 1\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 3\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 3",
"5\n1 2\n2 4\n3 4\n3 5\n1 4 1 2 3\n9\nQ 2\nQ 1\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nV 2 4\nQ 1",
"5\n1 2\n2 3\n3 4\n2 5\n1 4 1 2 5\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 2 4\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 2\nQ 2",
"5\n1 2\n2 4\n3 4\n3 5\n1 2 2 2 3\n9\nQ 2\nQ 1\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 1\nV 2 4\nQ 2",
"5\n1 2\n2 3\n3 4\n2 5\n1 4 1 2 5\n11\nQ 2\nQ 2\nQ 3\nQ 4\nU 2 2\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 2\nQ 3",
"5\n1 2\n2 3\n3 4\n2 5\n2 4 1 3 5\n11\nQ 2\nQ 2\nQ 3\nQ 4\nU 2 2\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 2\nQ 2",
"5\n1 2\n2 3\n3 4\n2 5\n1 2 1 4 3\n11\nQ 2\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 3",
"5\n1 2\n2 4\n3 4\n3 5\n1 2 1 2 1\n11\nQ 1\nQ 4\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 1",
"5\n1 2\n2 3\n3 4\n4 5\n1 2 1 4 3\n11\nQ 1\nQ 2\nQ 6\nQ 5\nU 5 1\nQ 1\nU 2 2\nQ 1\nQ 2\nU 5 4\nQ 1",
"5\n1 2\n2 3\n3 4\n2 5\n1 2 1 4 6\n11\nQ 1\nQ 2\nQ 3\nQ 7\nU 5 2\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 2",
"5\n1 2\n2 4\n3 4\n4 5\n2 2 1 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 3\nQ 2\nU 2 4\nQ 1",
"5\n1 2\n2 3\n3 4\n2 5\n1 2 4 1 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 1 2\nQ 1\nQ 2\nU 5 4\nQ 1",
"5\n1 2\n2 5\n3 4\n3 5\n1 2 2 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 2\nQ 1\nU 3 2\nQ 1\nQ 2\nU 2 4\nQ 1",
"5\n1 2\n2 3\n3 4\n2 5\n1 2 2 2 6\n11\nQ 1\nQ 2\nQ 3\nQ 7\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 4",
"5\n1 2\n2 3\n3 4\n2 5\n1 4 1 2 5\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 2 4\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 2\nQ 1",
"5\n1 2\n2 3\n3 4\n3 5\n1 2 2 2 3\n9\nQ 2\nQ 1\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 1\nV 2 4\nQ 2",
"5\n1 2\n2 3\n3 4\n2 5\n1 4 1 2 5\n11\nQ 2\nQ 2\nQ 3\nQ 4\nU 2 2\nQ 1\nU 3 2\nQ 1\nQ 3\nU 5 2\nQ 3",
"5\n1 2\n2 4\n3 4\n2 5\n2 4 1 3 5\n11\nQ 2\nQ 2\nQ 3\nQ 4\nU 2 2\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 2\nQ 2",
"5\n1 2\n2 4\n3 4\n4 5\n2 2 1 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 4\nQ 3\nQ 2\nU 2 4\nQ 1",
"5\n1 2\n2 5\n3 4\n3 5\n1 2 2 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 2\nQ 1\nU 3 2\nQ 2\nQ 2\nU 2 4\nQ 1",
"5\n1 3\n2 3\n3 4\n2 5\n1 4 1 2 5\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 2 4\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 2\nQ 1",
"5\n1 2\n2 3\n3 4\n3 5\n1 2 2 2 3\n9\nQ 2\nQ 1\nQ 4\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 1\nV 2 4\nQ 2",
"5\n1 2\n2 4\n3 4\n2 5\n2 4 1 3 5\n11\nQ 2\nQ 2\nQ 3\nQ 4\nU 2 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 2\nQ 2",
"5\n1 2\n2 3\n5 4\n2 5\n1 2 1 2 5\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 2",
"5\n1 2\n2 5\n3 4\n3 5\n1 2 2 2 1\n11\nQ 1\nQ 4\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 2\nU 5 4\nQ 1",
"5\n1 2\n2 4\n3 4\n4 5\n2 2 1 2 3\n11\nQ 1\nQ 4\nQ 3\nQ 4\nU 5 1\nQ 1\nU 3 4\nQ 3\nQ 2\nU 2 4\nQ 1",
"5\n1 2\n2 4\n3 4\n1 5\n1 2 1 2 3\n2\nQ 2\nQ 2\nQ 3\nQ 4\nU 5 1\nQ 1\nU 2 2\nQ 1\nQ 2\nV 2 7\nQ 1",
"5\n1 2\n2 5\n3 4\n3 5\n1 2 2 2 3\n11\nQ 1\nQ 2\nQ 3\nQ 4\nU 5 2\nQ 1\nU 3 2\nQ 2\nQ 2\nU 1 4\nQ 1",
"5\n1 2\n2 3\n3 4\n3 5\n1 2 1 2 3\n9\nQ 2\nQ 1\nQ 4\nQ 4\nU 5 1\nQ 1\nU 3 2\nQ 1\nQ 1\nV 2 4\nQ 2",
"5\n1 2\n2 4\n3 4\n2 5\n2 4 1 3 5\n11\nQ 2\nQ 2\nQ 3\nQ 4\nU 2 1\nQ 1\nU 3 4\nQ 1\nQ 2\nU 5 2\nQ 2"
],
"outputs": [
"2\n2\n0\n-1\n3\n2\n2\n0",
"2\n2\n0\n-1\n3\n3\n2\n0\n",
"2\n2\n0\n-1\n3\n2\n2\n2\n",
"2\n2\n0\n-1\n3\n2\n2\n-1\n",
"2\n2\n0\n-1\n3\n2\n2\n0\n",
"3\n2\n-1\n-1\n3\n3\n2\n0\n",
"2\n2\n0\n-1\n2\n0\n2\n2\n",
"2\n2\n0\n-1\n3\n3\n2\n2\n",
"2\n2\n0\n-1\n3\n3\n2\n3\n",
"2\n2\n0\n-1\n3\n2\n",
"0\n3\n0\n-1\n1\n3\n3\n-1\n",
"2\n2\n0\n-1\n2\n0\n2\n3\n",
"2\n2\n0\n-1\n4\n4\n2\n2\n",
"2\n2\n-1\n-1\n3\n2\n2\n2\n",
"0\n3\n0\n-1\n1\n3\n3\n0\n",
"3\n0\n0\n-1\n4\n4\n",
"2\n0\n0\n-1\n3\n2\n1\n1\n",
"0\n3\n0\n-1\n1\n3\n3\n2\n",
"0\n3\n0\n-1\n2\n3\n3\n3\n",
"2\n2\n0\n-1\n2\n2\n2\n-1\n",
"2\n2\n0\n-1\n3\n2\n3\n0\n",
"3\n1\n0\n-1\n4\n4\n2\n4\n",
"0\n3\n0\n-1\n2\n3\n3\n0\n",
"0\n3\n-1\n-1\n1\n3\n3\n2\n",
"2\n2\n0\n-1\n2\n3\n2\n-1\n",
"3\n0\n0\n-1\n4\n3\n1\n1\n",
"3\n1\n0\n-1\n4\n4\n2\n",
"2\n0\n0\n-1\n2\n0\n1\n3\n",
"2\n0\n0\n-1\n4\n4\n0\n2\n",
"3\n2\n-1\n-1\n2\n3\n2\n-1\n",
"2\n0\n0\n0\n2\n0\n1\n3\n",
"1\n1\n0\n-1\n4\n4\n2\n",
"2\n0\n0\n0\n2\n1\n1\n3\n",
"2\n0\n0\n-1\n2\n1\n1\n3\n",
"2\n2\n0\n-1\n2\n2\n2\n2\n",
"3\n3\n0\n-1\n3\n2\n3\n2\n",
"0\n4\n0\n-1\n1\n4\n4\n-1\n",
"0\n2\n-1\n-1\n2\n2\n2\n2\n",
"2\n0\n0\n-1\n3\n2\n0\n0\n",
"0\n2\n0\n-1\n3\n3\n3\n2\n",
"2\n2\n-1\n-1\n3\n2\n3\n0\n",
"2\n2\n0\n-1\n4\n4\n2\n3\n",
"3\n2\n-1\n-1\n-1\n3\n2\n-1\n",
"1\n3\n0\n-1\n4\n4\n2\n",
"2\n0\n-1\n0\n2\n1\n1\n3\n",
"2\n2\n-1\n-1\n3\n2\n2\n0\n",
"0\n2\n-1\n-1\n2\n0\n3\n-1\n",
"2\n0\n0\n-1\n4\n4\n2\n3\n",
"2\n0\n0\n-1\n4\n4\n2\n",
"2\n0\n-1\n0\n2\n0\n2\n3\n",
"0\n0\n-1\n0\n2\n0\n2\n3\n",
"-1\n-1\n0\n0\n2\n0\n1\n2\n",
"2\n2\n0\n-1\n2\n0\n2\n0\n",
"2\n2\n0\n-1\n3\n1\n2\n0\n",
"3\n-1\n-1\n-1\n3\n3\n2\n0\n",
"2\n2\n0\n-1\n2\n2\n3\n2\n",
"2\n2\n0\n",
"2\n0\n1\n-1\n3\n2\n",
"2\n2\n0\n-1\n",
"3\n0\n0\n-1\n4\n1\n",
"2\n0\n0\n-1\n2\n0\n2\n1\n",
"0\n2\n0\n-1\n2\n3\n3\n0\n",
"3\n1\n0\n-1\n4\n3\n2\n0\n",
"3\n1\n0\n-1\n4\n4\n1\n",
"2\n0\n-1\n-1\n2\n0\n1\n3\n",
"2\n0\n0\n0\n2\n0\n1\n1\n",
"1\n1\n0\n-1\n4\n4\n1\n",
"0\n3\n0\n-1\n2\n2\n3\n2\n",
"1\n4\n-1\n-1\n1\n4\n4\n-1\n",
"0\n2\n-1\n-1\n2\n2\n2\n-1\n",
"0\n2\n0\n-1\n3\n3\n-1\n2\n",
"1\n3\n-1\n-1\n-1\n0\n3\n-1\n",
"0\n3\n0\n0\n4\n4\n1\n",
"2\n0\n-1\n0\n2\n0\n1\n3\n",
"2\n0\n0\n-1\n4\n4\n4\n",
"0\n0\n-1\n0\n2\n0\n2\n-1\n",
"0\n0\n0\n0\n0\n-1\n2\n3\n",
"0\n0\n0\n0\n3\n2\n1\n-1\n",
"4\n-1\n-1\n-1\n4\n4\n2\n0\n",
"2\n0\n-1\n-1\n4\n4\n0\n2\n",
"2\n0\n-1\n-1\n2\n0\n2\n1\n",
"0\n2\n0\n-1\n2\n-1\n3\n0\n",
"3\n0\n0\n0\n4\n3\n1\n0\n",
"0\n3\n0\n-1\n0\n0\n3\n0\n",
"0\n2\n-1\n-1\n2\n2\n2\n0\n",
"2\n0\n-1\n0\n2\n0\n1\n0\n",
"2\n0\n0\n-1\n3\n3\n3\n",
"0\n0\n-1\n0\n2\n0\n-1\n-1\n",
"0\n0\n0\n0\n0\n-1\n3\n4\n",
"0\n2\n0\n-1\n2\n-1\n2\n0\n",
"0\n3\n0\n-1\n0\n3\n3\n0\n",
"1\n0\n-1\n0\n1\n0\n1\n0\n",
"2\n0\n-1\n-1\n3\n3\n3\n",
"0\n0\n0\n0\n2\n0\n3\n4\n",
"2\n2\n-1\n-1\n3\n2\n3\n3\n",
"2\n-1\n-1\n-1\n2\n2\n3\n0\n",
"0\n-1\n0\n-1\n2\n-1\n2\n0\n",
"1\n1\n",
"0\n3\n0\n-1\n0\n3\n3\n-1\n",
"2\n2\n-1\n-1\n3\n3\n3\n",
"0\n0\n0\n0\n2\n0\n0\n2\n"
]
}
|
Colorful Tree
A tree structure with some colors associated with its vertices and a sequence of commands on it are given. A command is either an update operation or a query on the tree. Each of the update operations changes the color of a specified vertex, without changing the tree structure. Each of the queries asks the number of edges in the minimum connected subgraph of the tree that contains all the vertices of the specified color.
Your task is to find answers of each of the queries, assuming that the commands are performed in the given order.
Input
The input consists of a single test case of the following format.
$n$
$a_1$ $b_1$
...
$a_{n-1}$ $b_{n-1}$
$c_1 ... c_n$
$m$
$command_1$
...
$command_m$
The first line contains an integer $n$ ($2 \leq n \leq 100 000$), the number of vertices of the tree. The vertices are numbered 1 through $n$. Each of the following $n - 1$ lines contains two integers $a_i$ ($1 \leq a_i \leq n$) and $b_i$ ($1 \leq b_i \leq n$), meaning that the $i$-th edge connects vertices $a_i$ and $b_i$. It is ensured that all the vertices are connected, that is, the given graph is a tree. The next line contains $n$ integers, $c_1$ through $c_n$, where $c_j$ ($1 \leq c_j \leq 100 000$) is the initial color of vertex $j$. The next line contains an integer $m$ ($1 \leq m \leq 100 000$), which indicates the number of commands. Each of the following $m$ lines contains a command in the following format.
$U$ $x_k$ $y_k$
or
$Q$ $y_k$
When the $k$-th command starts with U, it means an update operation changing the color of vertex $x_k$ ($1 \leq x_k \leq n$) to $y_k$ ($1 \leq y_k \leq 100 000$). When the $k$-th command starts with Q, it means a query asking the number of edges in the minimum connected subgraph of the tree that contains all the vertices of color $y_k$ ($1 \leq y_k \leq 100 000$).
Output
For each query, output the number of edges in the minimum connected subgraph of the tree containing all the vertices of the specified color. If the tree doesn't contain any vertex of the specified color, output -1 instead.
Sample Input 1
5
1 2
2 3
3 4
2 5
1 2 1 2 3
11
Q 1
Q 2
Q 3
Q 4
U 5 1
Q 1
U 3 2
Q 1
Q 2
U 5 4
Q 1
Sample Output 1
2
2
0
-1
3
2
2
0
Example
Input
5
1 2
2 3
3 4
2 5
1 2 1 2 3
11
Q 1
Q 2
Q 3
Q 4
U 5 1
Q 1
U 3 2
Q 1
Q 2
U 5 4
Q 1
Output
2
2
0
-1
3
2
2
0
|
{
"inputs": [
"2 0\n",
"2 1\n",
"3 2\n",
"904089164817530426 53747406876903279\n",
"860936792402722414 59551033597232946\n",
"316313018463929883 78259904441946885\n",
"1 3\n",
"216006901533424028 8313457244750219\n",
"883717267463724670 29585639347346605\n",
"1000000007 2\n",
"103872254428948073 97291596742897547\n",
"909771081413191574 18862935031728197\n",
"24 0\n",
"1000000007 1\n",
"626 560\n",
"889560480100219043 54181377424922141\n",
"451 938\n",
"73543340229981083 66918326344192076\n",
"4 1669\n",
"91859547444219924 75483775868568438\n",
"1332 332\n",
"16 8\n",
"1 411\n",
"1 692\n",
"152455635055802121 50394545488662355\n",
"463958371369193376 89203995753927042\n",
"8814960236468055 86463151557693391\n",
"0 3259862395629356\n",
"280 472\n",
"99999999999999999 0\n",
"911873413622533246 54684577459651780\n",
"10000000000000000 0\n",
"332382902893992163 15483141652464187\n",
"647858974461637674 18385058205826214\n",
"91142854626119420 900651524977956\n",
"488603693655520686 79239542983498430\n",
"431620727626880523 47616788361847228\n",
"672751296745170589 13026894786355983\n",
"1619 1813\n",
"353579407209009179 74469254935824590\n",
"313779810374175108 13838123840048842\n",
"1000000000000000 0\n",
"1000000007 70\n",
"268086842387268316 76502855388264782\n",
"250000002 1\n",
"1000000007 1000000007\n",
"1271 237\n",
"491414900908765740 49509676303815755\n",
"24 347\n",
"1000000007 0\n",
"1000000000000 0\n",
"375000003 2\n",
"1000000007 12\n",
"816689044159694273 6475970360049048\n",
"0 24\n",
"514028642164226185 95344332761644668\n",
"999999999 0\n",
"18 12\n",
"295961633522750187 84483303945499729\n",
"585664029992038779 34972826534657555\n",
"225761360057436129 49203610094504526\n",
"1 1000000000000000000\n",
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"348612312017571993 87570063840727716\n",
"1000000007 3\n",
"349532090641396787 12248820623854158\n",
"157600018563121064 54027847222622605\n",
"720433754707338458 94180351080265292\n",
"1769 422\n",
"167 887\n",
"1075 274\n",
"160 929\n",
"1000000007 5\n",
"1000000000000000000 1\n",
"568001660010321225 97167523790774710\n",
"3 1\n",
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"709818882593098388 59551033597232946\n",
"316313018463929883 108989792589951708\n",
"1 0\n",
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"1497482167524343307 29585639347346605\n",
"344988331 2\n",
"103872254428948073 34992747964652620\n",
"1703847489304295635 18862935031728197\n",
"1719715550 2\n",
"862 560\n",
"889560480100219043 94331563667532033\n",
"244 938\n",
"73543340229981083 23671972978857885\n",
"4 547\n",
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"1332 560\n",
"20 8\n",
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"1 279\n",
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"1 3259862395629356\n",
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"10000000000000000 1\n",
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"488603693655520686 118606541091591594\n",
"641168126102922013 47616788361847228\n",
"123293448140395797 13026894786355983\n",
"1619 1659\n",
"353579407209009179 25919528641091796\n",
"313779810374175108 623067752618237\n",
"1000000000000000 1\n",
"1000000007 109\n",
"477328860518674420 76502855388264782\n",
"250000002 2\n",
"1556168149 1000000007\n",
"366 237\n",
"5450628386824324 49509676303815755\n",
"24 53\n",
"484623904 0\n",
"1000000000100 0\n",
"257676481 1\n",
"1327344732304347389 6475970360049048\n",
"0 18\n",
"641535423604464631 95344332761644668\n",
"999999999 1\n",
"18 1\n",
"226867794597295065 84483303945499729\n",
"341728648440193666 34972826534657555\n",
"310741247879416592 49203610094504526\n",
"2 1000000000000000000\n",
"496884650289356472 107188213956410843\n",
"27548743055792468 87570063840727716\n",
"366063388 0\n",
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"117622171496853858 54027847222622605\n",
"720433754707338458 56540573069662221\n",
"1769 98\n",
"167 1533\n",
"1075 451\n",
"112 929\n",
"494118227 5\n",
"1000000000000001000 1\n",
"685703172497659565 97167523790774710\n",
"3 0\n",
"1 1\n",
"2 2\n",
"904089164817530426 89308777632294080\n",
"709818882593098388 20128378528533956\n",
"316313018463929883 189476887260833501\n",
"329437253483839553 15747317269872510\n",
"2072081342270478893 29585639347346605\n",
"289337564 2\n",
"103872254428948073 60175393930035510\n",
"529356803571608158 18862935031728197\n",
"1719715550 0\n",
"1451 560\n",
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"235 938\n",
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"4 128\n",
"36226917844851900 75483775868568438\n",
"1942 560\n",
"20 14\n",
"2 588\n",
"1 512\n",
"514499411041246 50394545488662355\n",
"463958371369193376 76617188574592387\n",
"241441872372696 75482010408135931\n",
"2 3259862395629356\n",
"852 472\n",
"375000003 3\n",
"0 1\n"
],
"outputs": [
"4\n",
"7\n",
"21\n",
"702270335\n",
"359730003\n",
"36284201\n",
"9\n",
"362896012\n",
"188389362\n",
"1000000004\n",
"283633261\n",
"800873185\n",
"48\n",
"1000000006\n",
"399405853\n",
"281123162\n",
"598946958\n",
"710215652\n",
"185365669\n",
"462306789\n",
"47520583\n",
"7937\n",
"485514976\n",
"860080936\n",
"697051907\n",
"41857490\n",
"430718856\n",
"0",
"632090765\n",
"600000012\n",
"926432198\n",
"860000007\n",
"719128379\n",
"375141527\n",
"211575546\n",
"316399174\n",
"311078131\n",
"260355651\n",
"481568710\n",
"771349161\n",
"438854949\n",
"986000007\n",
"729983755\n",
"288717798\n",
"0\n",
"1000000006\n",
"27878991\n",
"237095803\n",
"860029201\n",
"0\n",
"999986007\n",
"0\n",
"999995912\n",
"211796030\n",
"0",
"718282571\n",
"999999991\n",
"143361\n",
"11464805\n",
"699566354\n",
"54291755\n",
"719476261\n",
"109575135\n",
"551271547\n",
"1000000000\n",
"233938854\n",
"166795759\n",
"273505123\n",
"698926874\n",
"983959273\n",
"476211777\n",
"752935252\n",
"999999976\n",
"195\n",
"907490480\n",
"11\n",
"139886725\n",
"468399517\n",
"398397727\n",
"2\n",
"721874561\n",
"228961297\n",
"759906631\n",
"448110371\n",
"13943402\n",
"757724306\n",
"334273607\n",
"11383611\n",
"231617279\n",
"727105621\n",
"467348664\n",
"87101129\n",
"763883121\n",
"9985\n",
"737218380\n",
"94573653\n",
"28340939\n",
"371585080\n",
"947055719\n",
"12090201\n",
"804545049\n",
"258888705\n",
"720000006\n",
"69417934\n",
"942661614\n",
"638190513\n",
"957229484\n",
"778417992\n",
"846139028\n",
"666856683\n",
"953751238\n",
"593093420\n",
"972000006\n",
"97905581\n",
"935676220\n",
"1000000006\n",
"224672553\n",
"348437446\n",
"346205845\n",
"9458091\n",
"969247808\n",
"999986207\n",
"30705916\n",
"32447522\n",
"0\n",
"141807117\n",
"999999974\n",
"71\n",
"451007764\n",
"950319175\n",
"987437409\n",
"158428767\n",
"192052530\n",
"152360337\n",
"732126776\n",
"67691308\n",
"680737421\n",
"898976454\n",
"606302723\n",
"180899524\n",
"95728767\n",
"488729032\n",
"623566280\n",
"4195\n",
"827854774\n",
"6\n",
"3\n",
"13\n",
"72037275\n",
"927887793\n",
"35077433\n",
"974104414\n",
"333798956\n",
"314700495\n",
"738275612\n",
"815971589\n",
"439431079\n",
"451379995\n",
"109603259\n",
"867820341\n",
"495143450\n",
"957425933\n",
"828459582\n",
"2312481\n",
"638977\n",
"211655124\n",
"418385480\n",
"490514643\n",
"548330746\n",
"433223457\n",
"36270601\n",
"41950920\n",
"1000000006\n",
"0\n"
]
}
|
Nastya received a gift on New Year — a magic wardrobe. It is magic because in the end of each month the number of dresses in it doubles (i.e. the number of dresses becomes twice as large as it is in the beginning of the month).
Unfortunately, right after the doubling the wardrobe eats one of the dresses (if any) with the 50% probability. It happens every month except the last one in the year.
Nastya owns x dresses now, so she became interested in the [expected number](https://en.wikipedia.org/wiki/Expected_value) of dresses she will have in one year. Nastya lives in Byteland, so the year lasts for k + 1 months.
Nastya is really busy, so she wants you to solve this problem. You are the programmer, after all. Also, you should find the answer modulo 109 + 7, because it is easy to see that it is always integer.
Input
The only line contains two integers x and k (0 ≤ x, k ≤ 1018), where x is the initial number of dresses and k + 1 is the number of months in a year in Byteland.
Output
In the only line print a single integer — the expected number of dresses Nastya will own one year later modulo 109 + 7.
Examples
Input
2 0
Output
4
Input
2 1
Output
7
Input
3 2
Output
21
Note
In the first example a year consists on only one month, so the wardrobe does not eat dresses at all.
In the second example after the first month there are 3 dresses with 50% probability and 4 dresses with 50% probability. Thus, in the end of the year there are 6 dresses with 50% probability and 8 dresses with 50% probability. This way the answer for this test is (6 + 8) / 2 = 7.
|
{
"inputs": [
"2 10\n10 200 1\n10 100 100",
"2 10\n10 200 1\n10 100 101",
"2 10\n10 137 1\n10 100 101",
"0 10\n10 200 0\n10 100 100",
"2 10\n6 331 1\n0 110 100",
"3 10\n1 349 1\n16 100 101",
"2 10\n6 554 1\n0 100 100",
"1 10\n1 470 -1\n15 101 101",
"2 10\n6 28 1\n10 100 101",
"3 10\n6 318 1\n10 100 101",
"3 10\n6 121 1\n10 110 100",
"3 10\n1 279 0\n12 100 101",
"3 10\n1 250 1\n16 100 101",
"3 10\n1 614 0\n16 100 101",
"1 10\n6 313 1\n0 100 010",
"1 10\n1 678 -1\n14 101 101",
"3 10\n10 9 1\n10 110 100",
"2 10\n6 377 2\n0 100 100",
"1 10\n6 419 1\n1 100 101",
"1 10\n1 404 -1\n24 101 001",
"1 10\n6 118 3\n1 100 110",
"1 11\n4 344 -1\n0 111 100",
"2 10\n8 123 0\n0 100 101",
"2 20\n7 174 1\n6 110 101",
"3 10\n1 297 1\n26 101 111",
"3 10\n7 236 1\n10 100 101",
"1 7\n6 45 0\n13 111 100",
"3 2\n1 593 1\n16 011 100",
"2 20\n14 286 1\n6 110 101",
"1 1\n1 235 -2\n1 101 110",
"1 10\n6 77 2\n1 100 110",
"1 8\n1 716 0\n24 101 101",
"2 7\n6 202 2\n0 100 101",
"3 2\n1 402 1\n16 011 110",
"1 1\n1 426 -2\n2 101 110",
"1 17\n6 300 1\n-1 101 000",
"2 10\n6 200 1\n10 100 101",
"3 10\n6 200 1\n10 100 101",
"3 10\n1 200 1\n10 100 101",
"2 10\n10 200 0\n10 100 100",
"2 10\n6 200 1\n10 100 100",
"3 10\n6 200 1\n10 110 101",
"3 10\n1 200 0\n10 100 101",
"2 10\n7 137 1\n10 100 101",
"2 10\n6 200 1\n10 110 100",
"3 10\n6 200 1\n10 110 100",
"3 10\n1 200 0\n12 100 101",
"0 10\n10 200 0\n10 100 110",
"2 10\n7 137 1\n10 101 101",
"2 10\n6 200 1\n13 110 100",
"3 10\n1 200 1\n12 100 101",
"0 10\n10 267 0\n10 100 110",
"2 8\n7 137 1\n10 101 101",
"2 10\n6 200 1\n0 110 100",
"3 10\n1 200 1\n16 100 101",
"0 10\n10 267 -1\n10 100 110",
"2 8\n7 137 1\n10 111 101",
"0 10\n10 267 -1\n10 101 110",
"2 10\n6 331 1\n0 100 100",
"3 10\n1 349 0\n16 100 101",
"0 10\n10 470 -1\n10 101 110",
"3 10\n1 349 0\n16 100 100",
"0 10\n10 470 -1\n9 101 110",
"1 10\n6 554 1\n0 100 100",
"3 10\n1 349 0\n2 100 100",
"0 10\n1 470 -1\n9 101 110",
"1 10\n6 554 1\n0 100 110",
"0 10\n1 470 -1\n9 101 111",
"1 10\n6 554 1\n0 100 111",
"0 10\n1 470 -1\n15 101 111",
"0 10\n6 554 1\n0 100 111",
"0 10\n1 470 -1\n15 101 101",
"0 10\n6 554 1\n0 100 110",
"0 10\n6 554 2\n0 100 110",
"1 10\n1 470 -1\n21 101 101",
"0 10\n6 742 2\n0 100 110",
"0 10\n6 742 0\n0 100 110",
"0 10\n6 742 0\n0 110 110",
"0 11\n6 742 0\n0 110 110",
"0 11\n6 742 -1\n0 110 110",
"0 11\n6 344 -1\n0 110 110",
"0 11\n6 344 -1\n-1 110 110",
"0 11\n6 577 -1\n-1 110 110",
"0 11\n6 577 -1\n-1 010 110",
"0 11\n6 577 -1\n-1 000 110",
"2 10\n10 200 0\n10 100 101",
"2 10\n10 137 1\n10 110 101",
"2 10\n7 200 1\n10 100 100",
"3 15\n1 200 0\n10 100 101",
"0 10\n10 200 -1\n10 100 100",
"2 10\n7 137 1\n10 110 101",
"4 10\n6 200 1\n10 110 100",
"0 10\n10 200 0\n10 000 110",
"4 10\n7 137 1\n10 101 101",
"2 10\n6 200 2\n13 110 100",
"3 19\n1 200 1\n12 100 101",
"0 10\n10 327 0\n10 100 110",
"2 10\n6 200 2\n0 110 100",
"0 10\n10 267 0\n10 000 110",
"2 8\n7 137 1\n10 110 101",
"3 10\n1 349 1\n16 101 101"
],
"outputs": [
"200",
"200\n",
"137\n",
"0\n",
"331\n",
"349\n",
"554\n",
"470\n",
"100\n",
"318\n",
"121\n",
"279\n",
"250\n",
"614\n",
"313\n",
"678\n",
"110\n",
"377\n",
"419\n",
"404\n",
"118\n",
"344\n",
"123\n",
"174\n",
"297\n",
"236\n",
"45\n",
"593\n",
"286\n",
"235\n",
"77\n",
"716\n",
"202\n",
"402\n",
"426\n",
"300\n",
"200\n",
"200\n",
"200\n",
"200\n",
"200\n",
"200\n",
"200\n",
"137\n",
"200\n",
"200\n",
"200\n",
"0\n",
"137\n",
"200\n",
"200\n",
"0\n",
"137\n",
"200\n",
"200\n",
"0\n",
"137\n",
"0\n",
"331\n",
"349\n",
"0\n",
"349\n",
"0\n",
"554\n",
"349\n",
"0\n",
"554\n",
"0\n",
"554\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"470\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"200\n",
"137\n",
"200\n",
"200\n",
"0\n",
"137\n",
"200\n",
"0\n",
"137\n",
"200\n",
"200\n",
"0\n",
"200\n",
"0\n",
"137\n",
"349\n"
]
}
|
Example
Input
2 10
10 200 1
10 100 100
Output
200
|
{
"inputs": [
"5\n1 2 3 4 5",
"5\n1 2 3 0 5",
"5\n1 2 3 0 2",
"5\n1 2 4 0 2",
"5\n1 4 4 0 2",
"5\n1 4 4 1 2",
"5\n1 4 4 2 2",
"5\n1 6 4 2 2",
"5\n1 8 4 2 2",
"5\n1 8 3 2 2",
"5\n1 8 3 2 1",
"5\n2 8 3 2 1",
"5\n2 8 3 2 0",
"5\n2 8 3 3 0",
"5\n4 8 3 3 0",
"5\n4 6 3 3 0",
"5\n7 6 3 3 0",
"5\n2 6 3 3 0",
"5\n0 6 3 3 0",
"5\n0 6 3 3 -1",
"5\n0 3 3 3 -1",
"5\n0 3 5 3 -1",
"5\n0 3 5 2 -1",
"5\n0 3 5 2 0",
"5\n-1 3 5 2 0",
"5\n-1 3 5 1 0",
"5\n-1 3 5 1 -1",
"5\n-1 3 5 0 -1",
"5\n-1 3 5 0 0",
"5\n-1 3 4 0 0",
"5\n-1 4 4 0 0",
"5\n-1 4 4 0 1",
"5\n-1 4 4 1 0",
"5\n-1 2 4 1 0",
"5\n-1 2 4 1 -1",
"5\n-1 2 4 2 -1",
"5\n-1 2 3 2 -1",
"5\n-1 4 3 2 -1",
"5\n0 4 3 2 -1",
"5\n0 4 6 2 -1",
"5\n0 4 6 2 0",
"5\n0 5 6 2 0",
"5\n0 5 12 2 0",
"5\n0 0 12 2 0",
"5\n0 0 12 1 0",
"5\n0 0 12 1 1",
"5\n0 0 12 1 2",
"5\n0 1 12 1 2",
"5\n0 1 12 0 2",
"5\n0 2 12 0 2",
"5\n0 2 12 0 4",
"5\n1 2 12 0 4",
"5\n1 2 12 -1 4",
"5\n1 2 9 -1 4",
"5\n2 2 9 -1 4",
"5\n2 2 9 -2 4",
"5\n0 2 9 -1 4",
"5\n0 3 9 -1 4",
"5\n0 3 13 -1 4",
"5\n0 3 13 -2 4",
"5\n0 3 13 -2 2",
"5\n1 3 13 -2 2",
"5\n1 2 13 -2 2",
"5\n1 2 13 -4 2",
"5\n1 2 1 -4 2",
"5\n1 2 2 -4 2",
"5\n1 0 2 -4 2",
"5\n1 -1 2 -4 2",
"5\n1 -1 2 0 2",
"5\n1 -1 2 0 0",
"5\n1 -1 1 0 0",
"5\n1 -1 0 0 0",
"5\n1 -1 -1 0 0",
"5\n0 -1 -1 0 0",
"5\n0 -1 0 0 0",
"5\n0 -1 0 -1 0",
"5\n0 -1 0 -1 -1",
"5\n0 -1 -1 -1 -1",
"5\n0 -1 -2 -1 -1",
"5\n1 -1 -2 -1 -1",
"5\n1 0 -2 -1 -1",
"5\n1 0 -2 -2 -1",
"5\n1 0 -1 -2 -1",
"5\n2 0 -1 -2 -1",
"5\n2 0 -1 -2 -2",
"5\n2 0 -2 -2 -2",
"5\n2 -1 -2 -2 -2",
"5\n2 -1 -1 -2 -2",
"5\n4 -1 -1 -2 -2",
"5\n4 -1 -2 -2 -2",
"5\n6 -1 -2 -2 -2",
"5\n12 -1 -2 -2 -2",
"5\n12 -1 -2 -2 0",
"5\n12 -1 -2 -1 0",
"5\n0 -1 -2 -1 0",
"5\n-1 -1 -2 -1 0",
"5\n-1 -1 -2 0 0",
"5\n-1 -1 0 0 0",
"5\n-1 -1 0 0 -1",
"5\n-1 -2 0 0 -1",
"5\n-1 0 0 0 -1"
],
"outputs": [
"NOT READY\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"NOT READY\n",
"NOT READY\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"NOT READY\n",
"NOT READY\n",
"NOT READY\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"NOT READY\n",
"NOT READY\n",
"NOT READY\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n",
"NOT READY\n",
"READY FOR BATTLE\n",
"READY FOR BATTLE\n"
]
}
|
Kattapa, as you all know was one of the greatest warriors of his time. The kingdom of Maahishmati had never lost a battle under him (as army-chief), and the reason for that was their really powerful army, also called as Mahasena.
Kattapa was known to be a very superstitious person. He believed that a soldier is "lucky" if the soldier is holding an even number of weapons, and "unlucky" otherwise. He considered the army as "READY FOR BATTLE" if the count of "lucky" soldiers is strictly greater than the count of "unlucky" soldiers, and "NOT READY" otherwise.
Given the number of weapons each soldier is holding, your task is to determine whether the army formed by all these soldiers is "READY FOR BATTLE" or "NOT READY".
Note: You can find the definition of an even number here.
Input
The first line of input consists of a single integer N denoting the number of soldiers. The second line of input consists of N space separated integers A1, A2, ..., AN, where Ai denotes the number of weapons that the i^th soldier is holding.
Output
Generate one line output saying "READY FOR BATTLE", if the army satisfies the conditions that Kattapa requires or "NOT READY" otherwise (quotes for clarity).
Constraints
1 ≤ N ≤ 100
1 ≤ Ai ≤ 100
Example 1
Input:
1
1
Output:
NOT READY
Example 2
Input:
1
2
Output:
READY FOR BATTLE
Example 3
Input:
4
11 12 13 14
Output:
NOT READY
Example 4
Input:
3
2 3 4
Output:
READY FOR BATTLE
Example 5
Input:
5
1 2 3 4 5
Output:
NOT READY
Explanation
Example 1: For the first example, N = 1 and the array A = [1]. There is only 1 soldier and he is holding 1 weapon, which is odd. The number of soldiers holding an even number of weapons = 0, and number of soldiers holding an odd number of weapons = 1. Hence, the answer is "NOT READY" since the number of soldiers holding an even number of weapons is not greater than the number of soldiers holding an odd number of weapons.
Example 2: For the second example, N = 1 and the array A = [2]. There is only 1 soldier and he is holding 2 weapons, which is even. The number of soldiers holding an even number of weapons = 1, and number of soldiers holding an odd number of weapons = 0. Hence, the answer is "READY FOR BATTLE" since the number of soldiers holding an even number of weapons is greater than the number of soldiers holding an odd number of weapons.
Example 3: For the third example, N = 4 and the array A = [11, 12, 13, 14]. The 1^st soldier is holding 11 weapons (which is odd), the 2^nd soldier is holding 12 weapons (which is even), the 3^rd soldier is holding 13 weapons (which is odd), and the 4^th soldier is holding 14 weapons (which is even). The number of soldiers holding an even number of weapons = 2, and number of soldiers holding an odd number of weapons = 2. Notice that we have an equal number of people holding even number of weapons and odd number of weapons. The answer here is "NOT READY" since the number of soldiers holding an even number of weapons is not strictly greater than the number of soldiers holding an odd number of weapons.
Example 4: For the fourth example, N = 3 and the array A = [2, 3, 4]. The 1^st soldier is holding 2 weapons (which is even), the 2^nd soldier is holding 3 weapons (which is odd), and the 3^rd soldier is holding 4 weapons (which is even). The number of soldiers holding an even number of weapons = 2, and number of soldiers holding an odd number of weapons = 1. Hence, the answer is "READY FOR BATTLE" since the number of soldiers holding an even number of weapons is greater than the number of soldiers holding an odd number of weapons.
Example 5: For the fifth example, N = 5 and the array A = [1, 2, 3, 4, 5]. The 1^st soldier is holding 1 weapon (which is odd), the 2^nd soldier is holding 2 weapons (which is even), the 3^rd soldier is holding 3 weapons (which is odd), the 4^th soldier is holding 4 weapons (which is even), and the 5^th soldier is holding 5 weapons (which is odd). The number of soldiers holding an even number of weapons = 2, and number of soldiers holding an odd number of weapons = 3. Hence, the answer is "NOT READY" since the number of soldiers holding an even number of weapons is not greater than the number of soldiers holding an odd number of weapons.
|
{
"inputs": [
"1\n90447 91000",
"2\n96000 -72000\n-72000 54000",
"3\n0 10\n5 -5\n-5 -5",
"10\n1 2\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n17 18\n19 20",
"5\n1 1\n1 0\n0 1\n-1 0\n0 -1",
"3\n0 0\n0 1\n1 0",
"5\n1 1\n2 2\n3 3\n4 4\n5 5",
"1\n52551 91000",
"2\n96000 -130259\n-72000 54000",
"3\n0 10\n5 -3\n-5 -5",
"10\n1 0\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n17 18\n19 20",
"5\n1 1\n1 0\n0 2\n-1 0\n0 -1",
"3\n0 0\n0 1\n2 0",
"5\n1 1\n2 2\n3 3\n4 2\n5 5",
"1\n76279 91000",
"2\n49801 -130259\n-72000 54000",
"10\n1 0\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n4 18\n19 20",
"5\n1 1\n0 0\n0 2\n-1 0\n0 -1",
"5\n1 1\n2 2\n3 3\n4 2\n3 5",
"1\n93262 91000",
"10\n1 0\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n4 18\n19 21",
"5\n1 1\n0 1\n0 2\n-1 0\n0 -1",
"1\n148324 91000",
"2\n33334 -130259\n-72000 89448",
"3\n0 10\n1 -6\n-5 -5",
"10\n1 0\n3 4\n5 6\n7 8\n9 10\n11 12\n13 14\n15 16\n3 18\n19 21",
"5\n1 1\n2 0\n5 3\n4 2\n3 5",
"1\n232944 91000",
"2\n33334 -247097\n-72000 89448",
"10\n1 0\n3 4\n5 6\n7 8\n8 10\n11 12\n13 14\n15 16\n3 18\n19 21",
"5\n1 1\n2 0\n5 3\n4 1\n3 5",
"1\n323092 91000",
"2\n33334 -460653\n-72000 89448",
"3\n0 16\n1 -6\n-5 -3",
"3\n1 1\n0 0\n3 -1",
"5\n1 1\n2 -1\n5 3\n4 1\n3 5",
"1\n323092 178351",
"3\n0 18\n1 -6\n-5 -3",
"10\n1 0\n3 4\n5 6\n8 8\n8 10\n11 12\n13 4\n15 16\n3 18\n19 21",
"5\n1 1\n0 1\n1 0\n-2 0\n0 -1",
"5\n1 1\n4 -1\n5 3\n4 1\n3 5",
"1\n568221 178351",
"10\n1 0\n3 4\n5 6\n8 8\n8 10\n20 12\n13 4\n15 16\n3 18\n19 21",
"5\n1 1\n7 -1\n5 3\n4 1\n3 5",
"1\n568221 83257",
"3\n0 20\n1 -6\n-10 -3",
"10\n1 0\n3 7\n5 6\n8 8\n8 10\n20 12\n13 4\n15 16\n3 18\n19 21",
"5\n1 1\n7 -1\n5 0\n4 1\n3 5",
"1\n568221 48623",
"2\n13872 -460653\n-72000 104892",
"10\n1 0\n3 7\n2 6\n8 8\n8 10\n20 12\n13 4\n15 16\n3 18\n19 21",
"5\n1 1\n7 -1\n5 0\n4 1\n3 9",
"1\n568221 60327",
"5\n1 3\n0 1\n1 0\n-2 -2\n0 -1",
"1\n568221 71355",
"10\n1 0\n3 7\n2 6\n11 8\n8 10\n20 12\n13 7\n15 16\n3 18\n19 21",
"5\n1 3\n0 1\n1 0\n-4 -2\n0 -1",
"5\n1 1\n7 -2\n5 -1\n4 1\n3 9",
"1\n311727 71355",
"10\n1 0\n3 7\n2 10\n11 8\n8 10\n20 12\n13 7\n15 16\n3 18\n19 21",
"5\n1 1\n7 -2\n5 -1\n4 0\n3 9",
"1\n311727 72656",
"2\n13872 -232879\n-39358 153670",
"10\n1 0\n3 7\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 18\n19 21",
"5\n1 6\n0 1\n2 0\n-4 -2\n0 -1",
"1\n311727 85902",
"2\n13872 -200911\n-39358 153670",
"10\n1 0\n3 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 18\n19 21",
"5\n1 1\n7 -2\n5 -2\n4 0\n3 7",
"1\n311727 113970",
"2\n13872 -201534\n-39358 153670",
"10\n1 0\n3 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 18\n29 21",
"1\n21552 113970",
"2\n5694 -201534\n-39358 153670",
"3\n1 13\n1 -2\n-11 -5",
"10\n1 0\n3 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 27\n29 21",
"5\n1 6\n0 1\n2 0\n-4 -3\n1 0",
"1\n21552 24120",
"10\n0 0\n3 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 27\n29 21",
"5\n1 6\n0 1\n2 1\n-4 -3\n1 0",
"3\n2 5\n0 -1\n-1 -1",
"5\n1 1\n7 -2\n10 -2\n4 0\n3 10",
"1\n21552 17969",
"2\n6614 -201534\n-39358 141694",
"3\n1 13\n0 -2\n-11 -4",
"10\n0 0\n1 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 27\n29 21",
"5\n1 1\n7 -2\n10 -2\n2 0\n3 10",
"1\n4519 17969",
"10\n0 0\n1 13\n2 10\n11 8\n8 10\n17 12\n13 7\n15 16\n3 27\n29 35",
"5\n1 6\n-1 1\n4 1\n-4 -3\n1 0",
"5\n1 1\n7 -2\n15 -2\n2 0\n3 10",
"1\n4519 21907",
"2\n6614 -289203\n-47857 141694",
"10\n0 0\n1 13\n2 10\n11 8\n8 4\n17 12\n13 7\n15 16\n3 27\n29 35",
"5\n1 6\n-1 1\n4 2\n-4 -3\n1 0",
"5\n1 1\n7 -2\n15 -2\n2 0\n3 9",
"1\n3382 21907",
"2\n6614 -350970\n-47857 141694",
"3\n1 0\n-1 0\n-11 -4",
"10\n0 0\n1 13\n2 10\n11 15\n8 4\n17 12\n13 7\n15 16\n3 27\n29 35",
"5\n1 1\n7 -2\n15 -2\n2 0\n3 3",
"1\n464 21907",
"10\n0 0\n1 13\n2 10\n11 15\n8 4\n17 12\n13 7\n15 16\n3 27\n29 24",
"3\n2 6\n0 0\n-2 0",
"5\n1 1\n7 -2\n15 -2\n3 0\n3 3",
"1\n464 28468",
"3\n1 0\n0 -1\n-11 -4"
],
"outputs": [
"128303.000000000000000000000000000000000000000000000000",
"120000.000000000000000000000000000000000000000000000000",
"10.000000000000000000000000000000000000000000000000",
"148.660687473185055226120082139313966514489855137208",
"2.828427124746190097603377448419396157139343750753",
"1.414213562373095048801688724209698078569671875376",
"21.213203435596425732025330863145471178545078130654",
"105083.812269\n",
"161812.876747\n",
"10.0\n",
"147.186955944\n",
"3.60555127546\n",
"2.2360679775\n",
"19.8494332413\n",
"118741.255851\n",
"139454.460961\n",
"138.683091976\n",
"3.16227766017\n",
"18.3847763109\n",
"130302.726925\n",
"139.46325681\n",
"4.12310562562\n",
"174014.393014\n",
"134456.545534\n",
"11.7046999107\n",
"138.841636406\n",
"18.6010752377\n",
"250087.798855\n",
"249335.282231\n",
"138.224455145\n",
"18.0277563773\n",
"335662.688519\n",
"461857.49097\n",
"16.0\n",
"4.0\n",
"17.4928556845\n",
"369049.481323\n",
"18.0\n",
"131.137332594\n",
"2.82842712475\n",
"19.2353840617\n",
"595553.678556\n",
"137.207871494\n",
"21.9317121995\n",
"574288.109654\n",
"20.0\n",
"139.387947829\n",
"20.8806130178\n",
"570297.554764\n",
"460861.8218\n",
"137.36083867\n",
"22.360679775\n",
"571414.430838\n",
"4.472135955\n",
"572683.718003\n",
"141.598022585\n",
"5.0\n",
"21.5406592285\n",
"319789.397188\n",
"144.589072893\n",
"21.1896201004\n",
"320082.203293\n",
"233291.793737\n",
"142.635900109\n",
"7.61577310586\n",
"323346.371764\n",
"201389.330167\n",
"147.271857461\n",
"20.3960780544\n",
"331907.944209\n",
"202010.855005\n",
"153.71727294\n",
"115989.86854\n",
"201614.421091\n",
"13.0384048104\n",
"160.561514691\n",
"8.0622577483\n",
"32345.9905398\n",
"159.928108849\n",
"8.94427191\n",
"5.38516480713\n",
"25.9615099715\n",
"28060.1793473\n",
"201642.500857\n",
"13.4536240471\n",
"158.672618936\n",
"24.0416305603\n",
"18528.5272485\n",
"169.838158257\n",
"9.43398113206\n",
"28.8617393793\n",
"22368.2366314\n",
"289278.620373\n",
"165.0\n",
"10.295630141\n",
"28.6356421266\n",
"22166.51919\n",
"351032.314604\n",
"12.6491106407\n",
"170.651692051\n",
"28.0\n",
"21911.9133122\n",
"161.817798774\n",
"6.32455532034\n",
"29.0\n",
"28471.7811175\n",
"12.0830459736\n"
]
}
|
E869120 is initially standing at the origin (0, 0) in a two-dimensional plane.
He has N engines, which can be used as follows:
* When E869120 uses the i-th engine, his X- and Y-coordinate change by x_i and y_i, respectively. In other words, if E869120 uses the i-th engine from coordinates (X, Y), he will move to the coordinates (X + x_i, Y + y_i).
* E869120 can use these engines in any order, but each engine can be used at most once. He may also choose not to use some of the engines.
He wants to go as far as possible from the origin. Let (X, Y) be his final coordinates. Find the maximum possible value of \sqrt{X^2 + Y^2}, the distance from the origin.
Constraints
* 1 \leq N \leq 100
* -1 \ 000 \ 000 \leq x_i \leq 1 \ 000 \ 000
* -1 \ 000 \ 000 \leq y_i \leq 1 \ 000 \ 000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
x_2 y_2
: :
x_N y_N
Output
Print the maximum possible final distance from the origin, as a real value. Your output is considered correct when the relative or absolute error from the true answer is at most 10^{-10}.
Examples
Input
3
0 10
5 -5
-5 -5
Output
10.000000000000000000000000000000000000000000000000
Input
5
1 1
1 0
0 1
-1 0
0 -1
Output
2.828427124746190097603377448419396157139343750753
Input
5
1 1
2 2
3 3
4 4
5 5
Output
21.213203435596425732025330863145471178545078130654
Input
3
0 0
0 1
1 0
Output
1.414213562373095048801688724209698078569671875376
Input
1
90447 91000
Output
128303.000000000000000000000000000000000000000000000000
Input
2
96000 -72000
-72000 54000
Output
120000.000000000000000000000000000000000000000000000000
Input
10
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
Output
148.660687473185055226120082139313966514489855137208
|
{
"inputs": [
"4 5\nWRWRW\nBWRWB\nWRWRW\nRWBWR",
"4 5\nWRWRW\nBRWWB\nWRWRW\nRWBWR",
"4 5\nWRWRW\nBWRWB\nWRWRW\nRWBWQ",
"4 5\nWQWRW\nBWRXB\nRVWRW\nWQBWQ",
"4 3\nWQWRW\nBWRXB\nRVWRW\nRWBWQ",
"4 5\nWQWRW\nBWRXC\nRVWRW\nWQBWQ",
"4 10\nWRWQW\nBWRXB\nRVWRW\nRWBWQ",
"4 0\nWQXRW\nBWRXB\nVRWRW\nRWBWQ",
"4 16\nWRWQW\nBWRXB\nRVWRW\nRWBWQ",
"4 1\nWRWRW\nBWRWB\nVRWRW\nQWBWR",
"5 1\nWRWRW\nBWRWB\nVRWRW\nQWBWR",
"4 4\nWQWRW\nBWRXB\nRVWRX\nWRBWP",
"4 5\nWRXQW\nBWRXC\nRVWRW\nWQBWQ",
"5 5\nWRWRW\nBWRWB\nWRWRW\nQBWWQ",
"4 8\nWRWRW\nBWRWB\nVRWRW\nQWBWR",
"5 5\nWRWRW\nBVRWB\nWRWRW\nQBWWQ",
"3 5\nWRQWW\nZBRWB\nVRWVR\nWPBWQ",
"5 5\nWRWRW\nBVRWB\nWRWRV\nQBWWQ",
"6 1\nWQXRW\nBWRXB\nWRWSV\nQXBWR",
"4 2\nWSRWV\nCWRWB\nWRWRW\nRWBWR",
"5 5\nXRWRW\nBWRVB\nWRWRV\nQBWWQ",
"4 7\nWRWWR\nBVRWB\nWQWRV\nRVBWQ",
"3 5\nXRRWW\nBWRBV\nWRWRV\nQBWWQ",
"4 7\nWRWRX\nBBWSW\nWWWRR\nRWBWR",
"4 10\nWRWRW\nBRWWB\nWRWRW\nRWBVR",
"4 8\nWRWRW\nWRWBB\nWWWRR\nRWBXR",
"4 8\nWQWRX\nBWRXB\nVRWVR\nWQBWQ",
"4 9\nXRWRW\nBWBSW\nWWWRR\nRWBVR",
"4 8\nWRWQW\nCWRXB\nRUWRW\nXRBWQ",
"4 14\nWRWWR\nBVRWB\nWQWRV\nRVBWQ",
"4 5\nWRWRW\nWRWBB\nWRWRW\nRWBWR",
"4 5\nWRWRW\nBWRWB\nVRWRW\nRWBWQ",
"4 5\nWRWRW\nBWRXB\nVRWRW\nRWBWQ",
"4 5\nWRWRW\nBWRXB\nRVWRW\nRWBWQ",
"4 5\nWQWRW\nBWRXB\nRVWRW\nRWBWQ",
"4 5\nWQWRW\nBWRXB\nRVWRW\nWRBWQ",
"4 5\nWQWRW\nBWRXB\nRVWRV\nWQBWQ",
"4 5\nWQWRW\nBXRWB\nRVWRV\nWQBWQ",
"4 5\nWRRWW\nBWRWB\nWRWRW\nRWBWR",
"4 5\nWRWRW\nBRWWB\nWRVRW\nRWBWR",
"4 5\nWRWRW\nWRWBB\nWWWRR\nRWBWR",
"4 5\nWRWRW\nBWRWB\nWRWRW\nRWWBQ",
"4 5\nWRWRW\nBWRWB\nWRWRV\nRWBWQ",
"4 5\nWRXRW\nBWRXB\nVRWRW\nRWBWQ",
"4 5\nWRWQW\nBWRXB\nRVWRW\nRWBWQ",
"4 5\nWQWRW\nBWRXB\nRVWRW\nWRBWP",
"4 5\nWQWRW\nBYRWB\nRVWRV\nWQBWQ",
"4 5\nWRRWW\nBWRWB\nWRWRW\nQWBWR",
"4 5\nWRWRW\nWSWBB\nWWWRR\nRWBWR",
"4 5\nWRWRW\nBWRWB\nWRWRW\nQWWBQ",
"4 5\nWRWRW\nBWRWB\nWRWRV\nQWBWR",
"4 5\nWQXRW\nBWRXB\nVRWRW\nRWBWQ",
"4 5\nWQWRW\nBWRXB\nRVWRX\nWRBWP",
"4 5\nWRWQW\nBWRXC\nRVWRW\nWQBWQ",
"4 5\nWQWRW\nYBRWB\nRVWRV\nWQBWQ",
"4 5\nWRWRX\nWSWBB\nWWWRR\nRWBWR",
"4 5\nWRWRW\nBWRWB\nWRWRW\nQBWWQ",
"4 5\nWRWRW\nBWRWB\nVRWRW\nQWBWR",
"4 5\nWQWRX\nBWRXB\nRVWRX\nWRBWP",
"4 5\nWQWRW\nZBRWB\nRVWRV\nWQBWQ",
"4 5\nWRWRX\nBBWSW\nWWWRR\nRWBWR",
"4 0\nWQXRW\nBWRXB\nVRWSW\nRWBWQ",
"4 5\nWQWRX\nBXRWB\nRVWRX\nWRBWP",
"4 5\nWQWRW\nZBRWB\nRVWRV\nWPBWQ",
"4 5\nWRWRX\nBWWSB\nWWWRR\nRWBWR",
"4 0\nWQXRW\nBWRXB\nVRWSW\nQWBWR",
"4 5\nWQWRX\nBXRWB\nRWWRX\nWRBWP",
"4 5\nWRWQW\nZBRWB\nRVWRV\nWPBWQ",
"4 5\nXRWRW\nBWWSB\nWWWRR\nRWBWR",
"4 0\nWQXRW\nBWRXB\nVRWSV\nQWBWR",
"4 5\nWQWRX\nBXRXB\nRWWRX\nWRBWP",
"4 5\nWRQWW\nZBRWB\nRVWRV\nWPBWQ",
"4 5\nXRWRW\nBWWSB\nWWRRW\nRWBWR",
"4 0\nWQXRW\nBWRXB\nVRWSV\nQXBWR",
"4 5\nWQWRX\nBRXXB\nRWWRX\nWRBWP",
"4 1\nWQXRW\nBWRXB\nVRWSV\nQXBWR",
"4 1\nWQXRW\nBWRXB\nVRWSV\nQXCWR",
"4 5\nVRWRW\nBWRWB\nWRWRW\nRWBWR",
"4 5\nWRWRW\nBRWWB\nWRWRW\nRWBVR",
"4 5\nWRRWW\nBWRWB\nWRWRW\nRWBWQ",
"4 5\nWRWRW\nBWRXB\nWRWRW\nRWBWQ",
"4 5\nVRWRW\nBWRXB\nRVWRW\nRWBWQ",
"4 10\nWQWRW\nBWRXB\nRVWRW\nRWBWQ",
"4 5\nWQXRW\nBWRXB\nRVWRW\nWRBWQ",
"4 5\nWQWRW\nBWRYB\nRVWRW\nWQBWQ",
"4 5\nWQWRW\nBWRXB\nVRWVR\nWQBWQ",
"4 5\nWQVRW\nBXRWB\nRVWRV\nWQBWQ",
"4 5\nWRRWV\nBWRWB\nWRWRW\nRWBWR",
"4 5\nWRWRW\nWRWBB\nWWWRR\nRWBXR",
"4 5\nWRWRW\nBWRWB\nWRWRW\nQWWBR",
"4 5\nWRWRW\nBWRWB\nWRWRV\nRVBWQ",
"4 5\nWRXRW\nBWRYB\nVRWRW\nRWBWQ",
"4 5\nWQWRW\nBWRXC\nRVVRW\nWQBWQ",
"4 4\nWQWRW\nBYRWB\nRVWRV\nWQBWQ",
"4 5\nWRRWW\nBWRWB\nWSWRW\nQWBWR",
"4 5\nWRWRW\nWBWSB\nWWWRR\nRWBWR",
"4 5\nWRWRW\nBWRWB\nWRWRW\nQBWWR",
"4 5\nWQWRW\nYBRWB\nRVVRV\nWQBWQ",
"4 5\nWRWRX\nWSVBB\nWWWRR\nRWBWR",
"4 5\nWQWRX\nBWRXB\nRVWRX\nPWBRW",
"4 0\nWQWRW\nZBRWB\nRVWRV\nWQBWQ"
],
"outputs": [
"11",
"11\n",
"12\n",
"13\n",
"7\n",
"14\n",
"32\n",
"0\n",
"56\n",
"2\n",
"3\n",
"10\n",
"15\n",
"16\n",
"24\n",
"17\n",
"8\n",
"18\n",
"4\n",
"5\n",
"19\n",
"21\n",
"9\n",
"20\n",
"31\n",
"23\n",
"26\n",
"28\n",
"25\n",
"49\n",
"11\n",
"12\n",
"12\n",
"12\n",
"12\n",
"12\n",
"13\n",
"13\n",
"11\n",
"11\n",
"11\n",
"12\n",
"12\n",
"13\n",
"12\n",
"12\n",
"13\n",
"12\n",
"11\n",
"13\n",
"12\n",
"13\n",
"12\n",
"14\n",
"13\n",
"12\n",
"13\n",
"12\n",
"13\n",
"13\n",
"12\n",
"0\n",
"13\n",
"13\n",
"12\n",
"0\n",
"13\n",
"13\n",
"12\n",
"0\n",
"13\n",
"13\n",
"12\n",
"0\n",
"13\n",
"2\n",
"2\n",
"12\n",
"11\n",
"12\n",
"12\n",
"13\n",
"32\n",
"13\n",
"13\n",
"13\n",
"14\n",
"12\n",
"11\n",
"12\n",
"12\n",
"13\n",
"14\n",
"11\n",
"13\n",
"11\n",
"12\n",
"13\n",
"12\n",
"13\n",
"0\n"
]
}
|
problem
President K decided to make a flag for IOI 2016 in Russia. Chairman K first took out the old flag from the warehouse. This flag is divided into squares of N rows and M columns, and each square is painted in one of white, blue, and red.
Chairman K is trying to repaint some of the squares on this flag to make it the Russian flag. However, the Russian flag in this problem is as follows.
* Several lines (one or more lines) from the top are all painted in white.
* The next few lines (one or more lines) are all painted in blue.
* All the cells in the other lines (one or more lines) are painted in red.
Find the minimum number of squares that President K needs to repaint to turn the old flag into a Russian flag.
input
The input consists of 1 + N lines.
On the first line, two integers N and M (3 ≤ N ≤ 50, 3 ≤ M ≤ 50) are written separated by a blank. This means that the flags are separated by N rows and M columns.
The following N lines each contain a string of M characters, which represents the color information painted in the squares of the old flag. The jth character (1 ≤ i ≤ N, 1 ≤ j ≤ M) on the i-th line of the N-line represents the color of the cell on the i-th line and j-th column of the old flag. It is either B'or'R'. 'W' stands for white,'B' stands for blue, and'R' stands for red.
output
Output in one line the minimum number of squares that President K needs to repaint to turn the old flag into a Russian flag.
Input / output example
Input example 1
4 5
WRWRW
BWRWB
WRWRW
RWBWR
Output example 1
11
Input example 2
6 14
WWWWWWWWWWWWWW
WBBBWWRRWWBBBW
WWBWWRRRRWWBWW
BWBWWRRRRWWBWW
WBBWWWRRWWBBBW
WWWWWWWWWWWWWW
Output example 2
44
In I / O example 1, the old flag is colored as shown in the figure below.
fig01
In the figure below, repaint the 11 squares with an'X'.
fig02
This makes it possible to make the Russian flag as shown in the figure below.
fig03
Since it is not possible to make a Russian flag by repainting less than 11 squares, 11 is output.
In I / O example 2, the old flag is colored as shown in the figure below.
fig04
Creative Commons License
Information Olympics Japan Committee work "15th Japan Information Olympics JOI 2015/2016 Qualifying Competition Tasks"
Example
Input
4 5
WRWRW
BWRWB
WRWRW
RWBWR
Output
11
|
{
"inputs": [
"3\n17 136\n859 937\n16 641\n",
"4\n-1 3\n4 5\n6 2\n3 -5\n",
"3\n0 0\n5 5\n5 0\n",
"3\n217949 72327\n20730 141135\n667478 391012\n",
"28\n-999992 -308892\n-999961 -775849\n-999942 -893083\n-999456 -939329\n-999012 -979265\n-997835 -988395\n-989576 -999615\n-707413 -999804\n-356518 -999960\n425690 -999948\n816619 -999822\n996426 -999657\n998911 -998620\n999895 -957899\n999936 -732657\n999772 776916\n999714 916237\n997146 988196\n996127 992122\n985658 999257\n878494 999690\n700248 999995\n-73464 999954\n-462535 999888\n-996558 999759\n-999198 954171\n-999766 940472\n-1000000 740830\n",
"5\n-30 3\n-27 27\n25 19\n22 11\n-9 -19\n",
"7\n682441 915628\n544253 794138\n613454 689307\n748362 488382\n785654 635758\n813511 747405\n740114 896236\n",
"26\n-999979 -518088\n-999921 118990\n-999886 336599\n-999749 963071\n-999613 971778\n-997505 993563\n-988075 999871\n-724057 999931\n338004 999963\n939763 999692\n979017 999536\n997778 999063\n999010 994592\n999549 991252\n999866 130647\n999941 -152592\n999901 -975591\n998258 -992117\n992764 -999373\n845158 -999949\n592531 -999958\n-810995 -999934\n-988512 -999694\n-995382 -992825\n-997701 -979912\n-999550 -923898\n",
"28\n-999858 -784428\n-999517 -939769\n-999016 -999730\n-947991 -999977\n583432 -999987\n867592 -999817\n964501 -998866\n996003 -995533\n998716 -984290\n999618 -770526\n999783 -567026\n999971 -186389\n999952 107304\n999801 823582\n998874 906964\n997851 952716\n995210 986155\n990112 999169\n958740 999772\n855833 999915\n-86160 999966\n-983466 999718\n-986557 998983\n-992779 997480\n-999153 910765\n-999678 633173\n-999792 567889\n-999874 -13740\n",
"4\n-1000000 -1000000\n-1000000 1000000\n1000000 1000000\n1000000 -1000000\n",
"26\n-999979 -518088\n-999921 118990\n-999886 336599\n-999749 963071\n-999613 971778\n-997505 993563\n-988075 999871\n-724057 999931\n338004 999963\n939763 999692\n979017 999536\n997778 999063\n999010 994592\n999549 991252\n999866 130647\n999941 -152592\n999901 -975591\n998258 -992117\n992764 -999373\n845158 -999949\n592531 -999958\n-810995 -999934\n-988512 -999694\n-995382 -992825\n-997701 -979912\n-999550 -923898\n",
"28\n-999992 -308892\n-999961 -775849\n-999942 -893083\n-999456 -939329\n-999012 -979265\n-997835 -988395\n-989576 -999615\n-707413 -999804\n-356518 -999960\n425690 -999948\n816619 -999822\n996426 -999657\n998911 -998620\n999895 -957899\n999936 -732657\n999772 776916\n999714 916237\n997146 988196\n996127 992122\n985658 999257\n878494 999690\n700248 999995\n-73464 999954\n-462535 999888\n-996558 999759\n-999198 954171\n-999766 940472\n-1000000 740830\n",
"31\n-999895 -680066\n-999346 -911069\n-997066 -995888\n-933871 -999458\n-859686 -999993\n915737 -999963\n980078 -999252\n991475 -998112\n997928 -987831\n998589 -957777\n999526 -904903\n999931 -256314\n999918 618991\n999004 979093\n994226 996559\n992378 997893\n985535 998354\n842908 999545\n497158 999818\n58368 999831\n-524382 999768\n-870707 999721\n-896847 999681\n-930692 999452\n-960753 999218\n-994745 997730\n-998380 996409\n-999326 941484\n-999695 880174\n-999953 516095\n-999959 432711\n",
"31\n-999895 -680066\n-999346 -911069\n-997066 -995888\n-933871 -999458\n-859686 -999993\n915737 -999963\n980078 -999252\n991475 -998112\n997928 -987831\n998589 -957777\n999526 -904903\n999931 -256314\n999918 618991\n999004 979093\n994226 996559\n992378 997893\n985535 998354\n842908 999545\n497158 999818\n58368 999831\n-524382 999768\n-870707 999721\n-896847 999681\n-930692 999452\n-960753 999218\n-994745 997730\n-998380 996409\n-999326 941484\n-999695 880174\n-999953 516095\n-999959 432711\n",
"21\n-999986 557566\n-999907 933716\n-999221 982044\n-991618 996837\n-989578 998869\n-959290 999999\n941636 999993\n982544 999663\n999879 996043\n999991 618961\n999916 -733361\n999799 -901915\n999501 -995358\n995904 -999369\n883475 -999921\n355631 -999988\n-521129 -999838\n-777567 -999730\n-996849 -999383\n-999891 -926971\n-999957 -555457\n",
"5\n-12 -21\n25 12\n2 28\n-25 24\n-26 -16\n",
"23\n-998149 -915915\n-995073 -944069\n-987635 -988407\n-951050 -993464\n-922353 -996259\n-897593 -998630\n-395571 -999848\n891364 -999885\n998896 -999857\n999954 -241069\n999992 665232\n999954 972998\n997503 995272\n918826 998906\n805190 999725\n-160875 999945\n-868222 999408\n-910092 998323\n-989088 995823\n-996325 994987\n-999234 862952\n-999462 618604\n-999999 -892066\n",
"6\n13 -22\n26 -11\n30 12\n22 19\n-10 24\n-29 6\n",
"4\n1000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\n",
"6\n-29 6\n-28 27\n-2 18\n13 9\n20 -18\n19 -27\n",
"29\n-999821 -886199\n-996548 -965159\n-995362 -987300\n-981634 -998332\n-908076 -999145\n-527101 -999912\n446850 -999985\n816225 -999959\n938653 -998846\n974582 -992905\n997351 -984725\n998758 -966579\n999674 -891109\n999991 -582065\n999947 570950\n999860 851333\n999509 915545\n998980 973970\n998488 994168\n990799 998749\n736579 999807\n176123 999895\n-889019 999998\n-919642 999796\n-952356 998373\n-974729 997284\n-994908 993778\n-999862 963244\n-999863 157789\n",
"6\n-476965 -162114\n-528389 -150910\n-582349 -113696\n-668732 17055\n-505653 187057\n-320725 378075\n",
"6\n-14 2\n11 28\n15 -2\n15 -28\n13 -30\n9 -26\n",
"21\n-999986 557566\n-999907 933716\n-999221 982044\n-991618 996837\n-989578 998869\n-959290 999999\n941636 999993\n982544 999663\n999879 996043\n999991 618961\n999916 -733361\n999799 -901915\n999501 -995358\n995904 -999369\n883475 -999921\n355631 -999988\n-521129 -999838\n-777567 -999730\n-996849 -999383\n-999891 -926971\n-999957 -555457\n",
"21\n-999896 -977584\n-981090 -998920\n-955737 -999433\n-836670 -999598\n-131267 -999903\n873713 -999850\n988083 -997441\n997685 -976930\n998079 -967700\n999138 -906399\n999967 -779494\n999875 608972\n998802 997105\n997089 999540\n891311 999873\n46007 999962\n-991551 999757\n-999301 968587\n-999579 875737\n-999730 549856\n-999960 51168\n",
"23\n-998149 -915915\n-995073 -944069\n-987635 -988407\n-951050 -993464\n-922353 -996259\n-897593 -998630\n-395571 -999848\n891364 -999885\n998896 -999857\n999954 -241069\n999992 665232\n999954 972998\n997503 995272\n918826 998906\n805190 999725\n-160875 999945\n-868222 999408\n-910092 998323\n-989088 995823\n-996325 994987\n-999234 862952\n-999462 618604\n-999999 -892066\n",
"4\n-4 -20\n10 6\n-7 23\n-27 -17\n",
"6\n16 -23\n28 -4\n24 4\n14 14\n-13 5\n-27 -4\n",
"4\n-13 -21\n22 -14\n19 -2\n-20 27\n",
"29\n-999821 -886199\n-996548 -965159\n-995362 -987300\n-981634 -998332\n-908076 -999145\n-527101 -999912\n446850 -999985\n816225 -999959\n938653 -998846\n974582 -992905\n997351 -984725\n998758 -966579\n999674 -891109\n999991 -582065\n999947 570950\n999860 851333\n999509 915545\n998980 973970\n998488 994168\n990799 998749\n736579 999807\n176123 999895\n-889019 999998\n-919642 999796\n-952356 998373\n-974729 997284\n-994908 993778\n-999862 963244\n-999863 157789\n",
"28\n-999950 -887483\n-999941 -898020\n-999541 -954162\n-998380 -979624\n-996809 -989471\n-974206 -998846\n-814103 -999939\n-562253 -999986\n38935 -999954\n949101 -999859\n967558 -998977\n974753 -998193\n980440 -995185\n995399 -975723\n999674 -949939\n999839 -915815\n999975 -114127\n999981 971763\n999561 997999\n989473 999261\n917401 999944\n-468594 999853\n-693444 999675\n-914976 999234\n-997478 996529\n-999955 951845\n-999982 144675\n-999992 -224003\n",
"11\n-66147 342486\n-84392 250625\n-79482 200009\n114303 -75951\n143385 -63417\n228821 15223\n234858 79257\n222911 116017\n174646 182146\n101613 255473\n27282 308745\n",
"4\n1000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\n",
"28\n-999950 -887483\n-999941 -898020\n-999541 -954162\n-998380 -979624\n-996809 -989471\n-974206 -998846\n-814103 -999939\n-562253 -999986\n38935 -999954\n949101 -999859\n967558 -998977\n974753 -998193\n980440 -995185\n995399 -975723\n999674 -949939\n999839 -915815\n999975 -114127\n999981 971763\n999561 997999\n989473 999261\n917401 999944\n-468594 999853\n-693444 999675\n-914976 999234\n-997478 996529\n-999955 951845\n-999982 144675\n-999992 -224003\n",
"7\n-29 5\n-20 13\n-4 22\n8 20\n21 9\n16 -29\n-23 -30\n",
"6\n-30 30\n21 30\n29 5\n27 -7\n13 -20\n-24 -30\n",
"4\n-1000000 -1000000\n-1000000 1000000\n1000000 1000000\n1000000 -1000000\n",
"8\n22 -28\n29 -1\n28 9\n26 14\n19 22\n-3 29\n-9 26\n-29 -14\n",
"7\n682441 915628\n544253 794138\n613454 689307\n748362 488382\n785654 635758\n813511 747405\n740114 896236\n",
"3\n217949 72327\n20730 141135\n667478 391012\n",
"28\n-999858 -784428\n-999517 -939769\n-999016 -999730\n-947991 -999977\n583432 -999987\n867592 -999817\n964501 -998866\n996003 -995533\n998716 -984290\n999618 -770526\n999783 -567026\n999971 -186389\n999952 107304\n999801 823582\n998874 906964\n997851 952716\n995210 986155\n990112 999169\n958740 999772\n855833 999915\n-86160 999966\n-983466 999718\n-986557 998983\n-992779 997480\n-999153 910765\n-999678 633173\n-999792 567889\n-999874 -13740\n",
"9\n-30 -17\n-30 -12\n-28 24\n-21 29\n8 29\n18 14\n26 -11\n9 -29\n-25 -30\n",
"8\n-18 -20\n16 -28\n29 -29\n29 25\n15 27\n-19 30\n-28 18\n-30 -16\n",
"7\n-16 -30\n18 -12\n23 -1\n-3 5\n-20 5\n-22 1\n-23 -27\n",
"6\n-476965 -162114\n-528389 -150910\n-582349 -113696\n-668732 17055\n-505653 187057\n-320725 378075\n",
"11\n-66147 342486\n-84392 250625\n-79482 200009\n114303 -75951\n143385 -63417\n228821 15223\n234858 79257\n222911 116017\n174646 182146\n101613 255473\n27282 308745\n",
"21\n-999896 -977584\n-981090 -998920\n-955737 -999433\n-836670 -999598\n-131267 -999903\n873713 -999850\n988083 -997441\n997685 -976930\n998079 -967700\n999138 -906399\n999967 -779494\n999875 608972\n998802 997105\n997089 999540\n891311 999873\n46007 999962\n-991551 999757\n-999301 968587\n-999579 875737\n-999730 549856\n-999960 51168\n",
"3\n217949 72327\n20730 141135\n667478 663894\n",
"5\n-30 3\n-27 27\n25 19\n22 11\n-9 -28\n",
"26\n-999979 -518088\n-999921 118990\n-999886 336599\n-999749 894870\n-999613 971778\n-997505 993563\n-988075 999871\n-724057 999931\n338004 999963\n939763 999692\n979017 999536\n997778 999063\n999010 994592\n999549 991252\n999866 130647\n999941 -152592\n999901 -975591\n998258 -992117\n992764 -999373\n845158 -999949\n592531 -999958\n-810995 -999934\n-988512 -999694\n-995382 -992825\n-997701 -979912\n-999550 -923898\n",
"5\n-4 -21\n25 12\n2 28\n-25 24\n-26 -16\n",
"4\n1000 1000\n-1000 1100\n-1000 -1000\n1000 -1000\n",
"4\n-4 -20\n10 6\n-10 23\n-27 -17\n",
"4\n-13 -21\n22 -6\n19 -2\n-20 27\n",
"28\n-999950 -887483\n-999941 -898020\n-999541 -954162\n-998380 -979624\n-996809 -989471\n-974206 -998846\n-814103 -999939\n-562253 -999986\n39584 -999954\n949101 -999859\n967558 -998977\n974753 -998193\n980440 -995185\n995399 -975723\n999674 -949939\n999839 -915815\n999975 -114127\n999981 971763\n999561 997999\n989473 999261\n917401 999944\n-468594 999853\n-693444 999675\n-914976 999234\n-997478 996529\n-999955 951845\n-999982 144675\n-999992 -224003\n",
"4\n0000 1000\n-1000 1000\n-1000 -1000\n1000 -1000\n",
"7\n-29 5\n-20 13\n-4 22\n8 20\n21 9\n16 -29\n-20 -30\n",
"4\n-1000000 -1000000\n-1000000 1000010\n1000000 1000000\n1000000 -1000000\n",
"3\n217949 72327\n20730 141135\n667478 31198\n",
"9\n-30 -17\n-30 -12\n-28 24\n-21 29\n8 29\n36 14\n26 -11\n9 -29\n-25 -30\n",
"8\n-18 -20\n16 -28\n29 -22\n29 25\n15 27\n-19 30\n-28 18\n-30 -16\n",
"7\n-16 -30\n18 -12\n23 -1\n-3 5\n-20 7\n-22 1\n-23 -27\n",
"21\n-999896 -977584\n-981090 -998920\n-955737 -999433\n-836670 -999598\n-131267 -999903\n203740 -999850\n988083 -997441\n997685 -976930\n998079 -967700\n999138 -906399\n999967 -779494\n999875 608972\n998802 997105\n997089 999540\n891311 999873\n46007 999962\n-991551 999757\n-999301 968587\n-999579 875737\n-999730 549856\n-999960 51168\n",
"3\n17 69\n859 937\n16 641\n",
"4\n-1 3\n4 5\n6 2\n0 -5\n",
"3\n1 0\n5 5\n5 0\n",
"3\n280683 72327\n20730 141135\n667478 663894\n",
"5\n-30 3\n-27 27\n25 19\n20 11\n-9 -28\n",
"5\n0 -21\n25 12\n2 28\n-25 24\n-26 -16\n",
"4\n1000 1000\n-1000 1100\n-1000 -1000\n1000 -1786\n",
"4\n-4 -39\n10 6\n-10 23\n-27 -17\n",
"4\n-13 -21\n22 -6\n19 -2\n-24 27\n",
"4\n0000 1000\n-1000 1000\n-1000 -379\n1000 -1000\n",
"3\n217949 72327\n6264 141135\n667478 31198\n",
"9\n-30 -17\n-30 -12\n-28 24\n-27 29\n8 29\n36 14\n26 -11\n9 -29\n-25 -30\n",
"8\n-18 -20\n10 -28\n29 -22\n29 25\n15 27\n-19 30\n-28 18\n-30 -16\n",
"3\n17 12\n859 937\n16 641\n",
"4\n-1 3\n4 5\n6 1\n0 -5\n",
"3\n1 0\n5 5\n5 1\n",
"3\n280683 29080\n20730 141135\n667478 663894\n",
"5\n-30 3\n-27 27\n25 30\n20 11\n-9 -28\n",
"5\n0 -21\n25 12\n2 28\n-25 24\n-26 -1\n",
"4\n1000 1000\n-1000 1100\n-1728 -1000\n1000 -1786\n",
"4\n-4 -39\n10 6\n-10 20\n-27 -17\n",
"4\n-13 -21\n22 -6\n19 -2\n-24 52\n",
"4\n0000 1000\n-1000 1000\n-1000 -379\n1001 -1000\n",
"3\n217949 72327\n6264 78064\n667478 31198\n",
"9\n-30 -17\n-30 -12\n-28 24\n-27 29\n8 29\n36 14\n36 -11\n9 -29\n-25 -30\n",
"8\n-18 -20\n10 -28\n29 -33\n29 25\n15 27\n-19 30\n-28 18\n-30 -16\n",
"3\n17 12\n859 937\n16 1057\n",
"4\n-1 5\n4 5\n6 1\n0 -5\n"
],
"outputs": [
"66811.370415516887746\n",
"8.1583333333333333329\n",
"4.666666666666666667\n",
"22999661597.980510168\n",
"666355240785.78547126\n",
"269.93154354412514986\n",
"11812099113.198906063\n",
"666361287504.79009098\n",
"666134075600.89424652\n",
"666667333333.50004309\n",
"666361287504.79009098\n",
"666355240785.78547126\n",
"666145135876.54934293\n",
"666145135876.54934293\n",
"666453766184.64771605\n",
"281.26250791565549494\n",
"665633654239.28539926\n",
"293.07884867988966243\n",
"667333.5\n",
"308.28568389629316221\n",
"666005823973.81177771\n",
"19121483829.078974685\n",
"200.74140382398977316\n",
"666453766184.64771605\n",
"666126548753.50211442\n",
"665633654239.28539926\n",
"165.42397732771134305\n",
"209.47941088067327924\n",
"216.07819613731848751\n",
"666005823973.81177771\n",
"666225623675.06491923\n",
"15436765129.492549143\n",
"667333.5\n",
"666225623675.06491923\n",
"339.36312023933664495\n",
"470.61519132671378501\n",
"666667333333.50004309\n",
"364.55017568255569907\n",
"11812099113.198906063\n",
"22999661597.980510168\n",
"666134075600.89424652\n",
"451.08235391381990145\n",
"499.56600036815042035\n",
"206.02539574224311505\n",
"19121483829.078974685\n",
"15436765129.492549143\n",
"666126548753.502075195312500\n",
"35756046110.2309945226",
"308.2801311282",
"666358831414.6079000831",
"289.0516046264",
"684405.4678022212",
"162.6840779955",
"191.1056861190",
"666225628494.0333230495",
"549932.3816872411",
"331.0099259507",
"666668833340.3902065754",
"18826858661.6411153264",
"511.7550960338",
"485.4708957418",
"207.9144001321",
"665955557792.9263055325",
"71931.7258136343",
"8.7833333333",
"4.0625000000",
"35095331479.8769511469",
"301.1828482196",
"293.8347891422",
"854913.4674257650",
"243.1268260748",
"203.4203887524",
"472397.3291107740",
"19516752617.6137520019",
"516.2709172523",
"484.3927618292",
"76677.1311187669",
"9.0868686869",
"3.8712121212",
"36785861667.2475881986",
"348.2144744701",
"261.8747461929",
"1004446.2298619596",
"228.4563133619",
"345.6132469222",
"472479.1130488308",
"19111437385.6797773242",
"554.8901201943",
"514.7589784068",
"93991.3658479677",
"10.3560784314"
]
}
|
Ksusha is a vigorous mathematician. She is keen on absolutely incredible mathematical riddles.
Today Ksusha came across a convex polygon of non-zero area. She is now wondering: if she chooses a pair of distinct points uniformly among all integer points (points with integer coordinates) inside or on the border of the polygon and then draws a square with two opposite vertices lying in the chosen points, what will the expectation of this square's area be?
A pair of distinct points is chosen uniformly among all pairs of distinct points, located inside or on the border of the polygon. Pairs of points p, q (p ≠ q) and q, p are considered the same.
Help Ksusha! Count the required expectation.
Input
The first line contains integer n (3 ≤ n ≤ 105) — the number of vertices of Ksusha's convex polygon. Next n lines contain the coordinates of the polygon vertices in clockwise or counterclockwise order. The i-th line contains integers xi, yi (|xi|, |yi| ≤ 106) — the coordinates of the vertex that goes i-th in that order.
Output
Print a single real number — the required expected area.
The answer will be considered correct if its absolute and relative error doesn't exceed 10 - 6.
Examples
Input
3
0 0
5 5
5 0
Output
4.6666666667
Input
4
-1 3
4 5
6 2
3 -5
Output
8.1583333333
Input
3
17 136
859 937
16 641
Output
66811.3704155169
|
{
"inputs": [
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 6\n3\n10 10 10\n",
"4\n5\n1 2 1 2 4\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 2 1 2 2\n5\n1 2 1 2 6\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 0 3\n3\n14 11 10\n",
"4\n5\n1 2 1 0 2\n6\n1 4 2 1 2 2\n5\n1 2 1 2 3\n3\n18 20 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 0 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n0 2 1 2 2\n6\n1 2 0 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 4\n5\n1 2 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n18 10 10\n",
"4\n5\n1 3 1 2 4\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 4\n6\n1 2 0 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 4\n5\n1 0 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 0 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n18 10 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 2 0 2 2\n5\n1 2 1 2 6\n3\n10 10 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 -1 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 4\n6\n1 2 -1 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 -1 1 2 3\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 0\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 0 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 4 3\n3\n14 10 10\n",
"4\n5\n0 2 1 2 2\n6\n1 2 0 1 2 2\n5\n1 2 1 0 3\n3\n14 10 0\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 5\n5\n1 2 1 2 3\n3\n10 10 10\n",
"4\n5\n1 4 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n18 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 1 2 2\n5\n1 2 1 0 3\n3\n0 10 10\n",
"4\n5\n1 2 1 2 2\n6\n0 2 2 1 2 4\n5\n1 0 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 0 2\n6\n1 4 2 1 2 2\n5\n1 2 1 2 3\n3\n18 10 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 2 1 2 2\n5\n1 3 1 2 6\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 3 -1 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 2 1 2 2\n5\n1 2 1 4 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 3 2\n5\n1 2 1 0 3\n3\n14 11 10\n",
"4\n5\n0 2 1 2 2\n6\n1 2 0 1 2 2\n5\n1 2 1 -1 3\n3\n14 10 0\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 1 2 2\n5\n1 3 1 0 3\n3\n0 10 10\n",
"4\n5\n1 4 1 0 2\n6\n1 4 2 1 2 2\n5\n1 2 1 2 3\n3\n18 10 10\n",
"4\n5\n1 2 1 2 6\n6\n1 2 2 1 2 2\n5\n1 3 1 2 6\n3\n10 10 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 2 1 2 1\n5\n1 2 1 4 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 3 2\n5\n0 2 1 0 3\n3\n14 11 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 1 2 2\n5\n1 3 2 0 3\n3\n0 10 10\n",
"4\n5\n1 4 1 0 2\n6\n1 4 2 1 2 2\n5\n1 2 1 0 3\n3\n18 10 10\n",
"4\n5\n1 2 1 2 6\n6\n1 2 2 0 2 2\n5\n1 3 1 2 6\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 3 2 0 3\n3\n0 10 10\n",
"4\n5\n1 2 0 2 2\n6\n1 2 -1 0 2 2\n5\n1 3 2 0 3\n3\n0 10 10\n",
"4\n5\n1 2 0 2 2\n6\n0 2 -1 0 2 2\n5\n1 3 2 0 3\n3\n0 10 10\n",
"4\n5\n1 2 1 2 2\n6\n0 2 -1 0 2 2\n5\n1 3 2 0 3\n3\n0 10 10\n",
"4\n5\n1 2 1 2 2\n6\n0 2 -1 0 2 2\n5\n1 3 2 0 3\n3\n0 16 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 3 2 0 3\n3\n0 16 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 3 2 0 3\n3\n0 16 4\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 4 2 0 3\n3\n0 16 4\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 4 2 0 3\n3\n0 13 4\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 4 2 0 3\n3\n1 13 4\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 4 2 0 3\n3\n2 13 4\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 4 2 0 3\n3\n2 13 6\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 4 2 -1 3\n3\n2 13 6\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 1 2\n5\n1 4 2 -1 3\n3\n2 13 6\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 1 2\n5\n1 4 2 -1 6\n3\n2 13 6\n",
"4\n5\n1 2 1 2 2\n6\n1 2 0 1 2 2\n5\n1 2 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 4 2\n5\n1 2 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n0 2 2 1 2 2\n5\n1 2 1 2 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 0 1 3 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n0 2 1 2 2\n6\n1 2 0 1 2 2\n5\n1 2 1 0 3\n3\n16 10 10\n",
"4\n5\n1 3 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 2\n5\n1 2 1 2 3\n3\n18 4 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 2 1 2 2\n5\n1 2 1 2 6\n3\n1 10 10\n",
"4\n5\n1 3 1 2 4\n6\n1 2 2 1 2 2\n5\n1 2 0 2 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -2 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 0 3\n6\n1 2 2 0 2 2\n5\n1 2 1 2 6\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 0 2 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 2 5\n5\n1 4 1 2 3\n3\n10 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 1 2 2\n5\n1 2 1 -1 3\n3\n0 10 10\n",
"4\n5\n1 2 1 2 3\n6\n1 2 2 1 2 2\n5\n1 2 1 0 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 3 2\n5\n1 2 1 0 3\n3\n0 11 10\n",
"4\n5\n0 2 1 2 2\n6\n1 2 0 1 2 2\n5\n1 2 0 -1 3\n3\n14 10 0\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 1 2 0\n5\n1 3 1 0 3\n3\n0 10 10\n",
"4\n5\n1 4 1 0 0\n6\n1 4 2 1 2 2\n5\n1 2 1 2 3\n3\n18 10 10\n",
"4\n5\n1 2 1 2 6\n6\n1 2 2 1 2 2\n5\n2 3 1 2 6\n3\n10 10 10\n",
"4\n5\n1 2 1 2 3\n6\n0 2 2 1 2 1\n5\n1 2 1 4 3\n3\n14 10 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 2 1 3 2\n5\n0 2 1 0 3\n3\n14 11 18\n",
"4\n5\n1 2 1 2 6\n6\n1 2 2 0 2 2\n5\n1 3 1 2 0\n3\n10 10 10\n",
"4\n5\n1 2 0 2 2\n6\n1 2 -1 0 2 2\n5\n2 3 2 0 3\n3\n0 10 10\n",
"4\n5\n1 2 0 2 2\n6\n0 2 -1 0 2 4\n5\n1 3 2 0 3\n3\n0 10 10\n",
"4\n5\n1 2 1 2 2\n6\n0 2 -1 0 2 2\n5\n2 3 2 0 3\n3\n0 16 10\n",
"4\n5\n1 2 1 2 2\n6\n1 2 -1 0 2 2\n5\n1 3 2 1 3\n3\n0 16 10\n"
],
"outputs": [
"2\n1 2 1 2 2 \n2\n1 2 1 2 1 2 \n3\n1 2 1 2 3\n1\n1 1 1 \n",
"2\n1 2 1 2 2 \n2\n1 2 1 2 1 2 \n3\n1 2 1 2 3\n1\n1 1 1 \n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"3\n1 2 1 2 3\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n1\n1 1 1\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n2\n1 2 2\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n",
"2\n1 2 1 2 2\n2\n1 2 1 2 1 2\n3\n1 2 1 2 3\n3\n1 2 3\n"
]
}
|
The round carousel consists of n figures of animals. Figures are numbered from 1 to n in order of the carousel moving. Thus, after the n-th figure the figure with the number 1 follows. Each figure has its own type — the type of the animal corresponding to this figure (the horse, the tiger and so on). The type of animal of the i-th figure equals t_i.
<image> The example of the carousel for n=9 and t=[5, 5, 1, 15, 1, 5, 5, 1, 1].
You want to color each figure in one of the colors. You think that it's boring if the carousel contains two different figures (with the distinct types of animals) going one right after another and colored in the same color.
Your task is to color the figures in such a way that the number of distinct colors used is the minimum possible and there are no figures of the different types going one right after another and colored in the same color. If you use exactly k distinct colors, then the colors of figures should be denoted with integers from 1 to k.
Input
The input contains one or more test cases.
The first line contains one integer q (1 ≤ q ≤ 10^4) — the number of test cases in the test. Then q test cases follow. One test case is given on two lines.
The first line of the test case contains one integer n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of figures in the carousel. Figures are numbered from 1 to n in order of carousel moving. Assume that after the n-th figure the figure 1 goes.
The second line of the test case contains n integers t_1, t_2, ..., t_n (1 ≤ t_i ≤ 2 ⋅ 10^5), where t_i is the type of the animal of the i-th figure.
The sum of n over all test cases does not exceed 2⋅10^5.
Output
Print q answers, for each test case print two lines.
In the first line print one integer k — the minimum possible number of distinct colors of figures.
In the second line print n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ k), where c_i is the color of the i-th figure. If there are several answers, you can print any.
Example
Input
4
5
1 2 1 2 2
6
1 2 2 1 2 2
5
1 2 1 2 3
3
10 10 10
Output
2
1 2 1 2 2
2
2 1 2 1 2 1
3
2 3 2 3 1
1
1 1 1
|
{
"inputs": [
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 1 5\nD 1 5\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 2 5\nD 1 5\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nU 1 5\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 1 5\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 4 4\nU 1 5\nD 1 5\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nU 1 5\nD 2 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 1 5\nD 1 2\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 2 4\nU 1 5\nD 1 5\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 2 5\nD 1 5\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nU 1 5\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 3 3\nR 4 4\nU 1 5\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 1 4\nU 1 2\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 2 5\nD 1 2\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 1 3\nR 3 4\nU 2 5\nD 1 2\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nT 2 5\nD 1 5\n",
"4 5 4\nRRBB\nBBRR\nBBBBB\nRRRRR\nL 1 3\nR 1 4\nU 2 5\nD 1 2\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nU 1 5\nD 1 2\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 1 4\nU 1 5\nD 1 1\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 4 4\nU 1 5\nD 2 5\n",
"4 5 4\nRRBB\nRBRB\nBBBBB\nRRRRR\nL 3 3\nR 4 4\nU 1 5\nD 1 5\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nU 1 3\nD 1 2\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nV 1 5\nD 1 5\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nU 1 4\nD 1 2\n",
"4 5 4\nBBRR\nRRBB\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 1 5\nD 1 5\n",
"4 5 4\nRBRB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 2 5\nD 1 3\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 1 5\nD 2 2\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 2 4\nU 2 5\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 1 3\nR 1 4\nU 2 5\nD 2 2\n",
"4 5 4\nRRBB\nBBRR\nBBBBB\nRRRRR\nL 1 3\nR 1 3\nU 2 5\nD 1 2\n",
"4 5 0\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 1 5\nD 1 5\n",
"4 5 4\nBBRR\nRRBB\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 2 5\nD 1 5\n",
"4 5 4\nRRBB\nRRBB\nBBBBB\nRRRRR\nL 1 3\nR 1 3\nU 2 5\nD 1 2\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 1 4\nR 4 4\nU 1 5\nD 1 5\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 2 5\nD 1 3\n",
"4 5 4\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 1 4\nU 1 5\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 1 4\nU 1 5\nD 1 5\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nT 2 5\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 1 3\nR 1 4\nU 2 5\nD 1 2\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 1\nR 3 4\nT 2 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 2\nR 3 4\nT 2 5\nD 1 5\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nV 1 5\nD 1 5\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nQ 3 4\nT 2 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 4 4\nT 2 5\nD 1 5\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 1 4\nU 2 5\nD 1 2\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nK 2 1\nR 3 4\nT 2 5\nD 1 5\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 1 5\nD 1 5\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 1 5\nD 1 10\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 1 5\nD 2 10\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 1 5\nD 0 10\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 4 4\nU 1 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 7\nT 2 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 1\nR 3 4\nS 2 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 2\nR 6 4\nT 2 5\nD 1 5\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 4\nW 1 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 4 4\nT 2 10\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nK 2 1\nR 3 4\nT 1 5\nD 1 5\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 1\nV 1 5\nD 1 5\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 0 7\nV 1 5\nD 1 10\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 1 5\nC 2 10\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 0 5\nD 0 10\n",
"4 5 4\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 4\nU 2 5\nD 1 5\n",
"4 5 1\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 3 4\nR 4 4\nU 1 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 3\nR 3 7\nT 2 5\nE 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 2 0\nR 3 4\nS 2 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nK 2 2\nR 6 4\nT 2 5\nD 1 5\n",
"4 5 0\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 1 8\nD 1 5\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 1 7\nV 1 5\nD 1 10\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 3 7\nV 0 5\nE 0 10\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 1 0\nR 3 4\nS 2 5\nD 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nK 2 2\nR 6 4\nT 2 5\nE 1 5\n",
"4 5 0\nRRBB\nRBBR\nBBBBB\nRRRRR\nM 2 4\nR 3 7\nV 1 8\nD 1 5\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 1 7\nU 1 5\nD 1 10\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 4 4\nR 3 7\nV 0 5\nE 0 10\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 1 0\nR 3 4\nS 2 5\nC 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nK 2 2\nR 6 4\nT 1 5\nE 1 5\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 2 4\nR 1 7\nU 1 5\nE 1 10\n",
"4 5 1\nRRBB\nRBBR\nBBBBB\nRRRRR\nL 4 4\nR 3 7\nU 0 5\nE 0 10\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 0 0\nR 3 4\nS 2 5\nC 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nK 2 2\nR 6 4\nT 1 4\nE 1 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 0 0\nR 3 4\nS 2 5\nC 2 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nK 2 2\nR 6 4\nT 1 4\nE 1 7\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nL 0 0\nR 3 4\nS 2 5\nC 3 5\n",
"4 5 0\nBBRR\nRBBR\nBBBBB\nRRRRR\nK 2 2\nQ 6 4\nT 1 4\nE 1 7\n"
],
"outputs": [
"7\n7\n9\n4\n9\n",
"7\n7\n9\n5\n8\n",
"7\n8\n8\n5\n8\n",
"9\n9\n9\n4\n7\n",
"9\n9\n8\n5\n6\n",
"7\n8\n8\n5\n9\n",
"9\n9\n9\n4\n6\n",
"9\n9\n8\n3\n6\n",
"7\n7\n",
"7\n8\n",
"9\n8\n9\n4\n7\n",
"9\n9\n9\n7\n6\n",
"9\n9\n9\n5\n7\n",
"9\n8\n8\n6\n8\n",
"7\n",
"9\n6\n8\n6\n8\n",
"7\n8\n8\n5\n7\n",
"7\n8\n8\n5\n6\n",
"9\n9\n8\n5\n7\n",
"9\n8\n7\n2\n7\n",
"7\n8\n8\n7\n9\n",
"9\n8\n",
"7\n8\n8\n6\n8\n",
"9\n9\n7\n2\n7\n",
"9\n9\n9\n5\n8\n",
"9\n9\n9\n4\n5\n",
"9\n9\n8\n4\n7\n",
"9\n8\n8\n6\n7\n",
"9\n6\n9\n5\n7\n",
"9\n",
"9\n9\n7\n3\n8\n",
"9\n8\n7\n7\n9\n",
"7\n9\n",
"7\n7\n9\n5\n8\n",
"7\n8\n8\n5\n8\n",
"9\n9\n9\n4\n7\n",
"7\n7\n",
"9\n8\n8\n6\n8\n",
"7\n",
"7\n",
"7\n8\n",
"7\n7\n",
"7\n",
"9\n9\n9\n5\n7\n",
"7\n",
"9\n8\n",
"9\n8\n",
"9\n8\n",
"9\n8\n",
"7\n8\n",
"7\n",
"7\n",
"7\n",
"7\n8\n",
"7\n",
"7\n",
"9\n8\n",
"9\n8\n",
"9\n8\n",
"9\n8\n",
"9\n9\n9\n5\n8\n",
"7\n7\n",
"7\n",
"7\n",
"7\n",
"9\n",
"9\n8\n",
"9\n8\n",
"7\n",
"7\n",
"9\n",
"9\n8\n",
"9\n8\n",
"7\n",
"7\n",
"9\n8\n",
"9\n8\n",
"7\n",
"7\n",
"7\n",
"7\n",
"7\n",
"7\n"
]
}
|
This is a harder version of the problem H with modification queries.
Lester and Delbert work at an electronics company. They are currently working on a microchip component serving to connect two independent parts of a large supercomputer.
The component is built on top of a breadboard — a grid-like base for a microchip. The breadboard has n rows and m columns, and each row-column intersection contains a node. Also, on each side of the breadboard there are ports that can be attached to adjacent nodes. Left and right side have n ports each, and top and bottom side have m ports each. Each of the ports is connected on the outside to one of the parts bridged by the breadboard, and is colored red or blue respectively.
<image>
Ports can be connected by wires going inside the breadboard. However, there are a few rules to follow:
* Each wire should connect a red port with a blue port, and each port should be connected to at most one wire.
* Each part of the wire should be horizontal or vertical, and turns are only possible at one of the nodes.
* To avoid interference, wires can not have common parts of non-zero length (but may have common nodes). Also, a wire can not cover the same segment of non-zero length twice.
The capacity of the breadboard is the largest number of red-blue wire connections that can be made subject to the rules above. For example, the breadboard above has capacity 7, and one way to make seven connections is pictured below.
<image>
Up to this point statements of both versions are identical. Differences follow below.
As is common, specifications of the project change a lot during development, so coloring of the ports is not yet fixed. There are q modifications to process, each of them has the form of "colors of all ports in a contiguous range along one of the sides are switched (red become blue, and blue become red)". All modifications are persistent, that is, the previous modifications are not undone before the next one is made.
To estimate how bad the changes are, Lester and Delbert need to find the breadboard capacity after each change. Help them do this efficiently.
Input
The first line contains three integers n, m, q (1 ≤ n, m ≤ 10^5, 0 ≤ q ≤ 10^5) — the number of rows and columns of the breadboard, and the number of modifications respectively.
The next four lines describe initial coloring of the ports. Each character in these lines is either R or B, depending on the coloring of the respective port. The first two of these lines contain n characters each, and describe ports on the left and right sides respectively from top to bottom. The last two lines contain m characters each, and describe ports on the top and bottom sides respectively from left to right.
The next q lines describe modifications. Each of these lines contains a character s, followed by two integers l and r. If s is L or R, the modification is concerned with ports on the left/right side respectively, l and r satisfy 1 ≤ l ≤ r ≤ n, and ports in rows between l and r (inclusive) on the side switch colors. Similarly, if s is U or D, then 1 ≤ l ≤ r ≤ m, and ports in columns between l and r (inclusive) on the top/bottom side respectively switch colors.
Output
Print q + 1 integers, one per line — the breadboard capacity after 0, …, q modifications have been made to the initial coloring.
Example
Input
4 5 4
BBRR
RBBR
BBBBB
RRRRR
L 2 3
R 3 4
U 1 5
D 1 5
Output
7
7
9
4
9
|
{
"inputs": [
"2\n3 2\n2 4 7\n5 3\n1 2 3 4 5",
"2\n3 2\n2 4 7\n3 3\n1 2 3 4 5",
"2\n3 2\n2 4 7\n3 3\n1 2 3 4 9",
"2\n3 2\n2 4 7\n3 3\n1 2 3 4 7",
"2\n3 2\n2 4 10\n3 3\n1 2 3 4 7",
"2\n4 2\n1 4 7\n5 3\n1 2 3 4 9",
"2\n4 1\n1 4 7\n5 6\n1 2 5 6 9",
"2\n6 2\n2 4 7\n4 3\n1 2 3 4 12",
"2\n4 2\n1 4 5\n5 6\n1 2 3 4 9",
"2\n4 2\n1 4 11\n5 6\n1 2 3 6 9",
"2\n6 2\n2 4 10\n4 3\n1 2 3 4 12",
"2\n10 1\n1 5 7\n8 6\n1 4 5 6 9",
"2\n3 2\n2 4 8\n6 3\n1 2 3 4 5",
"2\n3 1\n2 4 7\n3 3\n1 2 3 4 7",
"2\n5 2\n1 4 7\n3 3\n1 2 3 4 5",
"2\n4 1\n1 4 7\n5 1\n1 2 5 6 9",
"2\n4 2\n1 4 5\n5 6\n1 2 3 4 16",
"2\n10 1\n1 5 7\n8 6\n1 4 5 6 17",
"2\n0 2\n2 4 7\n5 3\n1 2 3 4 6",
"2\n4 1\n2 4 7\n5 1\n1 2 5 6 9",
"2\n8 1\n1 6 10\n6 6\n1 2 5 6 9",
"2\n10 1\n1 5 7\n8 6\n1 4 5 6 31",
"2\n3 2\n2 4 7\n5 3\n1 2 3 4 8",
"2\n8 1\n2 6 10\n6 6\n1 2 5 6 9",
"2\n10 1\n1 5 7\n8 6\n1 4 5 6 58",
"2\n3 4\n2 4 7\n5 3\n1 2 3 4 8",
"2\n6 3\n2 4 7\n5 3\n1 2 3 4 12",
"2\n8 1\n2 8 10\n6 6\n1 2 5 6 9",
"2\n3 2\n3 4 7\n4 3\n1 2 3 4 7",
"2\n4 1\n1 4 14\n5 7\n1 2 5 6 9",
"2\n10 1\n1 6 7\n8 6\n1 2 5 6 18",
"2\n6 2\n2 4 10\n8 3\n1 2 3 8 11",
"2\n10 1\n1 5 8\n8 6\n1 4 5 6 17",
"2\n4 1\n2 4 7\n5 2\n1 2 5 6 9",
"2\n4 2\n1 4 8\n5 3\n1 2 3 4 16",
"2\n10 2\n1 5 7\n8 6\n1 4 5 6 31",
"2\n0 1\n2 4 7\n2 3\n1 2 3 4 6",
"2\n6 3\n2 4 7\n5 3\n1 2 3 4 23",
"2\n4 1\n1 6 14\n5 7\n1 2 5 6 9",
"2\n4 2\n2 4 7\n5 5\n1 2 3 4 15",
"2\n10 1\n1 6 7\n8 6\n1 2 5 6 15",
"2\n18 1\n1 6 7\n8 6\n1 3 5 6 10",
"2\n1 2\n1 3 12\n3 3\n1 2 3 4 5",
"2\n10 2\n2 5 7\n8 6\n1 4 5 6 31",
"2\n10 1\n2 6 7\n8 6\n1 2 5 6 15",
"2\n12 2\n2 4 18\n22 3\n1 2 4 8 12",
"2\n1 2\n1 3 7\n2 2\n1 2 3 4 10",
"2\n1 2\n2 3 7\n1 1\n1 2 3 4 10",
"2\n4 2\n2 4 13\n5 3\n1 2 3 4 5",
"2\n4 2\n1 4 7\n5 5\n1 2 3 4 7",
"2\n8 1\n1 4 7\n5 6\n1 2 5 6 18",
"2\n10 1\n2 6 7\n5 6\n1 2 5 6 9",
"2\n4 2\n1 2 7\n5 6\n1 2 5 6 15",
"2\n4 2\n1 4 7\n5 1\n1 2 5 6 9",
"2\n8 1\n1 6 10\n6 6\n1 2 5 6 11",
"2\n5 2\n1 4 6\n5 12\n1 2 4 6 9",
"2\n10 1\n1 5 7\n8 6\n1 4 5 6 33",
"2\n6 1\n2 4 7\n1 3\n1 2 3 4 12",
"2\n3 2\n3 4 14\n6 3\n1 2 3 4 5",
"2\n3 2\n2 4 12\n5 16\n1 2 3 4 5",
"2\n5 2\n2 4 7\n5 1\n1 2 3 4 17",
"2\n1 1\n1 4 11\n5 6\n1 2 3 6 9",
"2\n10 2\n1 5 7\n8 6\n1 4 5 6 21",
"2\n4 4\n2 4 7\n5 3\n1 2 3 4 16",
"2\n12 2\n2 4 10\n16 3\n1 3 4 8 12",
"2\n3 2\n1 5 7\n5 16\n1 2 3 4 17",
"2\n1 2\n2 3 7\n1 1\n1 2 3 8 10",
"2\n5 1\n2 4 7\n5 3\n1 2 3 4 18",
"2\n10 1\n1 6 7\n8 6\n1 4 5 6 33",
"2\n6 1\n1 4 7\n1 3\n1 2 3 4 12",
"2\n3 1\n3 4 6\n6 2\n1 2 3 4 5",
"2\n10 2\n1 5 13\n8 6\n1 4 5 6 21",
"2\n1 2\n1 5 14\n2 1\n1 2 3 4 10",
"2\n3 2\n2 6 7\n0 3\n1 2 3 4 19",
"2\n4 2\n1 5 8\n5 3\n1 2 3 8 30",
"2\n10 2\n1 5 21\n8 6\n1 4 5 6 21",
"2\n5 1\n3 4 7\n5 2\n1 2 3 4 8",
"2\n6 2\n3 5 7\n2 6\n1 2 3 4 16",
"2\n3 4\n2 6 7\n0 3\n1 2 3 4 19",
"2\n6 2\n1 4 5\n1 3\n1 2 3 4 12",
"2\n3 2\n2 4 10\n22 3\n1 2 4 9 21",
"2\n10 2\n1 5 34\n8 6\n1 4 5 6 21",
"2\n6 2\n3 5 7\n2 6\n1 2 3 4 8",
"2\n21 2\n2 6 7\n5 1\n1 2 5 6 9",
"2\n1 4\n1 6 11\n3 4\n1 2 3 4 5",
"2\n9 1\n3 4 10\n5 2\n1 2 3 4 8",
"2\n28 2\n1 2 7\n9 6\n2 4 5 6 59",
"2\n6 1\n2 4 10\n4 3\n1 2 3 4 12",
"2\n4 1\n1 4 7\n5 1\n1 3 5 6 9",
"2\n10 1\n2 5 7\n8 6\n1 4 5 6 31",
"2\n3 6\n2 4 6\n7 11\n1 2 3 4 5",
"2\n10 1\n2 5 7\n8 6\n1 4 5 6 58",
"2\n10 1\n1 6 7\n8 2\n1 2 5 6 18",
"2\n4 1\n1 4 7\n7 1\n1 4 5 6 9",
"2\n4 2\n1 4 15\n5 3\n1 2 3 4 16",
"2\n6 2\n2 4 10\n16 3\n1 2 4 8 23",
"2\n4 4\n2 4 7\n5 8\n1 2 3 6 11",
"2\n12 2\n2 4 18\n22 3\n1 3 4 8 12",
"2\n4 2\n1 4 5\n5 3\n1 2 3 4 14",
"2\n3 3\n2 4 5\n6 2\n1 2 3 4 5",
"2\n10 1\n1 3 7\n8 6\n1 4 5 6 33"
],
"outputs": [
"5\n0\n",
"5\n0\n",
"5\n4\n",
"5\n2\n",
"8\n2\n",
"4\n4\n",
"6\n4\n",
"5\n7\n",
"2\n4\n",
"8\n4\n",
"8\n7\n",
"7\n4\n",
"6\n0\n",
"7\n2\n",
"4\n0\n",
"6\n8\n",
"2\n11\n",
"7\n12\n",
"5\n1\n",
"7\n8\n",
"11\n4\n",
"7\n26\n",
"5\n3\n",
"12\n4\n",
"7\n53\n",
"4\n3\n",
"4\n7\n",
"14\n4\n",
"6\n2\n",
"13\n4\n",
"8\n13\n",
"8\n6\n",
"8\n12\n",
"7\n6\n",
"5\n11\n",
"4\n26\n",
"7\n1\n",
"4\n18\n",
"15\n4\n",
"5\n10\n",
"8\n10\n",
"8\n5\n",
"9\n0\n",
"5\n26\n",
"9\n10\n",
"16\n7\n",
"4\n5\n",
"5\n5\n",
"11\n0\n",
"4\n2\n",
"6\n13\n",
"9\n4\n",
"4\n10\n",
"4\n8\n",
"11\n6\n",
"3\n4\n",
"7\n28\n",
"7\n7\n",
"13\n0\n",
"10\n0\n",
"5\n12\n",
"10\n4\n",
"4\n16\n",
"4\n11\n",
"8\n8\n",
"4\n12\n",
"5\n9\n",
"7\n13\n",
"8\n28\n",
"6\n7\n",
"7\n0\n",
"10\n16\n",
"11\n5\n",
"5\n14\n",
"5\n25\n",
"18\n16\n",
"8\n3\n",
"6\n11\n",
"4\n14\n",
"2\n7\n",
"8\n16\n",
"31\n16\n",
"6\n3\n",
"5\n8\n",
"8\n0\n",
"11\n3\n",
"4\n54\n",
"10\n7\n",
"6\n9\n",
"8\n26\n",
"3\n0\n",
"8\n53\n",
"8\n15\n",
"6\n10\n",
"12\n11\n",
"8\n18\n",
"4\n6\n",
"16\n8\n",
"2\n9\n",
"2\n0\n",
"5\n28\n"
]
}
|
There is a line with 1000 cells numbered from 1 to 1000 from left to right and N coins placed on it. Coin i is placed at cell Xi, and no two coins are placed at the same cell.
Bob would like to move the coins to the N leftmost cells of the line. To do this, he is allowed to take a coin from any cell T and move it to cell T-j, where j is an integer between 1 and K, inclusive. This action is possible only if:
cell T-j actually exists and doesn't contain a coin;
each of the cells T-j+1, ..., T-1 contains a coin.
One coin movement takes exactly one second. Find the smallest time in which Bob can achieve his goal.
Input
The first line of the input file contains one integer T -- the number of test cases (no more than 10). Then T test cases follow, and every test case is described by two lines: the first of them contains two integers N and K (1 <= N, K <= 1000), the second of them contains N integers X1, ..., XN in strictly increasing order (1 <= Xi <= 1000).
Output
For each test case output one line containing the requested minimal time for Bob to put all the coins to the left side of the line.
Example
Input:
2
3 2
2 4 7
5 3
1 2 3 4 5
Output:
5
0
Explanation:
In the first example Bob can move the coin from cell 7 consequently to cells 6, 5, 3 and 1, then move the coin from cell 4 to cell 3. In the second example there is nothing to move.
|
{
"inputs": [
"4 3\nIN 1 4 10\nIN 2 3 20\nCOMPARE 1 2",
"10 4\nIN 10 8 2328\nIN 8 4 3765\nIN 3 8 574\nCOMPARE 4 8",
"3 5\nCOMPARE 1 2\nIN 1 2 5\nIN 2 3 3\nCOMPARE 2 3\nCOMPARE 1 3",
"3 4\nIN 2 1 2\nIN 3 1 2\nCOMPARE 1 3\nCOMPARE 2 3",
"3 5\nIN 1 2 5\nIN 1 2 5\nIN 2 3 10\nCOMPARE 1 2\nCOMPARE 2 3",
"3 4\nIN 2 1 1\nIN 3 1 2\nCOMPARE 1 3\nCOMPARE 2 3",
"4 3\nIN 1 4 10\nIN 3 3 20\nCOMPARE 1 2",
"10 4\nIN 10 8 2328\nIN 8 4 3765\nIN 3 8 40\nCOMPARE 4 8",
"3 5\nCOMPARE 1 2\nIN 1 2 6\nIN 2 3 3\nCOMPARE 2 3\nCOMPARE 1 3",
"3 5\nIN 1 2 5\nIN 1 2 5\nIN 1 3 10\nCOMPARE 1 2\nCOMPARE 2 3",
"3 4\nIN 3 1 1\nIN 3 1 2\nCOMPARE 1 3\nCOMPARE 2 3",
"3 4\nIN 3 1 2\nIN 3 1 2\nCOMPARE 1 3\nCOMPARE 2 3",
"5 4\nIN 3 1 2\nIN 3 1 2\nCOMPARE 2 3\nCOMPARE 2 3",
"4 3\nIN 1 4 10\nIN 2 1 20\nCOMPARE 1 2",
"3 5\nCOMPARE 1 2\nIN 1 2 5\nIN 2 3 3\nCOMPARE 2 3\nCOMPARE 1 1",
"3 4\nIN 2 1 0\nIN 3 1 2\nCOMPARE 1 3\nCOMPARE 2 3",
"4 3\nIN 1 4 10\nIN 3 3 20\nCOMPARE 1 1",
"3 5\nCOMPARE 1 2\nIN 1 2 5\nIN 2 3 2\nCOMPARE 2 3\nCOMPARE 1 1",
"4 3\nIN 1 4 10\nIN 2 3 20\nCOMPARE 1 4",
"10 4\nIN 10 8 4056\nIN 8 4 3765\nIN 3 8 574\nCOMPARE 4 8",
"3 4\nIN 2 1 2\nIN 3 1 2\nCOMPARE 2 3\nCOMPARE 2 3",
"10 4\nIN 10 8 2328\nIN 8 4 3765\nIN 3 8 43\nCOMPARE 4 8",
"5 4\nIN 2 1 2\nIN 3 1 2\nCOMPARE 1 3\nCOMPARE 2 3",
"3 4\nIN 2 1 0\nIN 3 1 3\nCOMPARE 1 3\nCOMPARE 2 3",
"5 4\nIN 2 1 2\nIN 3 1 2\nCOMPARE 1 4\nCOMPARE 2 3",
"3 4\nIN 2 1 0\nIN 3 1 6\nCOMPARE 1 3\nCOMPARE 2 3",
"5 4\nIN 2 1 1\nIN 3 1 2\nCOMPARE 1 4\nCOMPARE 2 3",
"3 4\nIN 1 1 0\nIN 3 1 6\nCOMPARE 1 3\nCOMPARE 2 3",
"3 4\nCOMPARE 1 2\nIN 1 2 9\nIN 2 3 3\nCOMPARE 2 3\nCOMPARE 1 3",
"5 4\nIN 2 1 1\nIN 3 1 2\nCOMPARE 1 1\nCOMPARE 2 3",
"3 3\nIN 1 1 0\nIN 3 1 6\nCOMPARE 1 3\nCOMPARE 2 3",
"5 4\nIN 2 1 1\nIN 3 1 2\nCOMPARE 1 1\nCOMPARE 3 3",
"3 4\nCOMPARE 2 2\nIN 1 2 9\nIN 2 1 3\nCOMPARE 2 3\nCOMPARE 1 3",
"5 4\nIN 2 1 1\nIN 3 1 2\nCOMPARE 2 1\nCOMPARE 3 3",
"3 5\nCOMPARE 1 2\nIN 1 2 5\nIN 2 3 0\nCOMPARE 2 3\nCOMPARE 1 3",
"3 3\nIN 1 1 0\nIN 3 1 5\nCOMPARE 1 3\nCOMPARE 2 5",
"3 4\nIN 1 2 0\nIN 3 1 12\nCOMPARE 1 3\nCOMPARE 2 3",
"10 4\nIN 6 8 802\nIN 8 4 3765\nIN 3 8 977\nCOMPARE 4 8",
"10 4\nIN 6 8 802\nIN 8 4 3765\nIN 3 8 977\nCOMPARE 6 8",
"8 4\nIN 2 1 1\nIN 3 1 0\nCOMPARE 2 3\nCOMPARE 2 3",
"10 4\nIN 6 8 802\nIN 8 4 3765\nIN 3 11 977\nCOMPARE 6 8",
"3 5\nCOMPARE 1 2\nIN 1 2 6\nIN 2 3 2\nCOMPARE 2 3\nCOMPARE 1 3",
"3 4\nIN 2 1 2\nIN 3 1 2\nCOMPARE 3 3\nCOMPARE 2 3",
"3 4\nIN 2 1 2\nIN 3 1 0\nCOMPARE 2 3\nCOMPARE 3 3",
"5 4\nIN 4 1 2\nIN 3 1 2\nCOMPARE 1 4\nCOMPARE 2 3",
"3 3\nIN 1 1 0\nIN 3 1 8\nCOMPARE 1 3\nCOMPARE 2 3",
"10 4\nIN 10 8 2407\nIN 8 4 3471\nIN 3 8 40\nCOMPARE 4 8",
"3 5\nCOMPARE 1 3\nIN 1 2 6\nIN 1 3 3\nCOMPARE 2 3\nCOMPARE 1 3",
"4 3\nIN 1 4 14\nIN 3 5 20\nCOMPARE 1 4",
"10 4\nIN 6 8 802\nIN 8 4 7322\nIN 3 8 977\nCOMPARE 4 8",
"10 4\nIN 10 8 2407\nIN 8 4 3471\nIN 4 8 40\nCOMPARE 4 8",
"10 4\nIN 4 8 802\nIN 8 4 3765\nIN 6 8 574\nCOMPARE 4 8",
"10 4\nIN 10 8 2644\nIN 8 4 3765\nIN 3 8 71\nCOMPARE 4 8",
"3 4\nIN 1 2 0\nIN 1 1 12\nCOMPARE 1 3\nCOMPARE 2 2",
"10 4\nIN 6 8 802\nIN 1 2 3765\nIN 3 8 977\nCOMPARE 6 8",
"5 5\nCOMPARE 1 2\nIN 1 4 6\nIN 2 3 2\nCOMPARE 2 3\nCOMPARE 1 3",
"5 4\nIN 3 1 3\nIN 3 1 4\nCOMPARE 2 3\nCOMPARE 1 3",
"10 4\nIN 10 8 2644\nIN 8 4 3765\nIN 3 10 71\nCOMPARE 4 8",
"10 4\nIN 10 8 2644\nIN 8 4 3765\nIN 3 8 138\nCOMPARE 4 8",
"3 5\nIN 1 2 4\nIN 1 2 5\nIN 2 3 10\nCOMPARE 1 2\nCOMPARE 2 3",
"5 4\nIN 3 1 2\nIN 3 2 2\nCOMPARE 1 3\nCOMPARE 2 3",
"5 4\nIN 4 1 1\nIN 3 1 2\nCOMPARE 1 4\nCOMPARE 2 3",
"3 5\nCOMPARE 1 2\nIN 1 2 9\nIN 2 1 3\nCOMPARE 2 3\nCOMPARE 1 3",
"4 3\nIN 1 4 9\nIN 2 2 20\nCOMPARE 1 4",
"4 4\nIN 2 1 1\nIN 3 1 3\nCOMPARE 1 3\nCOMPARE 2 3",
"10 4\nIN 10 8 4408\nIN 8 4 3765\nIN 3 4 40\nCOMPARE 4 8",
"3 4\nIN 1 2 1\nIN 3 1 12\nCOMPARE 1 3\nCOMPARE 2 3",
"10 4\nIN 6 8 802\nIN 8 4 5968\nIN 3 11 977\nCOMPARE 6 8",
"8 4\nIN 2 1 1\nIN 1 1 0\nCOMPARE 2 1\nCOMPARE 2 3",
"6 4\nIN 2 1 1\nIN 1 1 2\nCOMPARE 1 3\nCOMPARE 2 1",
"10 4\nIN 6 8 802\nIN 8 4 867\nIN 6 8 574\nCOMPARE 4 8",
"4 3\nIN 1 4 25\nIN 3 5 20\nCOMPARE 1 4",
"5 4\nIN 3 1 3\nIN 5 1 4\nCOMPARE 2 3\nCOMPARE 1 3",
"10 4\nIN 7 8 802\nIN 8 4 2581\nIN 6 8 574\nCOMPARE 4 8",
"3 4\nIN 2 1 3\nIN 3 1 4\nCOMPARE 2 3\nCOMPARE 1 3",
"10 4\nIN 10 8 2644\nIN 8 4 3946\nIN 3 8 138\nCOMPARE 4 8",
"4 3\nIN 2 4 10\nIN 2 3 20\nCOMPARE 2 4",
"8 4\nIN 2 1 1\nIN 1 1 1\nCOMPARE 2 1\nCOMPARE 2 3",
"5 5\nCOMPARE 1 2\nIN 1 4 6\nIN 2 2 2\nCOMPARE 2 2\nCOMPARE 1 3",
"5 4\nIN 3 1 3\nIN 5 1 1\nCOMPARE 2 3\nCOMPARE 1 3",
"20 4\nIN 10 12 2407\nIN 8 4 5780\nIN 4 8 75\nCOMPARE 4 8",
"4 3\nIN 1 4 18\nIN 2 2 5\nCOMPARE 1 4",
"10 4\nIN 6 2 802\nIN 8 4 5968\nIN 3 11 977\nCOMPARE 6 2",
"10 4\nIN 6 4 1041\nIN 8 4 7322\nIN 4 8 977\nCOMPARE 4 8",
"5 4\nIN 3 1 2\nIN 3 1 2\nCOMPARE 1 3\nCOMPARE 2 3",
"4 3\nIN 1 3 10\nIN 3 3 20\nCOMPARE 1 1",
"4 3\nIN 1 3 10\nIN 3 3 10\nCOMPARE 1 1",
"4 3\nIN 1 3 10\nIN 2 3 10\nCOMPARE 1 1",
"4 3\nIN 1 3 1\nIN 2 3 10\nCOMPARE 1 1",
"3 3\nCOMPARE 1 2\nIN 1 2 6\nIN 2 3 3\nCOMPARE 2 3\nCOMPARE 1 3",
"5 4\nIN 3 1 2\nIN 3 1 2\nCOMPARE 2 4\nCOMPARE 2 3",
"4 3\nIN 1 4 9\nIN 2 1 20\nCOMPARE 1 2",
"6 3\nIN 1 4 10\nIN 3 3 20\nCOMPARE 1 1",
"4 3\nIN 1 5 10\nIN 3 3 20\nCOMPARE 1 1",
"4 3\nIN 1 3 10\nIN 3 3 10\nCOMPARE 2 1",
"4 3\nIN 1 5 10\nIN 2 3 10\nCOMPARE 1 1",
"3 4\nIN 2 1 2\nIN 3 1 0\nCOMPARE 2 3\nCOMPARE 2 3",
"3 3\nCOMPARE 1 2\nIN 1 2 8\nIN 2 3 3\nCOMPARE 2 3\nCOMPARE 1 3",
"4 3\nIN 1 3 10\nIN 3 4 10\nCOMPARE 2 1",
"2 3\nIN 1 5 10\nIN 2 3 10\nCOMPARE 1 1",
"3 3\nCOMPARE 1 2\nIN 1 2 9\nIN 2 3 3\nCOMPARE 2 3\nCOMPARE 1 3",
"6 3\nIN 1 3 10\nIN 3 4 10\nCOMPARE 2 1",
"3 4\nCOMPARE 1 2\nIN 1 2 9\nIN 2 1 3\nCOMPARE 2 3\nCOMPARE 1 3",
"3 3\nIN 1 1 0\nIN 3 1 6\nCOMPARE 1 3\nCOMPARE 2 5",
"3 4\nCOMPARE 2 2\nIN 1 2 9\nIN 2 1 3\nCOMPARE 2 3\nCOMPARE 2 3"
],
"outputs": [
"WARNING",
"-3191",
"WARNING\n3\n11",
"-2\n2",
"15\n10",
"-2\n1\n",
"WARNING\n",
"-3725\n",
"WARNING\n3\n12\n",
"-5\n15\n",
"-1\nWARNING\n",
"-2\nWARNING\n",
"WARNING\nWARNING\n",
"-20\n",
"WARNING\n3\n0\n",
"-2\n0\n",
"0\n",
"WARNING\n2\n0\n",
"10\n",
"-3191\n",
"2\n2\n",
"-3722\n",
"-2\n2\n",
"-3\n0\n",
"WARNING\n2\n",
"-6\n0\n",
"WARNING\n1\n",
"-6\nWARNING\n",
"WARNING\n3\n",
"0\n1\n",
"-6\n",
"0\n0\n",
"0\nWARNING\n",
"3\n0\n",
"WARNING\n0\n5\n",
"-5\n",
"-12\n0\n",
"-2788\n",
"5544\n",
"1\n1\n",
"4567\n",
"WARNING\n2\n10\n",
"0\n2\n",
"2\n0\n",
"-4\nWARNING\n",
"-8\n",
"-3431\n",
"WARNING\n0\n3\n",
"14\n",
"-6345\n",
"-3471\n",
"1376\n",
"-3694\n",
"WARNING\n0\n",
"1779\n",
"WARNING\n2\nWARNING\n",
"WARNING\n-3\n",
"-3765\n",
"-3627\n",
"14\n10\n",
"0\n-2\n",
"-3\nWARNING\n",
"WARNING\nWARNING\nWARNING\n",
"9\n",
"-3\n1\n",
"-3805\n",
"-12\n-1\n",
"6770\n",
"1\nWARNING\n",
"WARNING\n5\n",
"-293\n",
"25\n",
"WARNING\n-7\n",
"-2007\n",
"3\n-4\n",
"-3808\n",
"-10\n",
"3\nWARNING\n",
"WARNING\n0\nWARNING\n",
"WARNING\n-4\n",
"-5780\n",
"18\n",
"802\n",
"-7322\n",
"-2\nWARNING\n",
"0\n",
"0\n",
"0\n",
"0\n",
"WARNING\n",
"WARNING\nWARNING\n",
"-20\n",
"0\n",
"0\n",
"WARNING\n",
"0\n",
"2\n2\n",
"WARNING\n",
"WARNING\n",
"0\n",
"WARNING\n",
"WARNING\n",
"WARNING\nWARNING\n",
"-6\n",
"0\nWARNING\n"
]
}
|
Problem
In 20XX, a scientist developed a powerful android with biotechnology. This android is extremely powerful because it is made by a computer by combining the cells of combat masters.
At this rate, the earth would be dominated by androids, so the N warriors decided to fight the androids. However, today's warriors are no match for androids, so they have to practice. Also, each of the N warriors is numbered 1 to N.
At this time, the sky city AIZU had a special room for training called the SRLU room. A year in this room is the same as a day in the outside world, so you can significantly increase your fighting power in a short period of time. The maximum number of people that can enter a room at the same time is two. Also, when the two enter the room, their fighting power will increase.
The warriors asked you to write a program to handle the following queries to see how they would enter the room in the time left.
The given query is as follows.
In addition, A and B appearing in the following explanation represent the warrior numbers, respectively. A and B are never equal.
IN A B C
A and B enter the room, and their fighting power increases by C respectively. At this time, (combat power of B just before entering the room)-(combat power of A just before entering the room) = C holds. Also, at this time, the combat power of B is guaranteed to be higher than the combat power of A.
COMPARE A B
Outputs the difference in combat power between A and B (current combat power of B)-(current combat power of A). If the difference cannot be identified, output WARNING.
Constraints
The input satisfies the following conditions.
* 2 ≤ N ≤ 100000
* 1 ≤ Q ≤ 100000
* 1 ≤ A, B ≤ N
* 1 ≤ C ≤ 5000
Input
N Q
query1
..
..
..
queryQ
First, the number of warriors N and the number of queries Q are given.
Then the query is given only Q times.
Output
It processes the given queries in order as described above, and outputs when the input of COMPARE is given.
Examples
Input
3 5
COMPARE 1 2
IN 1 2 5
IN 2 3 3
COMPARE 2 3
COMPARE 1 3
Output
WARNING
3
11
Input
4 3
IN 1 4 10
IN 2 3 20
COMPARE 1 2
Output
WARNING
Input
3 4
IN 2 1 2
IN 3 1 2
COMPARE 1 3
COMPARE 2 3
Output
-2
2
Input
10 4
IN 10 8 2328
IN 8 4 3765
IN 3 8 574
COMPARE 4 8
Output
-3191
Input
3 5
IN 1 2 5
IN 1 2 5
IN 2 3 10
COMPARE 1 2
COMPARE 2 3
Output
15
10
|
{
"inputs": [
"2 2\n20 18\n2 14\n",
"5 3\n-1 0 1 2 3\n-1 0 1\n",
"14 8\n-1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000 -1000000000\n1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000\n",
"5 7\n869535768 926886134 457905290 946881177 936471280\n-550057074 -517146573 -138904928 -683289266 -805395532 -979722367 -331183396\n",
"33 14\n-576562007 -218618150 -471719380 -583840778 -256368365 -68451917 -405045344 -775538133 -896830082 -439261765 -947070124 -716577019 -456110999 -689862512 -132480131 -10805271 -518903339 -196240188 -222292638 -828546042 -43887962 -161359263 -281422097 -484060534 963147664 -492377073 -154570101 -52145116 187803553 858844161 66540410 418777176 434025748\n-78301978 -319393213 -12393024 542953412 786804661 845642067 754996432 -985617475 -487171947 56142664 203173079 -268261708 -817080591 -511720682\n",
"24 24\n299931317 581208095 975349898 832722683 817690798 482251493 336949323 145902930 573001018 802990442 898055771 253410043 150981561 225791789 53290960 405421751 723296526 565432511 256399554 374970926 22699716 104391316 121063780 149329252\n-295118728 -830122321 -294539299 -905916790 -596056305 -12021689 -213837494 -341932332 -302359125 -999813713 -704441404 -713529724 -748686121 -646928807 -244549551 -826629397 -194449623 -807534699 -831064506 -889838257 -714860574 -14761264 -276778132 -479320983\n",
"6 30\n-524297819 -947277203 -444186475 -182837689 -385379656 -453917269\n834529938 35245081 663687669 585422565 164412867 850052113 796429008 -307345676 -127653313 426960600 211854713 -733687358 251466836 -33491050 -882811238 455544614 774581544 768447941 -241033484 441104324 -493975870 308277556 275268265 935941507 -152292053 -961509996 -740482111 -954176110 -924254634 -518710544\n",
"39 9\n44558618 981372779 318891054 283079237 285093436 907256321 414759796 652683534 79042330 249010687 7020063 309415438 788425492 138577429 714835649 954204512 795507844 389962019 507308352 408180613 194676444 44962879 922688019 101163040 327953325 560462120 183657590 273616448 226876035 233697890 720185285 689340674 372938362 15088928 283418109 796807778 149989495 694808087 276385512\n-681609072 -210918688 -757170622 -205635977 -597872997 -496188744 -97031207 -311654366 -389141528\n",
"50 50\n1 6 2 10 2 3 2 10 6 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 5 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 0\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 4 2 5 3 5 1 3 2 4 1 6 5 3 8 6\n",
"5 7\n-130464232 -73113866 -542094710 -53118823 -63528720\n449942926 482853427 861095072 316710734 194604468 20277633 668816604\n",
"12 25\n-464030345 -914672073 -483242132 -856226270 -925135169 -353124606 -294027092 -619650850 -490724485 -240424784 -483066792 -921640365\n279850608 726838739 -431610610 242749870 -244020223 -396865433 129534799 182767854 -939698671 342579400 330027106 893561388 -263513962 643369418 276245179 -99206565 -473767261 -168908664 -853755837 -270920164 -661186118 199341055 765543053 908211534 -93363867\n",
"5 7\n-130464232 -73113866 -542094710 -53118823 -63528720\n-775179088 631683023 -974858199 -157471745 -629658630 71825477 -6235611\n",
"5 32\n-540510995 -841481393 -94342377 -74818927 -93445356\n686714668 -82581175 736472406 502016312 575563638 -899308712 503504178 -644271272 -437408397 385778869 -746757839 306275973 -663503743 -431116516 -418708278 -515261493 -988182324 900230931 218258353 -714420102 -241118202 294802602 -937785552 -857537498 -723195312 -690515139 -214508504 -44086454 -231621215 -418360090 -810003786 -675944617\n",
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"50 50\n1 6 2 10 2 3 2 10 4 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 5 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 0\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 4 2 5 3 5 1 3 2 4 1 6 5 3 8 6\n",
"5 7\n-130464232 -73113866 -204605704 -53118823 -63528720\n449942926 482853427 861095072 316710734 194604468 20277633 668816604\n",
"12 25\n-464030345 -914672073 -483242132 -856226270 -925135169 -353124606 -294027092 -619650850 -490724485 -240424784 -483066792 -921640365\n279850608 1299327888 -431610610 242749870 -244020223 -396865433 129534799 182767854 -939698671 342579400 330027106 893561388 -263513962 643369418 276245179 -99206565 -473767261 -168908664 -853755837 -270920164 -661186118 199341055 765543053 908211534 -93363867\n",
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"15 29\n-716525085 -464205793 -577203110 -979997115 -491032521 -70793687 -770595947 -817983495 -767886763 -223333719 -971913221 -944656683 -200397825 -295615495 -945544540\n-877638425 -146878165 523758517 -158778747 -49535534 597311016 77325385 494128313 12111658 -4196724 63978619 477139483 375083042 726254399 -439255703 662913604 -481588088 673747948 -345999555 -723334478 -656721905 276267528 628773156 851420802 -585029291 -643535709 -968999740 -384418713 -510285542\n",
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"10 2\n1 6 2 10 3 3 2 10 6 4\n5 7\n",
"17 13\n-483786205 -947257449 -125949195 -294711143 -420288876 -812462057 -250049555 -911026413 -188146919 -129501682 -869006661 -649643966 -26976411 -275761039 -869067490 -272248209 -342067346\n691960220 529728842 -808170728 673157826 -70778491 642872105 299298867 -76674218 -902394063 377664752 723887448 -121522827 906464625\n",
"2 2\n20 18\n0 14\n",
"5 3\n-1 0 1 0 3\n-1 0 1\n",
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"6 30\n-524297819 -947277203 -444186475 -182837689 -385379656 -453917269\n834529938 35245081 643540671 585422565 164412867 850052113 796429008 -307345676 -127653313 426960600 211854713 -733687358 251466836 -33491050 -882811238 455544614 774581544 768447941 -241033484 441104324 -493975870 308277556 275268265 935941507 -152292053 -7505176 -740482111 -954176110 -924254634 -518710544\n",
"2 2\n15 18\n0 14\n",
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"24 24\n299931317 581208095 975349898 956924990 817690798 482251493 336949323 145902930 573001018 802990442 898055771 253410043 150981561 80836191 53290960 405421751 723296526 565432511 37843844 374970926 22699716 104391316 121063780 149329252\n-295118728 -830122321 -294539299 -905916790 -85862406 -12021689 -213837494 -341932332 -302359125 -999813713 -704441404 -713529724 -748686121 -646928807 -335862257 -826629397 -194449623 -807534699 -831064506 -889838257 -714860574 -14761264 -276778132 -479320983\n",
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"10 2\n1 6 4 10 3 3 4 14 12 2\n5 7\n",
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"50 50\n1 6 2 10 2 3 3 10 4 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 5 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 0\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 4 2 5 3 5 1 3 2 4 1 6 5 3 8 6\n",
"5 7\n-130464232 -73113866 -204605704 -53118823 -63528720\n87545370 482853427 861095072 316710734 194604468 20277633 668816604\n",
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"10 2\n1 6 4 10 3 3 2 10 6 4\n5 7\n",
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"5 3\n-1 0 1 0 3\n0 0 1\n",
"5 7\n1386172532 926886134 457905290 945180121 936471280\n-550057074 -517146573 -138904928 -683289266 -805395532 -12009979 -331183396\n",
"24 24\n299931317 581208095 975349898 956924990 817690798 482251493 336949323 145902930 573001018 802990442 898055771 253410043 150981561 80836191 53290960 405421751 723296526 565432511 256399554 374970926 22699716 104391316 121063780 149329252\n-295118728 -830122321 -294539299 -905916790 -596056305 -12021689 -213837494 -341932332 -302359125 -999813713 -704441404 -713529724 -748686121 -646928807 -335862257 -826629397 -194449623 -807534699 -831064506 -889838257 -714860574 -14761264 -276778132 -479320983\n",
"6 30\n-524297819 -947277203 -444186475 -182837689 -385379656 -453917269\n834529938 35245081 643540671 585422565 164412867 850052113 796429008 -307345676 -127653313 426960600 211854713 -733687358 251466836 -33491050 -367504346 455544614 774581544 768447941 -241033484 441104324 -493975870 308277556 275268265 935941507 -152292053 -7505176 -740482111 -954176110 -924254634 -518710544\n",
"50 50\n1 6 2 10 2 3 3 10 4 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 5 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 0\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 4 2 5 3 5 2 3 2 4 1 6 5 3 8 6\n",
"5 7\n-130464232 -73113866 -204605704 -53118823 -63528720\n87545370 482853427 1178494260 316710734 194604468 20277633 668816604\n",
"12 25\n-464030345 -914672073 -483242132 -856226270 -925135169 -353124606 -294027092 -619650850 -490724485 -240424784 -78320326 -921640365\n279850608 1299327888 -431610610 242749870 -244020223 -396865433 129534799 182767854 -939698671 342579400 330027106 893561388 -263513962 643369418 276245179 -99206565 -473767261 -168908664 -853755837 -270920164 -661186118 199341055 765543053 70538483 -93363867\n",
"10 13\n-749120991 -186261632 -335412349 -231354880 -195919225 -808736065 -55414768 -263383991 -664780611 -605377134\n718174936 -140362196 -669193674 -598621021 -464130929 314844539 -331183926 107203430 946959233 -826872392 -558199897 246556991 -666216081\n",
"15 29\n-716525085 -464205793 -577203110 -979997115 -491032521 -70793687 -770595947 -817983495 -767886763 -223333719 -971913221 -944656683 -200397825 -295615495 -945544540\n-877638425 -146878165 523758517 -158778747 -49535534 597311016 77325385 494128313 12111658 -4196724 63978619 477139483 375083042 726254399 -439255703 850069098 -481588088 673747948 -345999555 -744388840 -656721905 276267528 628773156 851420802 -585029291 -643535709 -968999740 -384418713 -510285542\n",
"10 2\n1 6 4 10 3 3 2 10 6 2\n5 7\n",
"5 3\n0 0 1 0 3\n0 0 1\n",
"5 7\n1386172532 926886134 457905290 945180121 936471280\n-550057074 -571772864 -138904928 -683289266 -805395532 -12009979 -331183396\n",
"24 24\n299931317 581208095 975349898 956924990 817690798 482251493 336949323 145902930 573001018 802990442 898055771 253410043 150981561 80836191 53290960 405421751 723296526 565432511 488170420 374970926 22699716 104391316 121063780 149329252\n-295118728 -830122321 -294539299 -905916790 -596056305 -12021689 -213837494 -341932332 -302359125 -999813713 -704441404 -713529724 -748686121 -646928807 -335862257 -826629397 -194449623 -807534699 -831064506 -889838257 -714860574 -14761264 -276778132 -479320983\n",
"6 30\n-524297819 -947277203 -444186475 -182837689 -101877869 -453917269\n834529938 35245081 643540671 585422565 164412867 850052113 796429008 -307345676 -127653313 426960600 211854713 -733687358 251466836 -33491050 -367504346 455544614 774581544 768447941 -241033484 441104324 -493975870 308277556 275268265 935941507 -152292053 -7505176 -740482111 -954176110 -924254634 -518710544\n",
"39 9\n44558618 171808877 318891054 283079237 285093436 907256321 414759796 652683534 79042330 249010687 7020063 309415438 788425492 138577429 714835649 954204512 795507844 604520066 507308352 408180613 194676444 44962879 922688019 101163040 327953325 691322069 183657590 273616448 226876035 233697890 720185285 689340674 372938362 15088928 283418109 796807778 149989495 694808087 276385512\n-681609072 -210918688 -757170622 -205635977 -597872997 -496188744 -155095247 -311654366 -389141528\n",
"50 50\n1 6 2 10 2 3 3 10 4 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 5 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 0\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 4 2 5 3 5 2 3 2 4 1 6 5 0 8 6\n",
"12 25\n-464030345 -914672073 -483242132 -856226270 -925135169 -353124606 -294027092 -619650850 -490724485 -240424784 -78320326 -921640365\n279850608 1299327888 -431610610 242749870 -244020223 -396865433 129534799 182767854 -939698671 342579400 330027106 893561388 -263513962 413850275 276245179 -99206565 -473767261 -168908664 -853755837 -270920164 -661186118 199341055 765543053 70538483 -93363867\n",
"24 24\n-700068683 -418791905 -24650102 -34128113 -182309202 -517748507 -663050677 -854097070 -426998982 -197009558 -101944229 -746589957 -849018439 -394887347 -946709040 -594578249 -276703474 -434567489 -743600446 -625029074 -977300284 -895608684 -878936220 -850670748\n704881272 226760560 705460701 94083210 403943695 987978311 786162506 658067668 697640875 186287 295558596 286470276 251313879 353071193 755450449 173370603 805550377 20882951 168935494 110161743 285139426 985238736 723221868 520679017\n",
"10 13\n-749120991 -186261632 -335412349 -231354880 -195919225 -808736065 -55414768 -263383991 -664780611 -605377134\n718174936 -140362196 -669193674 -598621021 -464130929 314844539 -331183926 107203430 946959233 -826872392 -84489586 246556991 -666216081\n",
"15 29\n-716525085 -464205793 -577203110 -979997115 -491032521 -70793687 -770595947 -817983495 -767886763 -223333719 -971913221 -944656683 -200397825 -295615495 -945544540\n-877638425 -146878165 523758517 -158778747 -49535534 597311016 77325385 494128313 12111658 -4196724 63978619 477139483 375083042 726254399 -439255703 850069098 -481588088 673747948 -345999555 -744388840 -656721905 276267528 628773156 1559996763 -585029291 -643535709 -968999740 -384418713 -510285542\n",
"10 2\n1 6 4 10 3 3 2 14 6 2\n5 7\n",
"5 7\n1386172532 926886134 457905290 945180121 936471280\n-550057074 -571772864 -138904928 -683289266 -48796831 -12009979 -331183396\n",
"24 24\n299931317 581208095 975349898 956924990 817690798 482251493 336949323 145902930 573001018 802990442 898055771 253410043 150981561 80836191 53290960 405421751 723296526 565432511 488170420 374970926 22699716 104391316 121063780 149329252\n-295118728 -830122321 -294539299 -905916790 -85862406 -12021689 -213837494 -341932332 -302359125 -999813713 -704441404 -713529724 -748686121 -646928807 -335862257 -826629397 -194449623 -807534699 -831064506 -889838257 -714860574 -14761264 -276778132 -479320983\n",
"6 30\n-524297819 -947277203 -444186475 -182837689 -101877869 -453917269\n834529938 35245081 643540671 585422565 164412867 850052113 796429008 -307345676 -127653313 426960600 211854713 -733687358 322015097 -33491050 -367504346 455544614 774581544 768447941 -241033484 441104324 -493975870 308277556 275268265 935941507 -152292053 -7505176 -740482111 -954176110 -924254634 -518710544\n",
"39 9\n44558618 171808877 318891054 283079237 285093436 907256321 414759796 652683534 79042330 249010687 7020063 309415438 788425492 138577429 714835649 954204512 795507844 604520066 507308352 408180613 194676444 44962879 922688019 101163040 327953325 691322069 183657590 273616448 226876035 233697890 720185285 689340674 372938362 15088928 283418109 796807778 149989495 443601362 276385512\n-681609072 -210918688 -757170622 -205635977 -597872997 -496188744 -155095247 -311654366 -389141528\n",
"50 50\n1 6 2 10 2 3 3 10 4 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 7 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 0\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 4 2 5 3 5 2 3 2 4 1 6 5 0 8 6\n",
"5 7\n-130464232 -73113866 -204605704 -53118823 -59351417\n87545370 482853427 1178494260 192231230 194604468 20277633 668816604\n",
"12 25\n-464030345 -914672073 -304742983 -856226270 -925135169 -353124606 -294027092 -619650850 -490724485 -240424784 -78320326 -921640365\n279850608 1299327888 -431610610 242749870 -244020223 -396865433 129534799 182767854 -939698671 342579400 330027106 893561388 -263513962 413850275 276245179 -99206565 -473767261 -168908664 -853755837 -270920164 -661186118 199341055 765543053 70538483 -93363867\n",
"24 24\n-700068683 -418791905 -24650102 -34128113 -182309202 -517748507 -663050677 -854097070 -426998982 -197009558 -101944229 -746589957 -849018439 -394887347 -946709040 -594578249 -276703474 -434567489 -743600446 -625029074 -977300284 -895608684 -878936220 -850670748\n1194737871 226760560 705460701 94083210 403943695 987978311 786162506 658067668 697640875 186287 295558596 286470276 251313879 353071193 755450449 173370603 805550377 20882951 168935494 110161743 285139426 985238736 723221868 520679017\n",
"10 13\n-749120991 -186261632 -335412349 -231354880 -195919225 -808736065 -55414768 -263383991 -664780611 -605377134\n718174936 -140362196 -669193674 -598621021 -464130929 314844539 -331183926 70053590 946959233 -826872392 -84489586 246556991 -666216081\n",
"15 29\n-716525085 -464205793 -577203110 -979997115 -491032521 -70793687 -770595947 -817983495 -767886763 -223333719 -971913221 -944656683 -200397825 -295615495 -945544540\n-877638425 -146878165 523758517 -158778747 -49535534 597311016 77325385 494128313 12111658 -4196724 63978619 477139483 375083042 726254399 -638114508 850069098 -481588088 673747948 -345999555 -744388840 -656721905 276267528 628773156 1559996763 -585029291 -643535709 -968999740 -384418713 -510285542\n",
"10 2\n1 6 4 10 3 3 4 14 6 2\n5 7\n",
"6 30\n-524297819 -947277203 -444186475 -182837689 -101877869 -453917269\n834529938 35245081 643540671 585422565 164412867 850052113 796429008 -307345676 -127653313 426960600 211854713 -733687358 322015097 -33491050 -367504346 455544614 977398030 768447941 -241033484 441104324 -493975870 308277556 275268265 935941507 -152292053 -7505176 -740482111 -954176110 -924254634 -518710544\n",
"50 50\n1 6 2 10 2 3 3 10 4 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 7 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 1\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 4 2 5 3 5 2 3 2 4 1 6 5 0 8 6\n",
"5 7\n-138600254 -73113866 -204605704 -53118823 -59351417\n87545370 482853427 1178494260 192231230 194604468 20277633 668816604\n",
"12 25\n-464030345 -914672073 -304742983 -856226270 -925135169 -353124606 -294027092 -619650850 -490724485 -240424784 -78320326 -921640365\n279850608 1299327888 -431610610 242749870 -244020223 -396865433 129534799 182767854 -939698671 342579400 330027106 893561388 -263513962 413850275 276245179 -99206565 -473767261 -168908664 -853755837 -270920164 -661186118 199341055 19074042 70538483 -93363867\n",
"24 24\n-700068683 -418791905 -24650102 -34128113 -182309202 -517748507 -663050677 -854097070 -426998982 -197009558 -101944229 -746589957 -849018439 -394887347 -946709040 -594578249 -276703474 -434567489 -743600446 -625029074 -977300284 -895608684 -878936220 -850670748\n1194737871 226760560 705460701 172892295 403943695 987978311 786162506 658067668 697640875 186287 295558596 286470276 251313879 353071193 755450449 173370603 805550377 20882951 168935494 110161743 285139426 985238736 723221868 520679017\n",
"10 13\n-749120991 -186261632 -335412349 -231354880 -195919225 -1242918326 -55414768 -263383991 -664780611 -605377134\n718174936 -140362196 -669193674 -598621021 -464130929 314844539 -331183926 70053590 946959233 -826872392 -84489586 246556991 -666216081\n",
"15 29\n-716525085 -464205793 -577203110 -979997115 -491032521 -70793687 -770595947 -817983495 -767886763 -223333719 -971913221 -944656683 -200397825 -295615495 -945544540\n-877638425 -146878165 523758517 -158778747 -49535534 597311016 77325385 494128313 12111658 -4196724 63978619 477139483 375083042 726254399 -638114508 850069098 -481588088 214206708 -345999555 -744388840 -656721905 276267528 628773156 1559996763 -585029291 -643535709 -968999740 -384418713 -510285542\n",
"24 24\n299931317 581208095 975349898 956924990 817690798 482251493 336949323 145902930 573001018 802990442 898055771 253410043 150981561 80836191 105056338 405421751 723296526 565432511 37843844 374970926 22699716 104391316 121063780 149329252\n-295118728 -830122321 -294539299 -905916790 -85862406 -12021689 -213837494 -341932332 -302359125 -999813713 -704441404 -713529724 -748686121 -646928807 -335862257 -826629397 -194449623 -807534699 -831064506 -889838257 -714860574 -14761264 -276778132 -479320983\n",
"39 9\n44558618 171808877 318891054 283079237 285093436 907256321 414759796 652683534 79042330 249010687 7020063 309415438 788425492 138577429 714835649 954204512 795507844 223762259 507308352 408180613 194676444 44962879 922688019 101163040 327953325 691322069 183657590 273616448 226876035 233697890 720185285 689340674 372938362 15088928 283418109 796807778 149989495 443601362 276385512\n-681609072 -210918688 -757170622 -205635977 -597872997 -496188744 -155095247 -67248663 -389141528\n",
"50 50\n1 6 2 10 2 3 1 10 4 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 7 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 1\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 4 2 5 3 5 2 3 2 4 1 6 5 0 8 6\n",
"24 24\n-700068683 -418791905 -24650102 -34128113 -182309202 -517748507 -663050677 -854097070 -426998982 -197009558 -101944229 -746589957 -849018439 -394887347 -946709040 -594578249 -321958052 -434567489 -743600446 -625029074 -977300284 -895608684 -878936220 -850670748\n1194737871 226760560 705460701 172892295 403943695 987978311 786162506 658067668 697640875 186287 295558596 286470276 251313879 353071193 755450449 173370603 805550377 20882951 168935494 110161743 285139426 985238736 723221868 520679017\n",
"10 13\n-749120991 -186261632 -335412349 -231354880 -195919225 -1242918326 -55414768 -263383991 -664780611 -605377134\n718174936 -134366682 -669193674 -598621021 -464130929 314844539 -331183926 70053590 946959233 -826872392 -84489586 246556991 -666216081\n",
"15 29\n-716525085 -464205793 -577203110 -979997115 -491032521 -70793687 -770595947 -817983495 -767886763 -223333719 -971913221 -944656683 -200397825 -35458688 -945544540\n-877638425 -146878165 523758517 -158778747 -49535534 597311016 77325385 494128313 12111658 -4196724 63978619 477139483 375083042 726254399 -638114508 850069098 -481588088 214206708 -345999555 -744388840 -656721905 276267528 628773156 1559996763 -585029291 -643535709 -968999740 -384418713 -510285542\n",
"10 2\n1 6 4 10 3 3 4 14 2 2\n5 7\n",
"24 24\n299931317 581208095 975349898 956924990 817690798 482251493 336949323 145902930 573001018 802990442 898055771 253410043 150981561 80836191 105056338 405421751 1127821089 565432511 37843844 374970926 22699716 104391316 121063780 149329252\n-295118728 -830122321 -294539299 -905916790 -85862406 -12021689 -213837494 -341932332 -302359125 -999813713 -704441404 -713529724 -748686121 -646928807 -335862257 -826629397 -194449623 -807534699 -831064506 -889838257 -714860574 -14761264 -276778132 -479320983\n",
"39 9\n44558618 171808877 318891054 283079237 285093436 907256321 414759796 652683534 79042330 249010687 7020063 309415438 788425492 138577429 714835649 108956958 795507844 223762259 507308352 408180613 194676444 44962879 922688019 101163040 327953325 691322069 183657590 273616448 226876035 233697890 720185285 689340674 372938362 15088928 283418109 796807778 149989495 443601362 276385512\n-681609072 -210918688 -757170622 -205635977 -597872997 -496188744 -155095247 -67248663 -389141528\n",
"50 50\n1 6 2 10 2 3 1 10 4 4 5 0 3 1 7 3 2 4 4 2 1 5 0 6 10 1 8 0 10 9 0 4 10 7 5 7 4 9 9 5 5 2 6 7 9 4 3 7 2 1\n0 5 9 4 4 6 1 8 2 1 6 6 8 6 4 4 7 2 1 8 6 7 4 9 8 3 0 2 0 10 7 1 4 9 4 6 2 5 3 5 2 3 2 4 1 6 5 0 8 6\n",
"5 7\n-138600254 -73113866 -204605704 -53118823 -59351417\n87545370 265489868 1178494260 192231230 194604468 1415578 668816604\n",
"24 24\n-700068683 -418791905 -24650102 -34128113 -182309202 -517748507 -663050677 -854097070 -426998982 -197009558 -101944229 -746589957 -849018439 -394887347 -946709040 -594578249 -321958052 -434567489 -743600446 -625029074 -977300284 -895608684 -878936220 -850670748\n1194737871 226760560 705460701 78055382 403943695 987978311 786162506 658067668 697640875 186287 295558596 286470276 251313879 353071193 755450449 173370603 805550377 20882951 168935494 110161743 285139426 985238736 723221868 520679017\n",
"10 13\n-749120991 -186261632 -335412349 -231354880 -195919225 -1999964756 -55414768 -263383991 -664780611 -605377134\n718174936 -134366682 -669193674 -598621021 -464130929 314844539 -331183926 70053590 946959233 -826872392 -84489586 246556991 -666216081\n",
"15 29\n-716525085 -464205793 -577203110 -979997115 -491032521 -70793687 -770595947 -817983495 -767886763 -223333719 -971913221 -944656683 -200397825 -35458688 -945544540\n-877638425 -146878165 523758517 -158778747 -49535534 597311016 77325385 494128313 12111658 -4196724 63978619 477139483 375083042 726254399 -638114508 850069098 -640904436 214206708 -345999555 -744388840 -656721905 276267528 628773156 1559996763 -585029291 -643535709 -968999740 -384418713 -510285542\n",
"10 2\n1 6 4 10 3 3 3 14 2 2\n5 7\n"
],
"outputs": [
"252\n",
"2\n",
"-1000000000000000000\n",
"-120782803247464704\n",
"883931400924882950\n",
"-640647347631440\n",
"504117593849498724\n",
"-1464096896176096\n",
"100\n",
"-1288212069119760\n",
"866064226130454915\n",
"127184126241438168\n",
"534123411186652380\n",
"-18990884587723\n",
"501307028237810934\n",
"941783658451562540\n",
"910849554065102112\n",
"663200522440413120\n",
"70\n",
"922371547895579571\n",
"822104826327386019\n",
"848714444125692276\n",
"-128749051707468352\n",
"883931400924882950\n",
"-640647347631440\n",
"504117593849498724\n",
"-1464096896176096\n",
"100\n",
"-1288212069119760\n",
"866064226130454915\n",
"250589226060621264\n",
"534123411186652380\n",
"-18990884587723\n",
"619427465725580472\n",
"941783658451562540\n",
"910849554065102112\n",
"663200522440413120\n",
"70\n",
"822104826327386019\n",
"252\n",
"1\n",
"-11131883004731186\n",
"500272453414904090\n",
"210\n",
"-2340221015125216\n",
"-6357623786431\n",
"854799498110125287\n",
"60\n",
"-1203506251955961\n",
"-454946923132516\n",
"-1014710234103264\n",
"84\n",
"484584688806843246\n",
"-84016560174026\n",
"883931400924882950\n",
"-640647347631440\n",
"-1464096896176096\n",
"100\n",
"-1288212069119760\n",
"866064226130454915\n",
"250589226060621264\n",
"-18990884587723\n",
"619427465725580472\n",
"941783658451562540\n",
"663200522440413120\n",
"70\n",
"822104826327386019\n",
"1\n",
"-11131883004731186\n",
"-640647347631440\n",
"500272453414904090\n",
"100\n",
"-1288212069119760\n",
"866064226130454915\n",
"619427465725580472\n",
"941783658451562540\n",
"70\n",
"1\n",
"-11131883004731186\n",
"-640647347631440\n",
"500272453414904090\n",
"-2340221015125216\n",
"100\n",
"866064226130454915\n",
"-6357623786431\n",
"619427465725580472\n",
"941783658451562540\n",
"70\n",
"-11131883004731186\n",
"-640647347631440\n",
"500272453414904090\n",
"-2340221015125216\n",
"100\n",
"-1203506251955961\n",
"866064226130454915\n",
"-6357623786431\n",
"619427465725580472\n",
"941783658451562540\n",
"70\n",
"500272453414904090\n",
"100\n",
"-1203506251955961\n",
"866064226130454915\n",
"-6357623786431\n",
"619427465725580472\n",
"941783658451562540\n",
"-454946923132516\n",
"-1014710234103264\n",
"100\n",
"-6357623786431\n",
"619427465725580472\n",
"941783658451562540\n",
"70\n",
"-454946923132516\n",
"-1014710234103264\n",
"100\n",
"-84016560174026\n",
"-6357623786431\n",
"619427465725580472\n",
"941783658451562540\n",
"70\n"
]
}
|
Nian is a monster which lives deep in the oceans. Once a year, it shows up on the land, devouring livestock and even people. In order to keep the monster away, people fill their villages with red colour, light, and cracking noise, all of which frighten the monster out of coming.
Little Tommy has n lanterns and Big Banban has m lanterns. Tommy's lanterns have brightness a1, a2, ..., an, and Banban's have brightness b1, b2, ..., bm respectively.
Tommy intends to hide one of his lanterns, then Banban picks one of Tommy's non-hidden lanterns and one of his own lanterns to form a pair. The pair's brightness will be the product of the brightness of two lanterns.
Tommy wants to make the product as small as possible, while Banban tries to make it as large as possible.
You are asked to find the brightness of the chosen pair if both of them choose optimally.
Input
The first line contains two space-separated integers n and m (2 ≤ n, m ≤ 50).
The second line contains n space-separated integers a1, a2, ..., an.
The third line contains m space-separated integers b1, b2, ..., bm.
All the integers range from - 109 to 109.
Output
Print a single integer — the brightness of the chosen pair.
Examples
Input
2 2
20 18
2 14
Output
252
Input
5 3
-1 0 1 2 3
-1 0 1
Output
2
Note
In the first example, Tommy will hide 20 and Banban will choose 18 from Tommy and 14 from himself.
In the second example, Tommy will hide 3 and Banban will choose 2 from Tommy and 1 from himself.
|
{
"inputs": [
"6\n0 6 7 6 7 0",
"4\n1 2 3 4",
"1\n1000000000",
"3\n1 2 3",
"6\n1 6 7 6 7 0",
"4\n1 4 3 4",
"1\n1000010000",
"3\n2 2 3",
"6\n1 10 7 6 7 0",
"4\n1 4 0 4",
"1\n1100010000",
"3\n4 2 3",
"6\n1 10 7 6 4 0",
"4\n0 4 0 4",
"1\n1100010100",
"3\n6 2 3",
"6\n1 10 7 4 4 0",
"4\n0 1 0 4",
"1\n1100110000",
"3\n6 2 5",
"6\n1 10 7 8 4 0",
"4\n0 1 0 6",
"1\n1100110100",
"3\n6 4 5",
"6\n1 10 7 16 4 0",
"4\n-1 1 0 6",
"1\n1110110100",
"3\n10 4 5",
"6\n1 17 7 16 4 0",
"4\n-1 2 0 6",
"1\n0110110100",
"3\n2 4 5",
"6\n1 20 7 16 4 0",
"4\n-1 2 -1 6",
"1\n0110110110",
"3\n2 2 5",
"6\n1 20 7 16 4 1",
"4\n-1 3 0 6",
"1\n0100110110",
"3\n2 2 4",
"6\n1 20 0 16 4 1",
"4\n-1 3 0 5",
"1\n0100010110",
"3\n2 1 4",
"6\n1 20 0 31 4 1",
"4\n-1 0 0 5",
"1\n0100010111",
"3\n2 1 8",
"6\n1 20 0 31 5 1",
"4\n-1 0 -1 5",
"1\n0100010101",
"3\n2 1 3",
"6\n2 20 0 31 5 1",
"4\n-1 0 -1 10",
"1\n0100110101",
"3\n2 0 3",
"6\n2 20 0 59 5 1",
"4\n-1 0 -1 9",
"1\n0101110101",
"3\n2 0 0",
"6\n2 20 0 59 10 1",
"4\n-1 0 0 9",
"1\n1101110101",
"3\n2 1 0",
"6\n2 20 0 59 10 0",
"4\n-1 0 0 2",
"1\n1101010101",
"3\n2 1 -1",
"6\n2 20 0 59 12 0",
"4\n-1 0 0 4",
"1\n1001010101",
"3\n2 1 -2",
"6\n0 20 0 59 12 0",
"4\n-1 1 0 4",
"1\n1011010101",
"3\n3 1 -2",
"6\n0 20 0 59 15 0",
"4\n-1 1 1 4",
"1\n0011010101",
"3\n3 0 -2",
"6\n0 20 1 59 15 0",
"4\n0 1 1 4",
"1\n1011110101",
"3\n3 0 0",
"6\n0 39 1 59 15 0",
"4\n0 1 0 2",
"1\n1010110101",
"3\n3 1 0",
"6\n0 39 1 80 15 0",
"4\n0 2 0 2",
"1\n1010010101",
"3\n4 0 0",
"6\n0 39 1 75 15 0",
"4\n0 4 0 2",
"1\n1000010101",
"3\n4 -1 0",
"6\n0 22 1 75 15 0",
"4\n-1 4 0 2",
"1\n1000010100",
"3\n4 -1 1",
"6\n-1 22 1 75 15 0",
"4\n-1 7 0 2",
"1\n0000010101",
"3\n4 0 1"
],
"outputs": [
"0 6 6 0 7 7",
"4 2 1 3",
"1000000000",
"3 1 2",
"0 6 6 1 7 7\n",
"4 4 1 3\n",
"1000010000\n",
"3 2 2\n",
"0 6 10 1 7 7\n",
"4 4 1 0\n",
"1100010000\n",
"3 4 2\n",
"0 6 10 1 7 4\n",
"4 4 0 0\n",
"1100010100\n",
"3 6 2\n",
"0 4 10 1 7 4\n",
"4 1 0 0\n",
"1100110000\n",
"5 6 2\n",
"0 8 10 1 7 4\n",
"6 1 0 0\n",
"1100110100\n",
"5 6 4\n",
"0 16 10 1 7 4\n",
"6 1 -1 0\n",
"1110110100\n",
"5 10 4\n",
"0 16 17 1 7 4\n",
"6 2 -1 0\n",
"0110110100\n",
"5 2 4\n",
"0 16 20 1 7 4\n",
"6 2 -1 -1\n",
"0110110110\n",
"5 2 2\n",
"1 16 20 1 7 4\n",
"6 3 -1 0\n",
"0100110110\n",
"4 2 2\n",
"1 16 20 1 0 4\n",
"5 3 -1 0\n",
"0100010110\n",
"4 2 1\n",
"1 31 20 1 0 4\n",
"5 0 -1 0\n",
"0100010111\n",
"8 2 1\n",
"1 31 20 1 0 5\n",
"5 0 -1 -1\n",
"0100010101\n",
"3 2 1\n",
"1 31 20 2 0 5\n",
"10 0 -1 -1\n",
"0100110101\n",
"3 2 0\n",
"1 59 20 2 0 5\n",
"9 0 -1 -1\n",
"0101110101\n",
"0 2 0\n",
"1 59 20 2 0 10\n",
"9 0 -1 0\n",
"1101110101\n",
"0 2 1\n",
"0 59 20 2 0 10\n",
"2 0 -1 0\n",
"1101010101\n",
"-1 2 1\n",
"0 59 20 2 0 12\n",
"4 0 -1 0\n",
"1001010101\n",
"-2 2 1\n",
"0 59 20 0 0 12\n",
"4 1 -1 0\n",
"1011010101\n",
"-2 3 1\n",
"0 59 20 0 0 15\n",
"4 1 -1 1\n",
"0011010101\n",
"-2 3 0\n",
"0 59 20 0 1 15\n",
"4 1 0 1\n",
"1011110101\n",
"0 3 0\n",
"0 59 39 0 1 15\n",
"2 1 0 0\n",
"1010110101\n",
"0 3 1\n",
"0 80 39 0 1 15\n",
"2 2 0 0\n",
"1010010101\n",
"0 4 0\n",
"0 75 39 0 1 15\n",
"2 4 0 0\n",
"1000010101\n",
"0 4 -1\n",
"0 75 22 0 1 15\n",
"2 4 -1 0\n",
"1000010100\n",
"1 4 -1\n",
"0 75 22 -1 1 15\n",
"2 7 -1 0\n",
"0000010101\n",
"1 4 0\n"
]
}
|
You are given an integer sequence of length n, a_1, ..., a_n. Let us consider performing the following n operations on an empty sequence b.
The i-th operation is as follows:
1. Append a_i to the end of b.
2. Reverse the order of the elements in b.
Find the sequence b obtained after these n operations.
Constraints
* 1 \leq n \leq 2\times 10^5
* 0 \leq a_i \leq 10^9
* n and a_i are integers.
Input
Input is given from Standard Input in the following format:
n
a_1 a_2 ... a_n
Output
Print n integers in a line with spaces in between. The i-th integer should be b_i.
Examples
Input
4
1 2 3 4
Output
4 2 1 3
Input
3
1 2 3
Output
3 1 2
Input
1
1000000000
Output
1000000000
Input
6
0 6 7 6 7 0
Output
0 6 6 0 7 7
|
{
"inputs": [
"1 3\n1 6\n3 5\n2 200\n25 99\n0 0",
"2 3\n1 6\n3 5\n2 200\n25 99\n0 0",
"2 6\n1 5\n3 5\n2 200\n25 99\n0 0",
"1 6\n1 5\n3 5\n2 200\n34 99\n0 0",
"1 6\n1 5\n3 9\n2 200\n34 99\n0 0",
"1 6\n1 8\n3 9\n2 200\n34 99\n0 0",
"1 6\n1 8\n3 9\n2 200\n34 62\n0 0",
"2 6\n1 8\n3 9\n2 200\n34 62\n0 0",
"2 6\n1 16\n3 9\n2 200\n34 62\n0 0",
"2 6\n1 16\n3 15\n2 200\n34 62\n0 0",
"2 6\n1 16\n2 15\n2 200\n34 62\n0 0",
"1 3\n1 6\n3 9\n2 200\n7 99\n0 0",
"2 6\n1 6\n3 5\n2 200\n25 16\n0 0",
"1 6\n1 5\n3 5\n2 200\n34 134\n0 0",
"1 6\n1 5\n3 9\n1 200\n34 99\n0 0",
"1 6\n1 8\n3 9\n2 287\n34 99\n0 0",
"2 4\n1 8\n3 9\n2 200\n34 62\n0 0",
"2 6\n1 16\n3 9\n2 200\n34 79\n0 0",
"2 6\n2 6\n3 5\n2 200\n25 16\n0 0",
"2 8\n1 5\n3 10\n2 200\n25 99\n0 0",
"1 8\n1 5\n3 9\n1 200\n34 99\n0 0",
"1 3\n1 6\n6 9\n2 377\n7 99\n0 0",
"2 6\n2 4\n3 5\n2 200\n25 16\n0 0",
"4 8\n1 5\n3 10\n2 200\n36 99\n0 0",
"4 8\n1 5\n3 10\n2 218\n36 99\n0 0",
"4 8\n1 5\n3 10\n2 72\n36 198\n0 0",
"1 3\n1 6\n3 5\n2 200\n7 163\n0 0",
"1 6\n1 5\n3 9\n2 200\n44 99\n0 0",
"2 6\n1 8\n3 9\n2 200\n34 99\n0 0",
"1 6\n2 8\n3 9\n2 200\n34 62\n0 0",
"2 7\n1 8\n3 9\n2 200\n34 62\n0 0",
"2 6\n1 16\n3 15\n2 369\n34 62\n0 0",
"2 6\n1 6\n3 5\n2 326\n25 16\n0 0",
"1 8\n1 5\n3 9\n1 200\n34 107\n0 0",
"2 4\n1 14\n3 9\n4 200\n34 62\n0 0",
"1 3\n1 2\n6 9\n2 377\n7 99\n0 0",
"1 3\n1 6\n6 18\n2 457\n7 99\n0 0",
"4 8\n1 5\n3 10\n2 62\n36 99\n0 0",
"7 8\n1 5\n3 10\n2 72\n36 198\n0 0",
"1 6\n2 8\n3 9\n2 200\n34 91\n0 0",
"2 7\n1 8\n3 4\n2 200\n34 62\n0 0",
"2 6\n1 16\n3 26\n2 369\n34 62\n0 0",
"1 6\n1 6\n3 9\n2 200\n12 99\n0 0",
"2 4\n1 8\n1 9\n2 183\n34 62\n0 0",
"2 3\n1 6\n6 9\n2 200\n7 24\n0 0",
"1 8\n1 5\n3 4\n1 200\n34 107\n0 0",
"1 6\n1 8\n4 9\n2 360\n34 99\n0 0",
"1 3\n1 6\n6 18\n2 457\n7 2\n0 0",
"2 8\n1 3\n3 10\n2 200\n36 99\n0 0",
"2 6\n1 8\n3 9\n2 200\n44 99\n0 0",
"1 6\n2 8\n3 15\n2 200\n34 91\n0 0",
"2 6\n1 6\n3 2\n2 255\n25 16\n0 0",
"2 7\n1 8\n1 9\n2 183\n34 62\n0 0",
"1 8\n1 5\n3 8\n1 200\n34 107\n0 0",
"1 5\n1 6\n6 18\n2 457\n7 2\n0 0",
"3 6\n1 5\n2 5\n4 375\n25 99\n0 0",
"1 9\n1 5\n3 5\n3 200\n63 99\n0 0",
"2 6\n1 8\n3 2\n2 200\n44 99\n0 0",
"1 6\n2 8\n3 15\n1 200\n34 91\n0 0",
"2 7\n2 8\n3 4\n2 200\n2 62\n0 0",
"2 3\n1 8\n1 9\n2 183\n34 62\n0 0",
"1 8\n1 5\n3 8\n2 200\n34 107\n0 0",
"1 4\n1 8\n4 9\n2 360\n30 99\n0 0",
"1 5\n1 10\n6 18\n2 457\n7 2\n0 0",
"1 9\n1 5\n3 5\n3 109\n63 99\n0 0",
"1 6\n2 8\n1 15\n1 200\n34 91\n0 0",
"2 3\n1 14\n1 9\n2 183\n34 62\n0 0",
"1 14\n1 5\n3 8\n2 200\n34 107\n0 0",
"1 4\n1 12\n4 9\n2 360\n30 99\n0 0",
"1 8\n1 10\n6 18\n2 457\n7 2\n0 0",
"3 6\n1 5\n2 8\n4 375\n41 99\n0 0",
"1 6\n2 8\n1 15\n2 200\n34 91\n0 0",
"2 7\n2 8\n5 8\n2 200\n2 62\n0 0",
"2 3\n1 14\n1 9\n2 15\n34 62\n0 0",
"1 4\n1 12\n4 9\n2 668\n30 99\n0 0",
"3 6\n1 5\n2 8\n6 375\n41 99\n0 0",
"2 6\n2 8\n1 15\n2 200\n34 91\n0 0",
"2 7\n2 8\n5 8\n2 200\n2 85\n0 0",
"1 14\n1 9\n3 8\n4 200\n34 107\n0 0",
"2 6\n1 5\n2 8\n6 375\n41 99\n0 0",
"2 6\n2 8\n1 8\n2 200\n34 91\n0 0",
"2 6\n2 8\n1 12\n2 200\n34 91\n0 0",
"1 3\n1 3\n3 5\n2 200\n7 99\n0 0",
"2 6\n1 6\n3 5\n2 109\n25 99\n0 0",
"2 6\n1 5\n3 5\n2 200\n25 106\n0 0",
"1 6\n1 8\n3 14\n2 200\n34 62\n0 0",
"2 6\n1 8\n3 9\n2 200\n34 24\n0 0",
"2 6\n1 16\n2 15\n2 200\n9 62\n0 0",
"2 4\n2 8\n3 9\n2 200\n34 62\n0 0",
"2 6\n1 16\n3 9\n2 334\n34 79\n0 0",
"2 6\n2 6\n3 5\n2 221\n25 16\n0 0",
"2 8\n1 5\n3 10\n1 200\n25 99\n0 0",
"1 6\n1 8\n5 9\n2 135\n34 99\n0 0",
"2 6\n1 16\n3 8\n2 200\n13 79\n0 0",
"1 6\n2 4\n3 5\n2 200\n25 16\n0 0",
"4 8\n1 5\n3 10\n2 258\n36 99\n0 0",
"4 8\n1 5\n3 10\n3 218\n36 99\n0 0",
"3 8\n1 5\n3 10\n2 218\n36 198\n0 0",
"1 3\n1 4\n3 5\n2 200\n7 163\n0 0",
"2 6\n1 8\n3 9\n3 200\n34 99\n0 0",
"2 11\n1 8\n3 9\n2 200\n34 62\n0 0"
],
"outputs": [
"0 1\n1 1\n1 0\n2 0\n0 2",
"0 1\n1 1\n1 0\n2 0\n0 2\n",
"0 1\n1 0\n1 0\n2 0\n0 2\n",
"1 1\n1 0\n1 0\n2 0\n0 2\n",
"1 1\n1 0\n0 1\n2 0\n0 2\n",
"1 1\n3 0\n0 1\n2 0\n0 2\n",
"1 1\n3 0\n0 1\n2 0\n0 15\n",
"0 1\n3 0\n0 1\n2 0\n0 15\n",
"0 1\n4 0\n0 1\n2 0\n0 15\n",
"0 1\n4 0\n1 0\n2 0\n0 15\n",
"0 1\n4 0\n1 1\n2 0\n0 15\n",
"0 1\n1 1\n0 1\n2 0\n0 2\n",
"0 1\n1 1\n1 0\n2 0\n4 0\n",
"1 1\n1 0\n1 0\n2 0\n0 33\n",
"1 1\n1 0\n0 1\n3 0\n0 2\n",
"1 1\n3 0\n0 1\n0 30\n0 2\n",
"1 0\n3 0\n0 1\n2 0\n0 15\n",
"0 1\n4 0\n0 1\n2 0\n0 13\n",
"0 1\n0 1\n1 0\n2 0\n4 0\n",
"2 0\n1 0\n1 0\n2 0\n0 2\n",
"3 0\n1 0\n0 1\n3 0\n0 2\n",
"0 1\n1 1\n0 1\n0 84\n0 2\n",
"0 1\n1 0\n1 0\n2 0\n4 0\n",
"1 0\n1 0\n1 0\n2 0\n0 2\n",
"1 0\n1 0\n1 0\n0 108\n0 2\n",
"1 0\n1 0\n1 0\n2 1\n0 2\n",
"0 1\n1 1\n1 0\n2 0\n0 81\n",
"1 1\n1 0\n0 1\n2 0\n0 1\n",
"0 1\n3 0\n0 1\n2 0\n0 2\n",
"1 1\n2 0\n0 1\n2 0\n0 15\n",
"0 6\n3 0\n0 1\n2 0\n0 15\n",
"0 1\n4 0\n1 0\n0 5\n0 15\n",
"0 1\n1 1\n1 0\n0 81\n4 0\n",
"3 0\n1 0\n0 1\n3 0\n0 53\n",
"1 0\n1 6\n0 1\n2 0\n0 15\n",
"0 1\n1 0\n0 1\n0 84\n0 2\n",
"0 1\n1 1\n0 1\n0 152\n0 2\n",
"1 0\n1 0\n1 0\n0 15\n0 2\n",
"3 0\n1 0\n1 0\n2 1\n0 2\n",
"1 1\n2 0\n0 1\n2 0\n0 6\n",
"0 6\n3 0\n2 0\n2 0\n0 15\n",
"0 1\n4 0\n1 6\n0 5\n0 15\n",
"1 1\n1 1\n0 1\n2 0\n0 2\n",
"1 0\n3 0\n0 1\n0 60\n0 15\n",
"0 1\n1 1\n0 1\n2 0\n3 1\n",
"3 0\n1 0\n2 0\n3 0\n0 53\n",
"1 1\n3 0\n0 1\n2 1\n0 2\n",
"0 1\n1 1\n0 1\n0 152\n1 0\n",
"2 0\n0 1\n1 0\n2 0\n0 2\n",
"0 1\n3 0\n0 1\n2 0\n0 1\n",
"1 1\n2 0\n1 0\n2 0\n0 6\n",
"0 1\n1 1\n1 0\n1 16\n4 0\n",
"0 6\n3 0\n0 1\n0 60\n0 15\n",
"3 0\n1 0\n3 0\n3 0\n0 53\n",
"1 0\n1 1\n0 1\n0 152\n1 0\n",
"1 0\n1 0\n1 0\n3 1\n0 2\n",
"0 1\n1 0\n1 0\n3 0\n0 2\n",
"0 1\n3 0\n1 0\n2 0\n0 1\n",
"1 1\n2 0\n1 0\n3 0\n0 6\n",
"0 6\n2 0\n2 0\n2 0\n0 15\n",
"0 1\n3 0\n0 1\n0 60\n0 15\n",
"3 0\n1 0\n3 0\n2 0\n0 53\n",
"2 0\n3 0\n0 1\n2 1\n0 2\n",
"1 0\n1 0\n0 1\n0 152\n1 0\n",
"0 1\n1 0\n1 0\n0 108\n0 2\n",
"1 1\n2 0\n1 1\n3 0\n0 6\n",
"0 1\n1 6\n0 1\n0 60\n0 15\n",
"1 6\n1 0\n3 0\n2 0\n0 53\n",
"2 0\n2 1\n0 1\n2 1\n0 2\n",
"3 0\n1 0\n0 1\n0 152\n1 0\n",
"1 0\n1 0\n2 0\n3 1\n0 2\n",
"1 1\n2 0\n1 1\n2 0\n0 6\n",
"0 6\n2 0\n3 0\n2 0\n0 15\n",
"0 1\n1 6\n0 1\n1 1\n0 15\n",
"2 0\n2 1\n0 1\n1 166\n0 2\n",
"1 0\n1 0\n2 0\n3 0\n0 2\n",
"0 1\n2 0\n1 1\n2 0\n0 6\n",
"0 6\n2 0\n3 0\n2 0\n1 16\n",
"1 6\n0 1\n3 0\n2 0\n0 53\n",
"0 1\n1 0\n2 0\n3 0\n0 2\n",
"0 1\n2 0\n3 0\n2 0\n0 6\n",
"0 1\n2 0\n2 1\n2 0\n0 6\n",
"0 1\n0 1\n1 0\n2 0\n0 2\n",
"0 1\n1 1\n1 0\n0 108\n0 2\n",
"0 1\n1 0\n1 0\n2 0\n1 13\n",
"1 1\n3 0\n1 6\n2 0\n0 15\n",
"0 1\n3 0\n0 1\n2 0\n2 1\n",
"0 1\n4 0\n1 1\n2 0\n1 15\n",
"1 0\n2 0\n0 1\n2 0\n0 15\n",
"0 1\n4 0\n0 1\n0 166\n0 13\n",
"0 1\n0 1\n1 0\n0 48\n4 0\n",
"2 0\n1 0\n1 0\n3 0\n0 2\n",
"1 1\n3 0\n0 1\n1 3\n0 2\n",
"0 1\n4 0\n3 0\n2 0\n0 13\n",
"1 1\n1 0\n1 0\n2 0\n4 0\n",
"1 0\n1 0\n1 0\n0 21\n0 2\n",
"1 0\n1 0\n1 0\n1 108\n0 2\n",
"3 0\n1 0\n1 0\n0 108\n0 2\n",
"0 1\n2 0\n1 0\n2 0\n0 81\n",
"0 1\n3 0\n0 1\n3 0\n0 2\n",
"0 2\n3 0\n0 1\n2 0\n0 15\n"
]
}
|
You are a teacher at a cram school for elementary school pupils.
One day, you showed your students how to calculate division of fraction in a class of mathematics. Your lesson was kind and fluent, and it seemed everything was going so well - except for one thing. After some experiences, a student Max got so curious about how precise he could compute the quotient. He tried many divisions asking you for a help, and finally found a case where the answer became an infinite fraction. He was fascinated with such a case, so he continued computing the answer. But it was clear for you the answer was an infinite fraction - no matter how many digits he computed, he wouldn’t reach the end.
Since you have many other things to tell in today’s class, you can’t leave this as it is. So you decided to use a computer to calculate the answer in turn of him. Actually you succeeded to persuade him that he was going into a loop, so it was enough for him to know how long he could compute before entering a loop.
Your task now is to write a program which computes where the recurring part starts and the length of the recurring part, for given dividend/divisor pairs. All computation should be done in decimal numbers. If the specified dividend/divisor pair gives a finite fraction, your program should treat the length of the recurring part as 0.
Input
The input consists of multiple datasets. Each line of the input describes a dataset. A dataset consists of two positive integers x and y, which specifies the dividend and the divisor, respectively. You may assume that 1 ≤ x < y ≤ 1,000,000.
The last dataset is followed by a line containing two zeros. This line is not a part of datasets and should not be processed.
Output
For each dataset, your program should output a line containing two integers separated by exactly one blank character.
The former describes the number of digits after the decimal point before the recurring part starts. And the latter describes the length of the recurring part.
Example
Input
1 3
1 6
3 5
2 200
25 99
0 0
Output
0 1
1 1
1 0
2 0
0 2
|
{
"inputs": [
"1 1\n0 0 2 0",
"2 1\n0 0 1 0\n1 1 0 1",
"3 2\n0 0 2 0\n1 -1 1 2\n0 1 2 1",
"1 1\n0 0 2 -1",
"2 2\n0 0 1 0\n1 1 0 1",
"3 2\n-1 0 2 0\n1 -1 1 2\n0 1 2 1",
"1 1\n1 0 2 -1",
"2 2\n-1 0 1 0\n1 1 0 1",
"1 0\n1 0 2 -1",
"1 1\n0 0 3 0",
"3 4\n-1 0 2 0\n1 -1 1 2\n0 1 2 1",
"2 4\n0 0 1 0\n1 1 0 1",
"1 2\n1 0 2 -1",
"1 1\n0 0 5 0",
"1 2\n2 0 2 -1",
"1 1\n1 0 5 0",
"1 2\n3 1 2 -1",
"1 1\n0 0 4 -1",
"1 1\n0 -1 2 -1",
"3 4\n0 0 2 0\n1 -1 1 2\n0 1 2 1",
"1 1\n0 0 6 0",
"1 1\n1 0 2 0",
"1 2\n1 0 2 -3",
"1 3\n3 -1 2 -1",
"1 1\n1 1 4 0",
"1 1\n1 0 6 1",
"1 3\n3 -2 2 -1",
"1 1\n1 1 4 -1",
"1 1\n0 1 4 -1",
"1 2\n0 0 2 -3",
"1 1\n-1 1 4 -1",
"1 1\n-1 1 4 -2",
"1 2\n3 0 3 0",
"1 2\n-1 1 4 -2",
"1 2\n0 -1 2 -8",
"1 2\n6 0 3 0",
"1 2\n0 -1 2 -15",
"1 4\n0 -1 2 -15",
"1 4\n0 0 2 -15",
"1 4\n0 0 2 -10",
"1 1\n0 0 7 0",
"1 2\n6 0 2 -1",
"3 4\n1 0 2 0\n1 -1 1 2\n0 1 2 1",
"1 1\n0 0 10 0",
"1 4\n3 -1 2 -1",
"1 3\n3 -1 1 -1",
"1 1\n-1 1 8 -1",
"1 1\n-1 1 4 -3",
"1 2\n-1 -1 2 -8",
"1 2\n0 -2 2 -15",
"1 4\n-1 -1 2 -15",
"1 4\n0 0 2 -24",
"1 4\n0 1 2 -10",
"1 1\n0 1 10 0",
"1 3\n3 -1 1 0",
"1 2\n2 1 -1 -2",
"1 2\n0 1 4 -2",
"1 3\n0 0 2 -2",
"1 1\n-2 1 8 -1",
"1 1\n-1 1 4 -8",
"1 2\n0 -4 2 -15",
"1 4\n-1 -2 2 -15",
"1 7\n0 0 2 -24",
"1 4\n0 2 2 -10",
"1 3\n0 0 3 -1",
"1 2\n-1 0 4 -2",
"1 1\n1 1 10 0",
"1 4\n1 0 4 -2",
"1 1\n0 0 8 1",
"1 2\n-1 1 4 -8",
"1 3\n0 -4 2 -15",
"1 4\n1 2 2 -10",
"1 4\n0 1 1 -1",
"1 2\n0 1 7 1",
"1 3\n-1 0 4 -2",
"1 1\n1 1 10 1",
"1 4\n1 0 4 -1",
"1 1\n3 -1 6 2",
"1 2\n-1 1 2 -8",
"1 2\n-1 -1 1 -13",
"1 3\n-1 -4 2 -15",
"1 4\n-2 0 2 -15",
"1 4\n1 2 2 -20",
"1 4\n-1 0 4 -2",
"1 1\n1 1 14 1",
"1 3\n0 1 -1 -4",
"1 3\n-1 -1 3 0",
"1 2\n-1 -1 2 -13",
"1 3\n-2 -4 2 -15",
"1 4\n1 1 2 -20",
"1 2\n0 1 8 0",
"1 6\n-1 -1 3 0",
"1 5\n-2 -4 2 -15",
"1 5\n-2 0 2 -28",
"1 1\n0 -1 0 -24",
"1 2\n4 1 13 -1",
"1 6\n-1 -1 0 0",
"1 5\n-2 0 2 -15",
"1 10\n-2 0 2 -28",
"1 1\n0 -1 -1 -24",
"1 7\n0 0 0 -1",
"1 5\n-1 0 2 -15",
"1 1\n0 -1 -1 -34"
],
"outputs": [
"2.8284271082",
"5.2793638507",
"11.1364603512",
"2.990697562442\n",
"3.733073986963\n",
"11.546143695802\n",
"2.378414230005\n",
"4.273255500439\n",
"nan\n",
"3.464101615138\n",
"8.164356503856\n",
"2.639681930853\n",
"1.681792830507\n",
"4.472135955000\n",
"1.414213562373\n",
"4.000000000000\n",
"2.114742526881\n",
"4.061086369738\n",
"2.828427124746\n",
"7.874666640553\n",
"4.898979485566\n",
"2.000000000000\n",
"2.514866859366\n",
"1.154700538379\n",
"3.556558820078\n",
"4.516201728706\n",
"1.373178095938\n",
"3.797657844232\n",
"4.229485053762\n",
"2.685349614283\n",
"4.641191574212\n",
"4.829472805533\n",
"0.000000000000\n",
"3.414952970348\n",
"3.815785604376\n",
"2.449489742783\n",
"5.318295896945\n",
"3.760603093086\n",
"3.890083026160\n",
"3.193436867575\n",
"5.291502622129\n",
"2.871621711026\n",
"7.518272681860\n",
"6.324555320337\n",
"1.000000000000\n",
"1.632993161855\n",
"6.072740553422\n",
"5.060879068870\n",
"3.902761357261\n",
"5.128927068689\n",
"3.783889673772\n",
"4.907462598694\n",
"3.343701524882\n",
"6.340307759445\n",
"1.726680042741\n",
"2.912950630244\n",
"3.162277660168\n",
"1.941967086829\n",
"6.386873735149\n",
"6.417360872193\n",
"4.728708045016\n",
"3.652624270867\n",
"3.709693029856\n",
"3.487911274760\n",
"2.053380192161\n",
"3.281818034911\n",
"6.018433396869\n",
"1.898828922116\n",
"5.678823028867\n",
"4.537759390049\n",
"3.860973950961\n",
"3.470100081956\n",
"1.495348781221\n",
"3.741657386774\n",
"2.679593204732\n",
"6.000000000000\n",
"1.778279410039\n",
"4.119534287814\n",
"4.355877174693\n",
"4.932651429119\n",
"3.899017696975\n",
"3.940072930322\n",
"4.692836620376\n",
"2.320595787106\n",
"7.211102550928\n",
"2.607430283783\n",
"2.344669308770\n",
"4.973794703615\n",
"3.950476749410\n",
"4.585171320859\n",
"4.015534272870\n",
"1.657931567872\n",
"3.060026132009\n",
"4.756828460011\n",
"9.591663046625\n",
"4.294076025711\n",
"0.970983543415\n",
"3.524108363403\n",
"3.363585661015\n",
"9.596192758890\n",
"0.755928946018\n",
"3.498234816679\n",
"11.491761925560\n"
]
}
|
In the west of Tokyo, there is a city named “Academy City.” There are many schools and laboratories to develop psychics in Academy City.
You are a psychic student of a school in Academy City. Your psychic ability is to give acceleration to a certain object.
You can use your psychic ability anytime and anywhere, but there are constraints. If the object remains stationary, you can give acceleration to the object in any direction. If the object is moving, you can give acceleration to the object only in 1) the direction the object is moving to, 2) the direction opposite to it, or 3) the direction perpendicular to it.
Today’s training menu is to move the object along a given course. For simplicity you can regard the course as consisting of line segments and circular arcs in a 2-dimensional space. The course has no branching. All segments and arcs are connected smoothly, i.e. there are no sharp corners.
In the beginning, the object is placed at the starting point of the first line segment. You have to move the object to the ending point of the last line segment along the course and stop the object at that point by controlling its acceleration properly. Before the training, a coach ordered you to simulate the minimum time to move the object from the starting point to the ending point.
Your task is to write a program which reads the shape of the course and the maximum acceleration amax you can give to the object and calculates the minimum time to move the object from the starting point to the ending point.
The object follows basic physical laws. When the object is moving straight in some direction, with acceleration either forward or backward, the following equations hold:
v = v0 + at
and
s = v0t + (1/2)at2
where v, s, v0, a, and t are the velocity, the distance from the starting point, the initial velocity (i.e. the velocity at the starting point), the acceleration, and the time the object has been moving in that direction, respectively. Note that they can be simplified as follows:
v2 − v02 = 2as
When the object is moving along an arc, with acceleration to the centroid, the following equations hold:
a = v2/r
wher v, a, and r are the velocity, the acceleration, and the radius of the arc, respectively. Note that the object cannot change the velocity due to the criteria on your psychic ability.
Input
The input has the following format:
N amax
xa,1 ya,1 xb,1 yb,1
xa,2 ya,2 xb,2 yb,2
.
.
.
N is the number of line segments; amax is the maximum acceleration you can give to the object; (xa,i, ya,i) and (xb,i, yb,i) are the starting point and the ending point of the i-th line segment, respectively. The given course may have crosses but you cannot change the direction there.
The input meets the following constraints: 0 < N ≤ 40000, 1 ≤ amax ≤ 100, and -100 ≤ xai, yai, xbi, ybi ≤ 100.
Output
Print the minimum time to move the object from the starting point to the ending point with an relative or absolute error of at most 10-6. You may output any number of digits after the decimal point.
Examples
Input
2 1
0 0 1 0
1 1 0 1
Output
5.2793638507
Input
1 1
0 0 2 0
Output
2.8284271082
Input
3 2
0 0 2 0
1 -1 1 2
0 1 2 1
Output
11.1364603512
|
{
"inputs": [
"4\n1 2 3 4",
"5\n3 3 3 3 3",
"4\n1 2 0 4",
"5\n5 3 3 3 3",
"4\n1 2 1 4",
"5\n4 3 3 3 3",
"4\n2 2 1 4",
"5\n4 3 6 3 3",
"5\n4 0 6 3 3",
"5\n4 0 4 3 3",
"4\n2 1 0 8",
"4\n2 1 -1 8",
"5\n4 0 7 3 1",
"5\n4 -2 10 3 1",
"4\n5 0 -2 8",
"4\n5 0 -2 7",
"4\n5 0 -2 6",
"5\n1 -2 18 4 1",
"5\n0 -2 18 4 1",
"5\n0 -4 9 4 1",
"5\n0 -4 7 4 1",
"4\n1 0 2 22",
"4\n1 1 2 22",
"4\n0 1 0 40",
"4\n0 0 -1 23",
"5\n5 3 2 3 3",
"5\n4 3 6 3 1",
"4\n2 1 0 14",
"5\n1 -4 9 4 1",
"4\n1 1 1 33",
"4\n0 1 1 40",
"4\n0 2 1 40",
"4\n0 1 1 74",
"4\n0 2 2 40",
"4\n0 1 -1 0",
"4\n2 0 1 33",
"4\n0 1 0 74",
"4\n1 2 2 40",
"5\n1 -4 3 4 2",
"4\n0 1 0 0",
"4\n-1 0 2 50",
"4\n2 2 2 40",
"5\n5 6 4 5 3",
"4\n2 1 2 33",
"4\n1 1 1 74",
"5\n5 6 4 9 3",
"5\n1 0 23 2 1",
"5\n1 -8 3 6 2",
"4\n3 1 3 27",
"5\n0 0 -1 32 2",
"4\n1 1 3 27",
"4\n-4 0 1 48",
"4\n0 2 0 33",
"4\n8 1 1 41",
"5\n2 -4 0 3 2",
"5\n0 1 0 46 2",
"4\n0 2 0 55",
"4\n-4 0 2 0",
"4\n1 0 0 67",
"4\n1 2 0 35",
"5\n9 3 2 9 6",
"5\n2 -4 0 3 0",
"5\n0 1 1 46 2",
"4\n-4 0 4 0",
"4\n-4 0 4 1",
"4\n0 -1 0 67",
"5\n9 3 2 34 6",
"4\n0 -1 3 35",
"4\n-8 0 4 1",
"5\n9 4 2 34 6",
"4\n-10 0 4 1",
"5\n61 0 3 4 0",
"5\n0 -1 0 61 2",
"4\n-10 0 4 0",
"5\n0 -2 0 61 2",
"4\n-8 0 1 2",
"5\n0 -2 0 105 2",
"4\n-8 0 0 2",
"5\n0 -2 0 141 2",
"4\n2 2 0 4",
"4\n2 1 0 4",
"5\n4 0 4 3 1",
"4\n4 1 -1 8",
"5\n4 -1 7 3 1",
"4\n4 0 -1 8",
"5\n4 -2 7 3 1",
"4\n5 0 -1 8",
"5\n1 -2 10 3 1",
"5\n1 -2 10 4 1",
"4\n5 1 -2 6",
"4\n5 1 0 6",
"5\n0 -4 18 4 1",
"4\n3 1 0 6",
"4\n5 1 0 12",
"4\n5 1 1 12",
"5\n0 0 7 4 1",
"4\n5 0 1 12",
"5\n0 0 0 4 1",
"4\n0 0 1 12",
"5\n0 0 0 4 2",
"4\n0 0 1 22",
"5\n0 0 -1 4 2"
],
"outputs": [
"11",
"21",
"7\n",
"23\n",
"8\n",
"22\n",
"10\n",
"24\n",
"16\n",
"14\n",
"11\n",
"9\n",
"13\n",
"12\n",
"6\n",
"5\n",
"4\n",
"18\n",
"15\n",
"2\n",
"0\n",
"25\n",
"26\n",
"40\n",
"21\n",
"20\n",
"19\n",
"17\n",
"3\n",
"37\n",
"42\n",
"43\n",
"76\n",
"44\n",
"-1\n",
"36\n",
"74\n",
"46\n",
"-2\n",
"1\n",
"49\n",
"48\n",
"29\n",
"39\n",
"78\n",
"32\n",
"27\n",
"-12\n",
"35\n",
"30\n",
"31\n",
"41\n",
"33\n",
"45\n",
"-5\n",
"47\n",
"55\n",
"-6\n",
"67\n",
"38\n",
"28\n",
"-7\n",
"50\n",
"-4\n",
"-3\n",
"65\n",
"53\n",
"34\n",
"-11\n",
"56\n",
"-15\n",
"64\n",
"59\n",
"-16\n",
"57\n",
"-13\n",
"101\n",
"-14\n",
"137\n",
"8\n",
"7\n",
"10\n",
"10\n",
"11\n",
"7\n",
"9\n",
"7\n",
"9\n",
"10\n",
"7\n",
"9\n",
"11\n",
"9\n",
"15\n",
"16\n",
"8\n",
"15\n",
"4\n",
"12\n",
"4\n",
"22\n",
"2\n"
]
}
|
Boy G was on a voyage with his father to celebrate his 13th birthday. However, during the voyage, unfortunately the ship was hit by a storm and the ship capsized. When he woke up, it was an uninhabited island. Partly due to the influence of the adventurer's father, he decided to live a survival life on an uninhabited island without being afraid of this situation. I managed to survive by defeating animals, grilling meat, collecting nuts to eat, and camping under large trees. However, it seems that the island has been strange recently. All the animals behave strangely, which may be a sign of something wrong. I have to escape from this island as soon as possible.
But how do you get away from the island? I can see another island over the sea, but I can't find a way to get there. At a loss, as he was walking along the coast, he suddenly found N boats. When I looked it up, they all seemed to work. Alright, let's use this boat to escape to the other island. However, a similar survival life may begin on the next island. Let's carry all the boats as a spare so that we will not be in trouble at that time. I have to do something early before something happens on this island.
Constraints
The input satisfies the following conditions.
* 1 ≤ N ≤ 1000
* 1 ≤ Ti ≤ 10000
Input
The integer N is given on the first line.
The second line is given N integers Ti, separated by blanks.
Output
Output the shortest time (minutes) required to finish carrying all the boats in one line.
Examples
Input
4
1 2 3 4
Output
11
Input
5
3 3 3 3 3
Output
21
|
{
"inputs": [
"5\n4 10 3 13 7\n8\n1 2 4\n2 1 3 3\n1 2 4\n1 3 3\n2 2 5 5\n1 1 5\n2 1 2 10\n1 2 3\n",
"6\n4 7 4 0 7 3\n5\n2 2 3 8\n1 1 5\n2 3 5 1\n2 4 5 6\n1 2 3\n",
"20\n34 20 8 27 49 36 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 4 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 5 41\n2 5 13 38\n1 3 9\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 9 48\n2 15 19 10\n",
"8\n0 7 5 6 5 1 0 4\n10\n1 1 4\n1 2 7\n1 2 3\n1 6 7\n2 4 8 1\n2 4 5 8\n1 3 5\n2 1 5 2\n1 5 8\n1 1 4\n",
"10\n26 6 27 28 28 19 14 8 0 24\n3\n2 7 8 16\n1 4 7\n2 6 9 10\n",
"4\n10 8 7 2\n20\n1 3 4\n1 3 4\n1 2 2\n2 1 4 10\n1 1 3\n2 1 2 4\n1 1 3\n2 1 3 2\n1 2 4\n2 3 4 8\n1 1 4\n2 1 2 3\n2 3 4 7\n1 1 3\n1 3 4\n1 4 4\n1 2 2\n2 3 3 7\n2 1 1 4\n1 4 4\n",
"10\n5 1 5 0 0 1 4 4 0 0\n8\n2 2 4 5\n2 2 10 5\n1 6 8\n1 1 6\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 26 45 41 40 50 12 10\n10\n2 2 6 32\n1 2 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"10\n10 2 10 7 9 6 7 1 10 3\n10\n2 2 4 8\n2 1 9 2\n2 7 10 10\n1 7 7\n2 1 5 5\n2 7 9 7\n1 2 3\n2 6 9 10\n2 2 4 4\n1 4 8\n",
"20\n34 20 8 27 49 36 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 4 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 5 41\n2 5 13 38\n1 3 9\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 13 48\n2 15 19 10\n",
"8\n0 7 5 6 5 1 0 4\n10\n1 1 4\n1 2 7\n1 2 3\n1 6 7\n2 4 8 1\n2 4 5 8\n1 3 3\n2 1 5 2\n1 5 8\n1 1 4\n",
"10\n5 1 2 0 0 1 4 4 0 0\n8\n2 2 4 5\n2 2 10 5\n1 6 8\n1 1 6\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 26 45 41 40 50 12 10\n10\n2 2 4 32\n1 2 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"10\n10 2 10 7 9 10 7 1 10 3\n10\n2 2 4 8\n2 1 9 2\n2 7 10 10\n1 7 7\n2 1 5 5\n2 7 9 7\n1 2 3\n2 6 9 10\n2 2 4 4\n1 4 8\n",
"5\n4 10 3 13 7\n8\n1 2 5\n2 1 3 3\n1 2 4\n1 3 3\n2 2 5 5\n1 1 5\n2 1 2 10\n1 2 3\n",
"20\n34 20 2 27 49 36 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 4 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 5 41\n2 5 13 38\n1 3 9\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 13 48\n2 15 19 10\n",
"10\n5 1 2 0 0 1 4 4 0 0\n8\n2 2 4 5\n2 2 10 5\n1 6 8\n1 1 3\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 26 45 41 40 50 12 10\n10\n2 2 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"20\n34 20 2 27 49 36 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 4 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 6 41\n2 5 13 38\n1 3 9\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 13 48\n2 15 19 10\n",
"10\n5 1 2 0 0 1 4 7 0 0\n8\n2 2 4 5\n2 2 10 5\n1 6 8\n1 1 3\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 3 45 41 40 50 12 10\n10\n2 2 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"20\n34 20 8 27 49 36 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 7 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 5 41\n2 5 13 38\n1 3 9\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 9 48\n2 15 19 10\n",
"10\n26 6 27 28 28 19 22 8 0 24\n3\n2 7 8 16\n1 4 7\n2 6 9 10\n",
"4\n10 8 7 2\n20\n1 3 4\n1 3 4\n1 2 2\n2 1 4 10\n1 1 3\n2 1 2 4\n1 1 3\n2 1 3 2\n1 2 4\n2 3 3 8\n1 1 4\n2 1 2 3\n2 3 4 7\n1 1 3\n1 3 4\n1 4 4\n1 2 2\n2 3 3 7\n2 1 1 4\n1 4 4\n",
"10\n5 1 5 0 0 2 4 4 0 0\n8\n2 2 4 5\n2 2 10 5\n1 6 8\n1 1 6\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 26 45 41 40 50 12 10\n10\n2 2 6 32\n1 2 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 1 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"10\n5 1 2 0 0 1 4 4 0 0\n8\n2 2 5 5\n2 2 10 5\n1 6 8\n1 1 6\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 26 45 41 68 50 12 10\n10\n2 2 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"20\n34 20 2 27 49 13 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 4 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 6 41\n2 5 13 38\n1 3 9\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 13 48\n2 15 19 10\n",
"10\n3 28 10 3 45 41 40 50 12 10\n10\n2 2 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 6 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"10\n5 1 2 0 0 1 4 7 0 0\n8\n2 4 5 5\n2 2 10 5\n1 6 8\n1 1 3\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 3 45 41 40 50 12 10\n10\n2 1 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 8\n",
"20\n34 20 8 27 49 36 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 7 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 5 41\n2 5 13 38\n1 3 12\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 9 48\n2 15 19 10\n",
"10\n3 28 10 41 45 41 40 50 12 10\n10\n2 2 6 32\n1 2 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 1 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"10\n10 2 10 7 9 10 7 1 10 3\n10\n2 2 4 8\n2 1 9 2\n2 7 10 1\n1 7 7\n2 2 5 5\n2 7 9 7\n1 2 3\n2 6 9 10\n2 2 4 4\n1 4 8\n",
"10\n3 54 10 26 45 41 68 50 12 10\n10\n2 2 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 6\n",
"10\n3 28 10 3 45 41 40 31 12 10\n10\n2 1 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 8\n",
"10\n3 28 10 41 45 41 40 50 12 10\n10\n2 2 6 32\n1 2 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 1 40\n1 3 6\n1 6 9\n2 2 9 13\n2 6 7 6\n",
"10\n5 1 2 0 0 1 4 4 0 0\n8\n2 2 5 5\n2 2 10 9\n1 6 8\n1 1 6\n2 1 4 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n10 2 10 7 9 10 7 1 10 3\n10\n2 2 4 8\n2 1 9 2\n2 7 10 1\n1 7 7\n2 2 5 7\n2 7 9 7\n1 2 3\n2 6 9 10\n2 2 4 4\n1 4 8\n",
"20\n34 20 8 27 49 36 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 7 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 5 41\n2 5 13 38\n1 1 12\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 9 83\n2 15 19 10\n",
"10\n26 6 40 28 28 19 22 8 0 48\n3\n2 7 8 9\n1 4 7\n2 6 9 10\n",
"10\n3 28 10 41 45 41 40 50 12 10\n10\n2 2 6 32\n1 2 10\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 1 40\n1 3 6\n1 6 9\n2 2 9 13\n2 6 7 6\n",
"10\n5 1 4 0 0 1 4 4 0 0\n8\n2 2 5 5\n2 2 10 9\n1 6 8\n1 1 6\n2 1 4 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n5 1 2 0 0 1 4 7 0 0\n8\n2 2 5 5\n2 2 10 5\n1 6 8\n1 1 3\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 3 45 41 40 50 12 10\n10\n2 2 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 8\n",
"10\n10 2 10 7 9 10 7 1 10 3\n10\n2 2 4 8\n2 1 9 2\n2 7 10 10\n1 7 7\n2 2 5 5\n2 7 9 7\n1 2 3\n2 6 9 10\n2 2 4 4\n1 4 8\n",
"10\n5 1 2 0 0 1 4 7 0 0\n8\n2 2 7 5\n2 2 10 5\n1 6 8\n1 1 3\n2 1 2 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n26 6 40 28 28 19 22 8 0 24\n3\n2 7 8 16\n1 4 7\n2 6 9 10\n",
"10\n5 1 2 0 0 1 4 4 0 0\n8\n2 2 5 5\n2 2 10 5\n1 6 8\n1 1 6\n2 1 4 4\n2 2 2 2\n2 5 6 1\n2 3 5 4\n",
"10\n3 28 10 3 45 41 40 50 12 10\n10\n2 2 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 6 6\n1 3 9\n2 2 9 13\n2 6 8 6\n",
"20\n34 20 8 27 49 36 10 9 35 22 41 2 35 50 24 21 11 33 30 16\n20\n2 1 8 9\n1 8 12\n2 4 16 14\n2 7 13 5\n1 8 16\n1 4 19\n2 1 19 16\n2 4 5 47\n1 4 20\n2 3 5 41\n2 5 13 38\n1 3 12\n1 13 15\n2 4 6 33\n1 12 12\n1 8 8\n1 17 17\n1 8 18\n2 2 9 83\n2 15 19 10\n",
"10\n26 6 40 28 28 19 22 8 0 48\n3\n2 7 8 16\n1 4 7\n2 6 9 10\n",
"10\n3 28 10 3 45 41 40 50 12 10\n10\n2 2 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 40\n1 6 6\n1 3 9\n2 2 9 13\n2 8 8 6\n",
"10\n3 28 10 3 45 41 40 31 12 10\n10\n2 1 4 32\n1 4 7\n2 8 10 16\n1 1 4\n2 6 9 48\n2 1 2 38\n1 3 6\n1 3 9\n2 2 9 13\n2 6 7 8\n"
],
"outputs": [
" 26\n 22\n 0\n 34\n 11\n",
" 38\n 28\n",
" 100\n 272\n 468\n 522\n 243\n 80\n 63\n 61\n 27\n 384\n",
" 18\n 24\n 12\n 1\n 32\n 20\n 27\n",
" 105\n",
" 9\n 9\n 8\n 15\n 23\n 27\n 17\n 12\n 7\n 7\n 7\n 7\n",
" 6\n 20\n",
" 222\n 163\n 170\n 256\n",
" 15\n 18\n 46\n",
"100\n272\n468\n522\n243\n80\n63\n61\n27\n384\n",
"18\n24\n12\n1\n5\n20\n27\n",
"6\n17\n",
"286\n163\n170\n256\n",
"15\n18\n34\n",
"33\n22\n0\n34\n11\n",
"100\n272\n468\n522\n237\n80\n63\n61\n27\n384\n",
"6\n8\n",
"184\n163\n170\n256\n",
"100\n272\n468\n522\n278\n80\n63\n61\n27\n384\n",
"7\n8\n",
"161\n140\n147\n233\n",
"100\n272\n471\n513\n246\n80\n63\n61\n27\n384\n",
"81\n",
"9\n9\n8\n15\n23\n27\n25\n12\n15\n15\n7\n15\n",
"9\n23\n",
"222\n163\n170\n256\n",
"6\n12\n",
"212\n163\n170\n348\n",
"100\n272\n445\n499\n237\n80\n63\n61\n27\n384\n",
"161\n140\n25\n233\n",
"7\n16\n",
"161\n172\n147\n233\n",
"100\n272\n471\n513\n372\n80\n63\n61\n27\n384\n",
"173\n114\n121\n207\n",
"4\n18\n52\n",
"212\n125\n170\n348\n",
"161\n172\n147\n278\n",
"173\n114\n121\n143\n",
"34\n64\n",
"4\n22\n52\n",
"100\n272\n471\n513\n444\n80\n63\n61\n27\n384\n",
"106\n",
"245\n114\n121\n143\n",
"34\n58\n",
"7\n8\n",
"161\n140\n147\n233\n",
"15\n18\n34\n",
"7\n8\n",
"81\n",
"6\n12\n",
"161\n140\n25\n233\n",
"100\n272\n471\n513\n372\n80\n63\n61\n27\n384\n",
"81\n",
"161\n140\n25\n233\n",
"161\n172\n147\n278\n"
]
}
|
You've got an array a, consisting of n integers a1, a2, ..., an. You are allowed to perform two operations on this array:
1. Calculate the sum of current array elements on the segment [l, r], that is, count value al + al + 1 + ... + ar.
2. Apply the xor operation with a given number x to each array element on the segment [l, r], that is, execute <image>. This operation changes exactly r - l + 1 array elements.
Expression <image> means applying bitwise xor operation to numbers x and y. The given operation exists in all modern programming languages, for example in language C++ and Java it is marked as "^", in Pascal — as "xor".
You've got a list of m operations of the indicated type. Your task is to perform all given operations, for each sum query you should print the result you get.
Input
The first line contains integer n (1 ≤ n ≤ 105) — the size of the array. The second line contains space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 106) — the original array.
The third line contains integer m (1 ≤ m ≤ 5·104) — the number of operations with the array. The i-th of the following m lines first contains an integer ti (1 ≤ ti ≤ 2) — the type of the i-th query. If ti = 1, then this is the query of the sum, if ti = 2, then this is the query to change array elements. If the i-th operation is of type 1, then next follow two integers li, ri (1 ≤ li ≤ ri ≤ n). If the i-th operation is of type 2, then next follow three integers li, ri, xi (1 ≤ li ≤ ri ≤ n, 1 ≤ xi ≤ 106). The numbers on the lines are separated by single spaces.
Output
For each query of type 1 print in a single line the sum of numbers on the given segment. Print the answers to the queries in the order in which the queries go in the input.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams, or the %I64d specifier.
Examples
Input
5
4 10 3 13 7
8
1 2 4
2 1 3 3
1 2 4
1 3 3
2 2 5 5
1 1 5
2 1 2 10
1 2 3
Output
26
22
0
34
11
Input
6
4 7 4 0 7 3
5
2 2 3 8
1 1 5
2 3 5 1
2 4 5 6
1 2 3
Output
38
28
|
{
"inputs": [
"2\n2\n1 2\n2 1\n4\n2 1 4 1\n2 4 1 4",
"2\n2\n1 2\n2 1\n4\n2 1 4 1\n2 5 1 4",
"2\n2\n2 2\n2 1\n4\n2 1 4 1\n4 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 1 4 1\n2 5 1 4",
"2\n2\n2 2\n2 1\n4\n2 1 4 1\n2 4 1 4",
"2\n2\n2 2\n2 1\n4\n2 1 4 1\n1 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 1 1 1\n2 5 1 4",
"2\n2\n2 2\n2 1\n3\n2 1 4 1\n1 4 1 4",
"2\n2\n2 2\n2 1\n4\n2 1 2 1\n4 4 1 4",
"2\n2\n2 2\n2 1\n3\n0 1 4 1\n1 4 1 4",
"2\n2\n2 2\n2 2\n3\n0 1 4 1\n1 4 1 4",
"2\n1\n2 2\n2 1\n4\n2 1 4 1\n2 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 1 4 1\n4 5 1 4",
"2\n2\n2 2\n4 1\n4\n2 1 4 1\n2 4 1 4",
"2\n2\n2 2\n2 1\n4\n2 1 4 1\n1 4 1 1",
"2\n2\n1 2\n2 1\n4\n1 1 1 1\n3 5 1 4",
"2\n2\n2 2\n2 2\n3\n2 1 4 1\n1 4 1 4",
"2\n2\n2 2\n2 1\n4\n2 1 2 2\n4 4 1 4",
"2\n2\n2 2\n2 2\n3\n0 1 4 1\n2 4 1 4",
"2\n2\n2 2\n3 2\n3\n0 1 4 1\n1 4 1 4",
"2\n2\n2 2\n4 1\n4\n2 2 4 1\n2 4 1 4",
"2\n2\n2 2\n2 1\n4\n2 1 2 2\n5 4 1 4",
"2\n2\n2 2\n4 1\n4\n2 2 4 2\n2 4 1 4",
"2\n2\n1 2\n2 1\n4\n2 1 4 1\n2 5 1 1",
"2\n2\n2 1\n2 1\n4\n2 1 4 1\n4 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 1 1 1\n2 5 1 3",
"2\n2\n2 2\n2 1\n4\n3 1 4 1\n4 4 1 4",
"2\n2\n2 2\n4 1\n3\n2 1 4 1\n1 4 1 4",
"2\n2\n2 2\n3 1\n4\n2 1 2 1\n4 4 1 4",
"2\n1\n2 3\n2 1\n4\n2 1 4 1\n2 4 1 4",
"2\n1\n1 2\n2 1\n4\n1 1 4 1\n4 5 1 4",
"2\n2\n2 2\n4 1\n4\n2 1 2 2\n4 4 1 4",
"2\n2\n2 2\n2 2\n3\n0 1 3 1\n2 4 1 4",
"2\n2\n2 2\n3 2\n3\n-1 1 4 1\n1 4 1 4",
"2\n2\n2 2\n2 1\n2\n2 1 2 2\n5 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 2 1 1\n2 5 1 3",
"2\n2\n3 2\n2 1\n4\n3 1 4 1\n4 4 1 4",
"2\n2\n2 2\n3 1\n3\n2 1 4 1\n1 4 1 4",
"2\n2\n2 2\n3 2\n4\n2 1 2 1\n4 4 1 4",
"2\n1\n2 3\n2 1\n4\n2 1 4 1\n2 4 1 1",
"2\n2\n2 2\n3 2\n3\n-1 1 2 1\n1 4 1 4",
"2\n2\n3 2\n2 1\n4\n3 1 4 1\n4 4 2 4",
"2\n2\n2 1\n3 2\n4\n2 1 2 1\n4 4 1 4",
"2\n2\n3 1\n2 1\n4\n3 1 4 1\n4 4 1 4",
"2\n2\n3 1\n2 1\n4\n5 1 4 1\n4 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 1 1 1\n2 5 1 1",
"2\n1\n2 2\n2 1\n4\n2 1 4 1\n4 4 1 4",
"2\n2\n2 2\n4 1\n4\n2 1 2 1\n4 4 1 4",
"2\n2\n2 2\n2 1\n3\n1 1 4 1\n1 4 1 4",
"2\n1\n2 2\n4 1\n4\n2 1 4 1\n2 4 1 4",
"2\n2\n2 2\n2 1\n4\n2 1 4 1\n1 5 1 1",
"2\n2\n2 2\n2 2\n3\n2 1 4 1\n2 4 1 4",
"2\n2\n4 2\n3 2\n3\n0 1 4 1\n1 4 1 4",
"2\n2\n2 2\n2 1\n2\n2 1 3 2\n5 4 1 4",
"2\n2\n2 2\n4 1\n4\n2 2 2 2\n2 4 1 4",
"2\n2\n1 2\n3 1\n4\n1 1 1 1\n2 5 1 3",
"2\n2\n2 2\n2 1\n4\n3 1 1 1\n4 4 1 4",
"2\n2\n1 2\n4 1\n3\n2 1 4 1\n1 4 1 4",
"2\n2\n2 1\n3 1\n4\n2 1 2 1\n4 4 1 4",
"2\n1\n2 3\n2 1\n4\n2 1 4 1\n2 5 1 4",
"2\n2\n2 2\n2 1\n3\n0 1 3 1\n2 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 2 1 1\n2 10 1 3",
"2\n2\n3 2\n2 1\n4\n5 1 4 1\n4 4 1 4",
"2\n1\n2 3\n2 0\n4\n2 1 4 1\n2 4 1 1",
"2\n2\n2 1\n3 2\n4\n2 1 2 1\n4 4 2 4",
"2\n2\n3 1\n2 1\n4\n3 1 4 1\n4 4 2 4",
"2\n1\n2 2\n2 1\n1\n2 1 4 1\n4 4 1 4",
"2\n2\n2 2\n4 1\n4\n2 2 2 1\n4 4 1 4",
"2\n2\n2 2\n2 1\n3\n1 1 0 1\n1 4 1 4",
"2\n1\n2 2\n4 2\n4\n2 1 4 1\n2 4 1 4",
"2\n2\n4 4\n3 2\n3\n0 1 4 1\n1 4 1 4",
"2\n2\n2 2\n4 1\n4\n4 2 2 2\n2 4 1 4",
"2\n2\n2 2\n1 1\n4\n3 1 1 1\n4 4 1 4",
"2\n1\n2 3\n2 1\n4\n2 1 4 1\n2 10 1 4",
"2\n2\n1 2\n2 1\n4\n1 4 1 1\n2 10 1 3",
"2\n2\n3 2\n2 1\n4\n4 1 4 1\n4 4 1 4",
"2\n1\n2 2\n2 1\n1\n2 1 4 1\n4 4 1 3",
"2\n2\n2 2\n4 1\n2\n2 2 2 1\n4 4 1 4",
"2\n2\n2 2\n2 2\n3\n1 1 0 1\n1 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 4 1 1\n2 20 1 3",
"2\n2\n3 2\n2 1\n4\n4 1 4 1\n4 4 1 3",
"2\n1\n2 2\n2 1\n2\n2 1 4 1\n4 4 1 3",
"2\n2\n2 1\n4 1\n2\n2 2 2 1\n4 4 1 4",
"2\n2\n2 2\n3 2\n3\n1 1 0 1\n1 4 1 4",
"2\n1\n4 2\n2 1\n2\n2 1 4 1\n4 4 1 3",
"2\n2\n2 1\n4 1\n2\n2 2 2 1\n5 4 1 4",
"2\n2\n2 2\n3 2\n3\n1 1 0 1\n1 4 0 4",
"2\n1\n4 2\n2 0\n2\n2 1 4 1\n4 4 1 3",
"2\n2\n1 1\n4 1\n2\n2 2 2 1\n5 4 1 4",
"2\n1\n4 3\n2 0\n2\n2 1 4 1\n4 4 1 3",
"2\n1\n4 3\n2 -1\n2\n2 1 4 1\n4 4 1 3",
"2\n2\n1 2\n4 1\n4\n1 1 4 1\n2 5 1 4",
"2\n2\n2 2\n2 1\n3\n0 1 4 1\n1 8 1 4",
"2\n2\n1 2\n2 1\n4\n1 1 1 1\n5 5 1 4",
"2\n2\n2 2\n3 2\n3\n1 1 4 1\n1 4 1 4",
"2\n2\n2 2\n4 1\n4\n2 1 4 1\n1 4 1 4",
"2\n2\n2 2\n4 2\n4\n2 2 4 2\n2 4 1 4",
"2\n2\n1 2\n2 1\n4\n1 1 1 1\n4 5 1 3",
"2\n2\n2 2\n3 1\n2\n2 1 2 1\n4 4 1 4",
"2\n1\n2 3\n2 1\n4\n2 1 3 1\n2 4 1 4",
"2\n1\n1 2\n2 0\n4\n1 1 4 1\n4 5 1 4"
],
"outputs": [
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n1\n",
"1\n1\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n1\n",
"1\n1\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n1\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n1\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n1\n",
"1\n2\n",
"1\n1\n",
"1\n1\n",
"1\n1\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n2\n",
"1\n1\n",
"1\n2\n",
"1\n2\n"
]
}
|
Little Egor is a huge movie fan. He likes watching different kinds of movies: from drama movies to comedy movies, from teen movies to horror movies. He is planning to visit cinema this weekend, but he's not sure which movie he should watch.
There are n movies to watch during this weekend. Each movie can be characterized by two integers Li and Ri, denoting the length and the rating of the corresponding movie. Egor wants to watch exactly one movie with the maximal value of Li × Ri. If there are several such movies, he would pick a one with the maximal Ri among them. If there is still a tie, he would pick the one with the minimal index among them.
Your task is to help Egor to pick a movie to watch during this weekend.
Input
The first line of the input contains an integer T denoting the number of test cases.
The first line of the test case description contains an integer n.
The second line of the test case description contains n integers L1, L2, ...,Ln. The following line contains n integers R1, R2, ..., Rn.
Output
For each test case, output a single integer i denoting the index of the movie that Egor should watch during this weekend. Note that we follow 1-based indexing.
Constraints
1 ≤ T ≤ 5
1 ≤ n ≤ 100
1 ≤ Li, Ri ≤ 100
Example
Input:
2
2
1 2
2 1
4
2 1 4 1
2 4 1 4
Output:
1
2
Explanation
In the first example case, both films have the same value of L × R, but the first film has a better rating.
In the second example case, the second and the fourth movies are equally good, but the second movie has a smaller index.
|
{
"inputs": [
"6\n382253568 723152896 37802240 379425024 404894720 471526144",
"4\n5 6 8 10",
"3\n8 12 40",
"6\n382253568 723152896 37802240 379425024 590201381 471526144",
"3\n10 12 40",
"3\n16 36 16",
"4\n5 6 13 10",
"6\n382253568 723152896 32183854 379425024 590201381 471526144",
"4\n5 6 22 10",
"3\n10 12 27",
"6\n348324507 723152896 32183854 379425024 590201381 471526144",
"4\n5 6 24 10",
"3\n10 12 31",
"6\n348324507 1154626501 32183854 379425024 590201381 471526144",
"4\n10 6 24 10",
"3\n13 12 31",
"6\n586050932 1154626501 32183854 379425024 590201381 471526144",
"4\n10 6 24 15",
"3\n6 12 31",
"6\n586050932 1154626501 31409214 379425024 590201381 471526144",
"4\n10 6 7 15",
"3\n4 12 31",
"6\n586050932 1154626501 31409214 41028353 590201381 471526144",
"4\n10 6 11 15",
"3\n4 23 31",
"6\n586050932 1154626501 31409214 41028353 46444612 471526144",
"4\n10 6 11 19",
"3\n4 11 31",
"6\n586050932 1154626501 31409214 41028353 52438452 471526144",
"4\n14 6 11 19",
"3\n4 7 31",
"6\n586050932 1154626501 31409214 27068201 52438452 471526144",
"4\n14 6 15 19",
"3\n4 7 52",
"6\n586050932 1154626501 31409214 27068201 52438452 243833698",
"4\n27 6 15 19",
"3\n7 7 52",
"6\n586050932 1154626501 31409214 27068201 10685560 243833698",
"4\n27 6 15 9",
"3\n7 7 25",
"6\n586050932 1154626501 30334838 27068201 10685560 243833698",
"4\n27 6 17 9",
"3\n7 13 25",
"6\n586050932 1892549229 30334838 27068201 10685560 243833698",
"4\n12 6 17 9",
"3\n2 13 25",
"6\n586050932 1892549229 30334838 27068201 19465326 243833698",
"4\n12 6 26 9",
"3\n4 13 25",
"6\n586050932 1892549229 59907007 27068201 19465326 243833698",
"4\n12 2 26 9",
"3\n7 13 5",
"6\n586050932 1892549229 59907007 27068201 236966 243833698",
"4\n12 3 26 9",
"3\n7 13 8",
"6\n105530884 1892549229 59907007 27068201 236966 243833698",
"4\n9 6 26 9",
"3\n7 13 12",
"6\n105530884 1892549229 59907007 27068201 236966 442481745",
"4\n9 6 43 9",
"3\n7 13 22",
"6\n105530884 1892549229 59907007 27068201 236966 136055793",
"4\n9 6 43 16",
"3\n7 13 16",
"6\n105530884 1320359906 59907007 27068201 236966 136055793",
"4\n13 6 43 16",
"3\n9 13 16",
"6\n71148002 1320359906 59907007 27068201 236966 136055793",
"4\n13 6 43 24",
"3\n9 25 16",
"6\n71148002 1320359906 59907007 21985869 236966 136055793",
"4\n10 6 43 24",
"3\n9 36 16",
"6\n71148002 1320359906 59907007 21985869 236966 233525638",
"4\n10 5 43 24",
"6\n71148002 1320359906 59907007 21985869 236966 400136429",
"4\n10 5 43 30",
"3\n13 36 16",
"6\n71148002 1320359906 81412222 21985869 236966 400136429",
"4\n10 5 43 27",
"3\n1 36 16",
"6\n71148002 1055849701 81412222 21985869 236966 400136429",
"4\n10 4 43 27",
"3\n1 36 21",
"6\n71148002 1055849701 81412222 21985869 236966 734273188",
"3\n1 36 38",
"6\n71148002 1055849701 81412222 34292530 236966 734273188",
"3\n1 36 66",
"6\n71148002 1055849701 81412222 7499695 236966 734273188",
"3\n1 36 58",
"6\n71148002 1800176736 81412222 7499695 236966 734273188",
"3\n1 36 65",
"6\n71148002 1800176736 81412222 7499695 179710 734273188",
"3\n2 36 65",
"6\n71148002 1800176736 117468765 7499695 179710 734273188",
"3\n2 36 114",
"6\n71148002 1800176736 117468765 5864889 179710 734273188",
"6\n71148002 1800176736 117468765 5864889 179710 1171612875",
"6\n71148002 1800176736 117468765 5864889 174453 1171612875",
"6\n71148002 1800176736 57659801 5864889 174453 1171612875",
"6\n71148002 1800176736 26596048 5864889 174453 1171612875",
"6\n71148002 1800176736 24185535 5864889 174453 1171612875",
"6\n71148002 1800176736 24185535 5864889 179543 1171612875"
],
"outputs": [
"8",
"0",
"2",
"0\n",
"1\n",
"2\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
}
|
There are N positive integers written on a blackboard: A_1, ..., A_N.
Snuke can perform the following operation when all integers on the blackboard are even:
* Replace each integer X on the blackboard by X divided by 2.
Find the maximum possible number of operations that Snuke can perform.
Constraints
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^9
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
Output
Print the maximum possible number of operations that Snuke can perform.
Examples
Input
3
8 12 40
Output
2
Input
4
5 6 8 10
Output
0
Input
6
382253568 723152896 37802240 379425024 404894720 471526144
Output
8
|
{
"inputs": [
"2\n4\nbbcb\naada\naada\n3\nabc\nbbb\nbbb\n",
"9\n5\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbbcb\naada\naada\n5\nabc\nbbb\nbbb\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbcbb\naada\naada\n2\nabc\nbbb\nbbb\n",
"9\n5\nbcdbbcc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbbcb\naaad\naada\n5\nabc\nbbb\nbbb\n",
"2\n6\nbbcb\naada\naada\n1\nabc\nbbb\nbbb\n",
"9\n13\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n5\nbcdbbcc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\naaaedde\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\ncbcbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n2\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n5\nbcdbbcc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\nbcdabcbebbcedcddcadaabaaeacd\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nccbca\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\naaaedde\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\ncbcbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n2\nb\na\na\n1\na\na\na\n11\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n6\nccbbb\naaabc\nccbca\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\naaaedde\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n8\ncbcbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n2\nb\na\na\n1\na\na\na\n11\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n6\nbcdbbcc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\nbcdabcbebbcedcddcadaabaaeacd\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n6\nbbbcc\naaabc\nccbca\n3\nccbcccbacbbbbbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n6\nbcdbbbc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacacccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nccbca\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n3\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\ncccbdcb\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\ncbcbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n7\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n5\nbcdbbcc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nccbca\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncccbcdc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nccbca\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n6\nbcdbbcc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\nbcdabcbebbcedcddcadaabaaeacd\nddbacaaabdaeedaacbabebccebbd\n9\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncdcbccc\n3\nccbcb\ncbaaa\nccbaa\n6\nbbbcc\naaabc\nccbca\n3\nccbcccbacbbbbbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n6\nbcdbbbc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\nbcdabcbebbcedcddcadaabaaeacd\nddbacaaabdaeedaacbabebccebbd\n7\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacacccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n6\nbcdbbbc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naabbc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacacccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbbcb\naada\ndaaa\n5\nbac\nbbb\nbbb\n",
"9\n16\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n3\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\ncccbdcb\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n7\ncbcbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbcbb\naada\naada\n3\naac\nbbb\nbcb\n",
"2\n4\nbbcb\naada\naada\n1\nabc\nbbb\nbbb\n",
"2\n4\nbbcb\naada\naada\n2\nabc\nbbb\nbbb\n",
"2\n4\nbbcb\naada\naada\n1\n`bc\nbbb\nbbb\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\ncbcbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbcbb\naada\naada\n3\nabc\nbbb\nbbb\n",
"2\n4\nbcbb\naada\naada\n2\nbbc\nbbb\nbbb\n",
"9\n10\nbcdbccc\naaaedde\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\ncbcbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbbcb\naada\naada\n3\ncba\nbbb\nbbb\n",
"2\n6\nbcbb\naada\naada\n1\nabc\nbbb\nbbb\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbcbb\naada\naad`\n2\nbbc\nbbb\nbbb\n",
"2\n4\nbbcb\naada\nabda\n3\ncba\nbbb\nbbb\n",
"9\n5\nbcdbbcc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\nbcdabcbebbcedcddcadaabaaeacd\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbbcb\naada\nabda\n3\ncba\nbcb\nbbb\n",
"2\n4\nbbcb\naada\nabda\n3\ncba\nbcb\nbbc\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n6\nccbbb\naaabc\nccbca\n3\nccbcccbacbbbbbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n6\nbcdbbbc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\nbcdabcbebbcedcddcadaabaaeacd\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbbcb\nadaa\nabda\n3\ncba\nbcb\nbbc\n",
"9\n6\nbcdbbbc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\nbcdabcbebbcedcddcadaabaaeacd\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacacccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n6\nbcdbbbc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacccc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacacccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbcbb\naada\nadaa\n3\nabc\nbbb\nbbb\n",
"2\n4\nbbcb\naada\naada\n5\nbac\nbbb\nbbb\n",
"2\n4\nbcbb\naada\naada\n2\nacc\nbbb\nbbb\n",
"2\n4\nbcbb\naada\naada\n3\naac\nbbb\nbbb\n",
"2\n4\nbcbb\naaad\naada\n5\nabc\nbbb\nbbb\n",
"2\n6\nbbcb\naada\naada\n1\nabd\nbbb\nbbb\n",
"2\n4\nbbcb\naada\naada\n3\ncba\nbba\nbbb\n",
"2\n4\nacbb\naada\naad`\n2\nbbc\nbbb\nbbb\n",
"9\n10\nbcdbccc\naaaedde\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\ncbcbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbacbacbcccb\n2\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbbcb\naada\nabda\n3\ndba\nbbb\nbbb\n",
"2\n4\nbbcb\naada\nabda\n3\ncba\nbcc\nbbc\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n6\nccbbb\naaabc\nccbca\n3\nccbcccbacbbbbbcccb\nbbabcccbacaaccbaac\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"9\n6\nbcdbbbc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\nbcdabcbebbcedcddcadaabaaeacd\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccadcc\ncdcbccc\n3\nccacb\ncbaaa\ncbbaa\n4\nccbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccb`caaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbbbc\nadaa\nabda\n3\ncba\nbcb\nbbc\n",
"2\n4\nbcbb\naada\naaad\n3\nabc\nbbb\nbbb\n",
"9\n10\nbcdbccc\nad`edae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabacecbe\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\naaabc\nccbca\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n1\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nbcbb\naada\naada\n2\ncac\nbbb\nbbb\n",
"2\n4\nbcbb\naaad\naada\n3\nabc\nbbb\nbbb\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedbb\ncccacdc\ncdcbccc\n3\nccacb\ncbaaa\nccbaa\n7\ncbbbb\naaabc\nacbcc\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n",
"2\n4\nacbb\naada\naad`\n3\nbbc\nbbb\nbbb\n",
"2\n4\nbbcb\nadaa\nabda\n3\ndba\nbbb\nbbb\n",
"9\n10\nbcdbccc\nadaedae\neecdaca\n5\ndbeedcbcbaccdddbdcbcabbcecae\ndcaeaabaadacddcdecbbebcbadcb\nddbacaaabdaeedaacbabebccebbd\n5\nbdbedab\ncccacdc\ncccbcdc\n3\nccacb\ncbaaa\nccbaa\n4\nccbbb\nabaac\nccbca\n3\nccbcccbacbbabbcccb\nbbabcccbacaaccbaab\nbcccabcbabbacbcccb\n26\nb\na\na\n2\na\na\na\n7\nfffbaegccd\naaagebfccd\naaagebfccd\n"
],
"outputs": [
"YES\nbadc\nNO\n",
"YES\nabcde\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nbadc\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"NO\nNO\n",
"YES\nabcde\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\ncabd\nNO\n",
"YES\nbadcef\nNO\n",
"YES\nabcdefghijklm\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcde\nYES\nacedb\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nba\nYES\na\nYES\negcdbaf\n",
"YES\nabcde\nYES\nabdce\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\nacbd\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nba\nYES\na\nYES\negcdbafhijk\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\nacbdef\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbadefgh\nYES\nacb\nYES\nba\nYES\na\nYES\negcdbafhijk\n",
"YES\nabcdef\nYES\nabdce\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\nabcdef\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcdef\nYES\nacedb\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\nacbd\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncba\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nacbdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbadefg\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcde\nYES\nacedb\nYES\nbceda\nNO\nYES\nacbd\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nNO\nYES\nabc\nYES\nacbd\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcdef\nYES\nabdce\nYES\nbcedafghi\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nbac\nYES\nabcdef\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcdef\nYES\nabdce\nYES\nbcedafg\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdef\nYES\nacedb\nYES\nbceda\nNO\nYES\nbcad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcd\nNO\n",
"YES\nabcdefghijklmnop\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncba\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nacbdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbadefg\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"NO\nYES\nbac\n",
"YES\nbadc\nNO\n",
"YES\nbadc\nNO\n",
"YES\nbadc\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nbadc\nNO\n",
"NO\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"NO\nNO\n",
"YES\nbadc\nNO\n",
"YES\nabcde\nYES\nabdce\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nbadc\nNO\n",
"YES\nbadc\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\nacbdef\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcdef\nYES\nabdce\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"NO\nNO\n",
"YES\nabcdef\nYES\nabdce\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\nabcdef\nYES\nacedb\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"YES\ncabd\nNO\n",
"YES\nbadc\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nbadcef\nNO\n",
"YES\nbadc\nNO\n",
"NO\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbad\nYES\nacb\nYES\nba\nYES\na\nYES\negcdbaf\n",
"YES\nbadc\nNO\n",
"YES\nbadc\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\nacbdef\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"YES\nabcdef\nYES\nabdce\nYES\nbceda\nNO\nYES\ncbad\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\nacbd\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\na\nYES\negcdbaf\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nYES\nbceda\nYES\nabc\nYES\ncbadefg\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n",
"NO\nNO\n",
"NO\nNO\n",
"YES\nabcdefghij\nYES\nacedb\nNO\nYES\nabc\nYES\nacbd\nYES\nacb\nYES\nbacdefghijklmnopqrstuvwxyz\nYES\nab\nYES\negcdbaf\n"
]
}
|
Vasya owns three strings s , a and b, each of them consists only of first k Latin letters.
Let a template be such a string of length k that each of the first k Latin letters appears in it exactly once (thus there are k! distinct templates). Application of template p to the string s is the replacement of each character in string s with p_i, i is the index of this letter in the alphabet. For example, applying template "bdca" to a string "aabccd" yields string "bbdcca".
Vasya wants to know if there exists such a template which yields a string lexicographically greater than or equal to string a and lexicographically less than or equal to string b after applying it to s.
If there exist multiple suitable templates, print any of them.
String a is lexicographically less than string b if there is some i (1 ≤ i ≤ n) that a_i < b_i and for any j (1 ≤ j < i) a_j = b_j.
You are required to answer t testcases independently.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^6) — the number of testcases.
In hacks you can only use t = 1.
Each of the next t lines contains the description of the testcase in the following form:
The first line of the testcase contains a single integer k (1 ≤ k ≤ 26) — the length of the template.
The second line of the testcase contains the string s (1 ≤ |s| ≤ 10^6).
The third line of the testcase contains the string a.
The fourth line of the testcase contains the string b.
Strings s, a and b have the same length (|s| = |a| = |b|) and consist only of the first k Latin letters, all letters are lowercase.
It is guaranteed that string a is lexicographically less than or equal to string b.
It is also guaranteed that the total length of strings over all testcase won't exceed 3 ⋅ 10^6.
Output
Print the answers to all testcases in the following form:
If there exists no suitable template then print "NO" in the first line.
Otherwise print "YES" in the first line and the template itself in the second line (k lowercase letters, each of the first k Latin letters should appear exactly once).
If there exist multiple suitable templates, print any of them.
Example
Input
2
4
bbcb
aada
aada
3
abc
bbb
bbb
Output
YES
badc
NO
|
{
"inputs": [
"2\n1\n2\n\nSAMPLE",
"2\n2\n2\n\nSAMPLE",
"2\n4\n2\n\nSAMPLE",
"2\n4\n1\n\nSALPLE",
"2\n7\n1\n\nSALPLE",
"2\n6\n1\n\nSALPLE",
"2\n5\n1\n\nTALPLE",
"2\n10\n1\n\nTALLPD",
"2\n3\n1\n\nTALLPD",
"2\n1\n2\n\nSAMPKE",
"2\n6\n2\n\nSAMPLE",
"2\n13\n1\n\nSALPLE",
"2\n1\n1\n\nTALPLE",
"2\n10\n2\n\nTALLPD",
"2\n2\n3\n\nSALPLE",
"2\n2\n1\n\nTALPLE",
"2\n3\n2\n\nTALLPD",
"2\n1\n4\n\nSAMPKD",
"2\n5\n2\n\nEPMLAT",
"2\n1\n6\n\nSAMPKD",
"2\n8\n2\n\nRAMPLE",
"2\n15\n2\n\nTALLPD",
"2\n15\n4\n\nTALLPD",
"2\n15\n6\n\nTALLPD",
"2\n11\n2\n\nSAMQLD",
"2\n5\n4\n\nDPLLAT",
"2\n11\n3\n\nSMAQLD",
"2\n3\n3\n\nAPSKEL",
"2\n11\n1\n\nSOAQLD",
"2\n4\n3\n\nAPLKES",
"2\n1\n3\n\nSAMPLE",
"2\n10\n3\n\nTALLPD",
"2\n20\n2\n\nRAMPLE",
"2\n2\n6\n\nSAMPKD",
"2\n29\n2\n\nTALLPD",
"2\n16\n2\n\nRAMPLD",
"2\n6\n4\n\nTALLPD",
"2\n15\n12\n\nTALLPD",
"2\n8\n4\n\nSAMQLD",
"2\n15\n11\n\nDPLLAT",
"2\n16\n4\n\nDPLLAT",
"2\n11\n4\n\nSMAQLD",
"2\n11\n5\n\nSNAQLD",
"2\n1\n5\n\nSAMPLE",
"2\n6\n3\n\nSALPLE",
"2\n7\n2\n\nTLALPD",
"2\n13\n3\n\nTALLPD",
"2\n49\n2\n\nTALLPD",
"2\n9\n2\n\nRAMPLD",
"2\n3\n4\n\nTALLPD",
"2\n15\n14\n\nTALLPD",
"2\n15\n19\n\nDPLLAT",
"2\n10\n4\n\nSMAQLD",
"2\n5\n3\n\nDPLTAL",
"2\n20\n5\n\nSNAQLD",
"2\n2\n4\n\nAPLEKS",
"2\n13\n4\n\nTALLPD",
"2\n27\n2\n\nRANPLE",
"2\n3\n8\n\nTALLPD",
"2\n25\n14\n\nTALLPD",
"2\n7\n19\n\nDPLLAT",
"2\n18\n2\n\nDLQMAS",
"2\n20\n8\n\nSNAQLD",
"2\n7\n3\n\nDPLALT",
"2\n7\n4\n\nEOMLAT",
"2\n49\n3\n\nSALLPD",
"2\n50\n14\n\nTALLPD",
"2\n3\n6\n\nAPLEKS",
"2\n8\n1\n\nLTAPLE",
"2\n5\n7\n\nDPLLAS",
"2\n49\n1\n\nSALLPD",
"2\n7\n18\n\nTALLPD",
"2\n20\n6\n\nRNAQLD",
"2\n5\n14\n\nDPLLAS",
"2\n19\n4\n\nTALMOD",
"2\n4\n6\n\nSALPEJ",
"2\n50\n10\n\nTAKLPD",
"2\n7\n16\n\nTALLPD",
"2\n13\n2\n\nDRQAOK",
"2\n3\n12\n\nSKELPA",
"2\n10\n14\n\nDPLLAS",
"2\n7\n8\n\nCOMLAT",
"2\n2\n5\n\nTELOKA",
"2\n27\n10\n\nTAKLPD",
"2\n31\n2\n\nDAQMKS",
"2\n20\n7\n\nRNAQKD",
"2\n4\n9\n\nSPLAEJ",
"2\n4\n4\n\nSMAQLD",
"2\n20\n10\n\nRNAQKD",
"2\n24\n2\n\nROASMD",
"2\n6\n14\n\nDPKLAS",
"2\n2\n8\n\nTEMOKA",
"2\n31\n3\n\nD@QMKS",
"2\n20\n4\n\nRNAQKD",
"2\n4\n12\n\nTEKLPA",
"2\n14\n2\n\nDLAMPS",
"2\n26\n10\n\nCPLKAT",
"2\n47\n3\n\nD@QMKS",
"2\n4\n5\n\nBPSLEK",
"2\n6\n13\n\nDOKLAS",
"2\n2\n9\n\nTAMOKE"
],
"outputs": [
"1.000000\n4.000000",
"4.000000\n4.000000\n",
"10.500000\n4.000000\n",
"10.500000\n1.000000\n",
"20.428571\n1.000000\n",
"17.111111\n1.000000\n",
"13.800000\n1.000000\n",
"30.400000\n1.000000\n",
"7.222222\n1.000000\n",
"1.000000\n4.000000\n",
"17.111111\n4.000000\n",
"40.384615\n1.000000\n",
"1.000000\n1.000000\n",
"30.400000\n4.000000\n",
"4.000000\n7.222222\n",
"4.000000\n1.000000\n",
"7.222222\n4.000000\n",
"1.000000\n10.500000\n",
"13.800000\n4.000000\n",
"1.000000\n17.111111\n",
"23.750000\n4.000000\n",
"47.044444\n4.000000\n",
"47.044444\n10.500000\n",
"47.044444\n17.111111\n",
"33.727273\n4.000000\n",
"13.800000\n10.500000\n",
"33.727273\n7.222222\n",
"7.222222\n7.222222\n",
"33.727273\n1.000000\n",
"10.500000\n7.222222\n",
"1.000000\n7.222222\n",
"30.400000\n7.222222\n",
"63.700000\n4.000000\n",
"4.000000\n17.111111\n",
"93.689655\n4.000000\n",
"50.375000\n4.000000\n",
"17.111111\n10.500000\n",
"47.044444\n37.055556\n",
"23.750000\n10.500000\n",
"47.044444\n33.727273\n",
"50.375000\n10.500000\n",
"33.727273\n10.500000\n",
"33.727273\n13.800000\n",
"1.000000\n13.800000\n",
"17.111111\n7.222222\n",
"20.428571\n4.000000\n",
"40.384615\n7.222222\n",
"160.346939\n4.000000\n",
"27.074074\n4.000000\n",
"7.222222\n10.500000\n",
"47.044444\n43.714286\n",
"47.044444\n60.368421\n",
"30.400000\n10.500000\n",
"13.800000\n7.222222\n",
"63.700000\n13.800000\n",
"4.000000\n10.500000\n",
"40.384615\n10.500000\n",
"87.024691\n4.000000\n",
"7.222222\n23.750000\n",
"80.360000\n43.714286\n",
"20.428571\n60.368421\n",
"57.037037\n4.000000\n",
"63.700000\n23.750000\n",
"20.428571\n7.222222\n",
"20.428571\n10.500000\n",
"160.346939\n7.222222\n",
"163.680000\n43.714286\n",
"7.222222\n17.111111\n",
"23.750000\n1.000000\n",
"13.800000\n20.428571\n",
"160.346939\n1.000000\n",
"20.428571\n57.037037\n",
"63.700000\n17.111111\n",
"13.800000\n43.714286\n",
"60.368421\n10.500000\n",
"10.500000\n17.111111\n",
"163.680000\n30.400000\n",
"20.428571\n50.375000\n",
"40.384615\n4.000000\n",
"7.222222\n37.055556\n",
"30.400000\n43.714286\n",
"20.428571\n23.750000\n",
"4.000000\n13.800000\n",
"87.024691\n30.400000\n",
"100.354839\n4.000000\n",
"63.700000\n20.428571\n",
"10.500000\n27.074074\n",
"10.500000\n10.500000\n",
"63.700000\n30.400000\n",
"77.027778\n4.000000\n",
"17.111111\n43.714286\n",
"4.000000\n23.750000\n",
"100.354839\n7.222222\n",
"63.700000\n10.500000\n",
"10.500000\n37.055556\n",
"43.714286\n4.000000\n",
"83.692308\n30.400000\n",
"153.680851\n7.222222\n",
"10.500000\n13.800000\n",
"17.111111\n40.384615\n",
"4.000000\n27.074074\n"
]
}
|
Daenerys Targaryen has set her eyes on The kingdom of Dorne. Dornishmen, known for their strong sense of national identity, have refused to surrender to the whims of Daenerys. Fearing the imminent attack on their kingdom and knowing their strength as Spearmen, they have devised a battle plan which they think will give them an upperhand. They have divided the battlefield as an N*N chessboard grid and have put one soldier on each of the square in the grid.
On seeing this master plan Danerys has decided to send in her dragon Drogon first. Drogon is supposed to first kill one soldier on one of the square on the chessboard grid and land on it. Then, using fire, it will kill all soldiers in horizontal, vertical and diagonal squares from end to end relative to the square it is standing on (just like a 'Queen' piece but unlike Queen, it will kill all men in one go in all the squares a Queen can cover if standing on the particular square) and then will return back. Daenerys is very happy with the strategy but she has a small problem. Drogon, being a dragon, can not be tamed and hence will uniformly at random choose any square for its landing. Daenerys, given N, wants to know what is the expected number of soldiers Drogon will kill.
Can you help Daenerys to calculate the expected number if soldiers Drogon will kill.
Input
The first line contains T, the number of test cases.
Each test case contains only one integer N denoting the dimension of the N*N chessboard grid.
Output
The output should contain 1 real number per test case denoting the expected number of soldiers Drogon will kill for the given sized grid.
Constraints
1 ≤ T ≤ 10^6
1 ≤ N ≤ 10^5
Note
Output value should be within 1e-6 of the correct value(Output should be printed to exactly six places of decimal precision).
Partial marks are awarded if any test case passes.
SAMPLE INPUT
2
1
2
SAMPLE OUTPUT
1.000000
4.000000
Explanation
In first test case, grid is 1*1, and hence Drogon will kill the only soldier present on the single square.
In second test case, grid is 2*2. Whichever be the square Drogon lands by killing the soldier, it can kill all other soldiers (as they are covered by its 'Queen like' fire attack).
|
{
"inputs": [
"8\nfced\nxyz\nr\ndabcef\naz\naa\nbad\nbabc\n",
"1\nshh\n",
"1\nsoo\n",
"1\naaaab\n",
"1\nabcdefghijkm\n",
"1\nabczz\n",
"1\naadde\n",
"1\ndaa\n",
"1\nefhi\n",
"2\nrtsuvwyz\nzyxwvutsrqponmlkjihgfedcbaaa\n",
"1\nabbdf\n",
"69\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\n",
"1\nsooo\n",
"1\nshhhh\n",
"1\nshohrukh\n",
"1\nshohr\n",
"1\nbcef\n",
"1\nabcef\n",
"1\nsdfalusdbfja\n",
"1\nabde\n",
"44\nops\ntest\nyes\nno\nac\nbc\ncb\nz\na\nq\nr\nu\nqq\nop\npo\nxu\nux\nxy\nyx\na\nab\nabc\nabcd\nabcde\nabcdef\nabcdefg\nbcdefg\ncdefg\ndefg\nefgd\nefef\nabacaba\nabz\naoi\nioi\ncodeforces\nklmn\nnmlk\nkln\nklmnl\nkmn\nkklmn\nklmnn\naklkmn\n",
"1\nabcxyz\n",
"1\nshhh\n",
"1\nsho\n",
"1\nshohruk\n",
"2\nabcdefghijklmnopqrstuvwxyz\nzyxwvutsrqponmlkjihgfedcba\n",
"1\nshohru\n",
"1\nshoh\n",
"1\nf\n",
"1\nhsh\n",
"2\nrtsuwwyz\nzyxwvutsrqponmlkjihgfedcbaaa\n",
"69\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nbbc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\n",
"44\nops\ntest\nyes\nno\nac\nbc\ncb\nz\na\nq\nr\nu\nqq\nop\npo\nxu\nux\nxy\nyx\na\nab\nabc\ndcba\nabcde\nabcdef\nabcdefg\nbcdefg\ncdefg\ndefg\nefgd\nefef\nabacaba\nabz\naoi\nioi\ncodeforces\nklmn\nnmlk\nkln\nklmnl\nkmn\nkklmn\nklmnn\naklkmn\n",
"2\nabcdefghijklmnopqrstuvwxyz\nzyxwvutsrqponmljjihgfedcba\n",
"1\ne\n",
"8\nfced\nxyz\nr\ndabcef\naz\naa\naad\nbabc\n",
"44\nops\ntest\nyes\non\nac\nbc\ncb\nz\na\nq\nr\nu\nqq\nop\npo\nxu\nux\nxy\nyx\na\nab\nabc\ndcba\nabcde\nabcdef\nabcdefg\nbcdefg\ncdefg\ndefg\nefgd\nefef\nabacaba\nabz\naoi\nioi\ncodeforces\nklmn\nnmlk\nklm\nklmnl\nkmn\nkklmn\nklmnn\naklkmn\n",
"1\nspo\n",
"1\naaaaa\n",
"1\nmkjihgfedcba\n",
"1\nabbzz\n",
"1\neddaa\n",
"1\neihf\n",
"1\naabdf\n",
"1\nooso\n",
"1\nsihhh\n",
"1\nhkurhohs\n",
"1\nshoir\n",
"1\nbcfe\n",
"1\nabcee\n",
"1\nsdfalusdcfja\n",
"1\nadbe\n",
"1\nacbxyz\n",
"1\nhshh\n",
"1\nohs\n",
"1\nshohruj\n",
"1\nshohrt\n",
"1\nshoi\n",
"1\nsih\n",
"1\noos\n",
"1\nebcdafghijkm\n",
"1\nabzcz\n",
"1\nfddaa\n",
"1\nehhf\n",
"2\nzywwustr\nzyxwvutsrqponmlkjihgfedcbaaa\n",
"1\nfdbaa\n",
"69\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nacb\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nbbc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\n",
"1\nosoo\n",
"1\nhhhis\n",
"1\nhkuriohs\n",
"1\nohsir\n",
"1\nccfe\n",
"1\nabcfe\n",
"1\nsdfakusdcfja\n",
"1\nebda\n",
"44\nops\ntest\nyes\non\nac\nbc\ncb\nz\na\nq\nr\nu\nqq\nop\npo\nxu\nux\nxy\nyx\na\nab\nabc\ndcba\nabcde\nabcdef\nabcdefg\nbcdefg\ncdefg\ndefg\nefgd\nefef\nabacaba\nabz\naoi\nioi\ncodeforces\nklmn\nnmlk\nkln\nklmnl\nkmn\nkklmn\nklmnn\naklkmn\n",
"1\nzcbxya\n",
"1\nhhsh\n",
"1\nshn\n",
"1\njurhohs\n",
"2\nzyxwvutsrqponmlkjihgfedcba\nzyxwvutsrqponmljjihgfedcba\n",
"1\nsohhrt\n",
"1\nshpi\n",
"1\nd\n",
"8\ndecf\nxyz\nr\ndabcef\naz\naa\naad\nbabc\n",
"1\ntih\n",
"1\nons\n",
"1\nebcdaeghijkm\n",
"1\nbbzcz\n",
"1\naaddf\n",
"1\nfhhe\n",
"2\nzywwustr\nzyxvvutsrqponmlkjihgfedcbaaa\n",
"1\nfebaa\n",
"69\nabc\nabc\nabc\nabc\nabc\ncba\nabc\nabc\nabc\nacb\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nbbc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\n",
"1\noson\n",
"1\nhhiis\n",
"1\nhkuriosh\n",
"1\nohrir\n",
"1\nccfd\n",
"1\naecfb\n",
"1\najfcdsukafds\n",
"1\nadce\n",
"1\nzcbyxa\n",
"1\nhrhh\n",
"1\nsin\n",
"1\njurgohs\n",
"2\nzyxwvutsrqponmlkjihgfedcba\nzyxwvutsrqponmljjiigfedcba\n",
"1\nsorhht\n",
"1\nsphi\n",
"1\ng\n",
"8\ndecf\nxyz\nr\ndabcef\naz\naa\nada\nbabc\n",
"1\nuih\n",
"1\nonr\n",
"1\nebcdaefhijkm\n",
"1\nzczbb\n",
"1\naacdf\n",
"1\nhfhe\n",
"2\nzywwustr\nzyxvvutsrqponmlkjihgfedcbaab\n",
"1\nfebba\n",
"69\nabc\nabc\nabc\nabc\nabc\ncba\nabc\nabc\nabc\nacb\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\ncba\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nbbc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\nabc\n",
"1\nnoso\n",
"1\nsiihh\n",
"1\nhkurjosh\n",
"1\nphrir\n",
"1\ncbfd\n"
],
"outputs": [
"YES\nYES\nYES\nYES\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\nNO\n",
"NO\n",
"YES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\nYES\nNO\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nNO\nYES\nYES\nNO\nNO\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nYES\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\nYES\n",
"NO\n",
"NO\n",
"YES\n",
"No\n",
"No\nNo\n",
"Yes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\n",
"No\nNo\nNo\nYes\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nNo\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nNo\nNo\nNo\nNo\nNo\nYes\nYes\nNo\nNo\nNo\nNo\nNo\nNo\n",
"Yes\nNo\n",
"Yes\n",
"Yes\nYes\nYes\nYes\nNo\nNo\nNo\nNo\n",
"No\nNo\nNo\nYes\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nNo\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nNo\nNo\nNo\nNo\nNo\nYes\nYes\nYes\nNo\nNo\nNo\nNo\nNo\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\nNo\n",
"No\n",
"Yes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\nNo\nNo\nYes\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nNo\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nNo\nNo\nNo\nNo\nNo\nYes\nYes\nNo\nNo\nNo\nNo\nNo\nNo\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\nNo\n",
"No\n",
"No\n",
"Yes\n",
"Yes\nYes\nYes\nYes\nNo\nNo\nNo\nNo\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\nNo\n",
"No\n",
"Yes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\nNo\n",
"No\n",
"No\n",
"Yes\n",
"Yes\nYes\nYes\nYes\nNo\nNo\nNo\nNo\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\nNo\n",
"No\n",
"Yes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nNo\nYes\nYes\nYes\nYes\nYes\nYes\nYes\nYes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
}
|
A string is called diverse if it contains consecutive (adjacent) letters of the Latin alphabet and each letter occurs exactly once. For example, the following strings are diverse: "fced", "xyz", "r" and "dabcef". The following string are not diverse: "az", "aa", "bad" and "babc". Note that the letters 'a' and 'z' are not adjacent.
Formally, consider positions of all letters in the string in the alphabet. These positions should form contiguous segment, i.e. they should come one by one without any gaps. And all letters in the string should be distinct (duplicates are not allowed).
You are given a sequence of strings. For each string, if it is diverse, print "Yes". Otherwise, print "No".
Input
The first line contains integer n (1 ≤ n ≤ 100), denoting the number of strings to process. The following n lines contains strings, one string per line. Each string contains only lowercase Latin letters, its length is between 1 and 100, inclusive.
Output
Print n lines, one line per a string in the input. The line should contain "Yes" if the corresponding string is diverse and "No" if the corresponding string is not diverse. You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.
Example
Input
8
fced
xyz
r
dabcef
az
aa
bad
babc
Output
Yes
Yes
Yes
Yes
No
No
No
No
|
{
"inputs": [
"2 4\n5000\n",
"2 2\n7\n",
"3 1\n9\n",
"3 3\n9\n",
"8934829 12\n5048272609027744689584230909741172415239400471666476392160572093949157832786399486962245730213411626\n",
"5893919 9\n2210309498556502639082865806054288036968702568515503990010345752069086486014544763616785766171083029\n",
"3286427 3\n32824120217168867503177075773101487258651027053054498182388625841560564426484376370000468826643786\n",
"8030623 1\n7391946705\n",
"4540993 10\n5694761289449694169154104450970948644405389630203784854430413891269455104899781759279256470945063996\n",
"6243073 4\n54400052247879189148039137626578952762968555544521623972286314204888279306920422704563468161626006\n",
"999999937 1\n3501092449\n",
"9293491 7\n48319797892187743808453690342431892528370716043453177493057646722749549949137439033049576518430270\n",
"5 12\n1594355\n",
"1221971 1\n79131359\n",
"4679 2\n96533885\n",
"875509 1\n9748849576\n",
"3677111 1\n3947614679\n",
"100003 2\n97389782\n",
"100003 17\n11308756195429026209159218281779131898260926255198579096122089230609019579878999794185954258912170\n",
"7040413 1\n78640343\n",
"9709009 1\n2634859963\n",
"1672457 15\n3847806708076502739500476173585865162224673529150721814545285545371388410787530016329736665854635480\n",
"999999929 10\n252415489202912310205276639219302507423145151212606944393620004151279088543717368355582320756277628\n",
"8428969 1\n51642713\n",
"59 3\n1278\n",
"70979 1\n56655195\n",
"13 2\n825\n",
"999999937 11\n5288940788755459409564349320259509293731609366571637200283425133566419952358519527220164588187924778\n",
"79 2\n484521\n",
"17 1\n935747\n",
"4884179 10\n75275670396386658491762589457701754821709330221849314456866064056828965964277393680113615925466793\n",
"3 1\n8\n",
"5 102\n6488994830394029396353515227107480047703257955061407081771245058930506496128212235396729161430031\n",
"2 203\n1364314877317006994721955753062669519721387443256362764663300316014405415427100793395824989466006051\n",
"3 1\n67\n",
"251 3\n34106727\n",
"17 1\n3343\n",
"2 23\n2825666196\n",
"2 43\n91294524189682126912108591094343060560279041112882482536264020611963632671143642291897074749724140970161480778960471179126432402190291911033525586159516887280471798432987512205195031180182769198893571\n",
"6648143 1\n5875544750\n",
"1994623 4\n16382948906033764999878837315878029135617293130932808617919331691967251084555542282238971884256579\n",
"999999929 1\n708929754\n",
"4055801 1\n57128202\n",
"7542851 4\n6595054484074093529836320042218879209936747749396675376618286577189222598359156018487897406667640759\n",
"11688134 12\n5048272609027744689584230909741172415239400471666476392160572093949157832786399486962245730213411626\n",
"3440726 9\n2210309498556502639082865806054288036968702568515503990010345752069086486014544763616785766171083029\n",
"3831934 3\n32824120217168867503177075773101487258651027053054498182388625841560564426484376370000468826643786\n",
"8030623 1\n8641516670\n",
"1567869 10\n5694761289449694169154104450970948644405389630203784854430413891269455104899781759279256470945063996\n",
"6243073 6\n54400052247879189148039137626578952762968555544521623972286314204888279306920422704563468161626006\n",
"9293491 8\n48319797892187743808453690342431892528370716043453177493057646722749549949137439033049576518430270\n",
"5 12\n2991314\n",
"855628 1\n79131359\n",
"583 2\n96533885\n",
"6402911 1\n3947614679\n",
"100003 17\n18580071218961098658682262015650325911220697425344681590168959402198553990540614601964111273756422\n",
"12954805 1\n78640343\n",
"9709009 1\n903531837\n",
"1672457 15\n5958415233296762517097732670319609267323863986226998946636925694140536101060933017382507439682509511\n",
"103178557 10\n252415489202912310205276639219302507423145151212606944393620004151279088543717368355582320756277628\n",
"8428969 1\n77661059\n",
"10242 1\n56655195\n",
"13 2\n365\n",
"999999937 11\n9476257952581648606597104632834909899595744501945054213430990425427555479576135994656336999419433820\n",
"79 1\n484521\n",
"32 1\n935747\n",
"4884179 10\n124403885599420044779667233782301618593119670117126307540854312724754791649167467904415003237954582\n",
"6 1\n8\n",
"5 102\n11703928027112134594581066347972062326013914147812539339312918742411613311500348710569435704987054\n",
"2 203\n1890196107535787728914374370909670948941288315085510828543375564895246171473807483059502848253901452\n",
"3 1\n5\n",
"251 3\n53466194\n",
"21 1\n3343\n",
"2 16\n2825666196\n",
"2 65\n91294524189682126912108591094343060560279041112882482536264020611963632671143642291897074749724140970161480778960471179126432402190291911033525586159516887280471798432987512205195031180182769198893571\n",
"1417758 1\n5875544750\n",
"1994623 3\n16382948906033764999878837315878029135617293130932808617919331691967251084555542282238971884256579\n",
"4532209 1\n57128202\n",
"9205270 4\n6595054484074093529836320042218879209936747749396675376618286577189222598359156018487897406667640759\n",
"3 2\n9\n",
"3440726 1\n2210309498556502639082865806054288036968702568515503990010345752069086486014544763616785766171083029\n",
"3831934 3\n57690633707740095176684068190474999389173485004028841837162446914081704817638420683472143331885658\n",
"12900831 1\n8641516670\n",
"1567869 6\n5694761289449694169154104450970948644405389630203784854430413891269455104899781759279256470945063996\n",
"6243073 6\n62762765848818004189318063446990052339305527337962970124461689613425993370292463874558846896873831\n",
"9293491 8\n1873158102251266770800319767878680990194564308353105302945484994732473080446823127097851823203625\n",
"583 2\n41823387\n",
"875509 1\n496738728\n",
"875509 2\n9748849576\n",
"100003 3\n97389782\n",
"32 3\n1278\n",
"999999929 2\n708929754\n",
"11688134 16\n5048272609027744689584230909741172415239400471666476392160572093949157832786399486962245730213411626\n",
"5 12\n5490680\n",
"855628 2\n79131359\n"
],
"outputs": [
"8576851\n",
"3\n",
"17\n",
"0\n",
"203584930\n",
"509168733\n",
"218416035\n",
"16151750\n",
"194137151\n",
"872781381\n",
"365423796\n",
"199732363\n",
"0\n",
"344669306\n",
"31957885\n",
"206824394\n",
"731336001\n",
"0\n",
"92344311\n",
"299757593\n",
"497869486\n",
"732273771\n",
"410991035\n",
"25668431\n",
"0\n",
"873157860\n",
"70548\n",
"734024483\n",
"136267727\n",
"349474793\n",
"549377788\n",
"9\n",
"689966800\n",
"200605144\n",
"1518\n",
"243909930\n",
"3955866\n",
"684631706\n",
"466618476\n",
"907664841\n",
"802566567\n",
"0\n",
"694460592\n",
"278827366\n",
"894680531",
"253220384",
"511313967",
"989115484",
"484521208",
"882984504",
"583519259",
"0",
"993849269",
"177063922",
"535228594",
"687615289",
"528657220",
"313706651",
"365590364",
"635283441",
"683891697",
"89563323",
"11504",
"481801280",
"79529734",
"716409718",
"201143986",
"12",
"249742690",
"504199689",
"3",
"876114251",
"3953028",
"656065714",
"665329085",
"113756665",
"678383980",
"4576296",
"474082244",
"6",
"424750631",
"766563843",
"964582524",
"652140553",
"329440945",
"802965426",
"541110776",
"958908017",
"0",
"0",
"0",
"0",
"0",
"0",
"0"
]
}
|
For a given prime integer p and integers α, A calculate the number of pairs of integers (n, k), such that 0 ≤ k ≤ n ≤ A and <image> is divisible by pα.
As the answer can be rather large, print the remainder of the answer moduly 109 + 7.
Let us remind you that <image> is the number of ways k objects can be chosen from the set of n objects.
Input
The first line contains two integers, p and α (1 ≤ p, α ≤ 109, p is prime).
The second line contains the decimal record of integer A (0 ≤ A < 101000) without leading zeroes.
Output
In the single line print the answer to the problem.
Examples
Input
2 2
7
Output
3
Input
3 1
9
Output
17
Input
3 3
9
Output
0
Input
2 4
5000
Output
8576851
Note
In the first sample three binominal coefficients divisible by 4 are <image>, <image> and <image>.
|
{
"inputs": [
"1 3\n0 3",
"5 21600\n2 14\n3 22\n1 3\n1 10\n1 9",
"3 7\n2 0\n3 2\n0 3",
"7 57\n0 25\n3 10\n2 4\n5 15\n3 22\n2 14\n1 15",
"1 3\n0 0",
"5 21600\n2 14\n3 22\n1 3\n0 10\n1 9",
"7 57\n0 25\n3 10\n2 4\n5 15\n3 22\n2 14\n1 9",
"1 0\n1 -1",
"7 149\n0 25\n3 10\n2 4\n2 20\n3 22\n2 23\n1 2",
"7 28\n0 25\n3 10\n2 4\n5 20\n3 22\n2 14\n1 9",
"7 149\n0 25\n3 10\n0 4\n0 8\n3 23\n1 23\n1 2",
"7 446\n0 25\n3 0\n4 -1\n5 0\n0 22\n0 14\n1 6",
"3 5\n2 0\n3 2\n0 3",
"1 3\n0 -1",
"5 21600\n2 14\n3 22\n1 3\n0 10\n1 3",
"3 5\n2 0\n3 2\n1 3",
"7 57\n0 25\n3 10\n3 4\n5 15\n3 22\n2 14\n1 9",
"1 3\n1 -1",
"5 21600\n2 14\n3 22\n1 3\n0 10\n1 2",
"7 57\n0 25\n3 10\n3 4\n5 20\n3 22\n2 14\n1 9",
"1 5\n1 -1",
"5 21600\n2 14\n3 22\n1 1\n0 10\n1 2",
"7 57\n0 25\n3 10\n2 4\n5 20\n3 22\n2 14\n1 9",
"5 21600\n4 14\n3 22\n1 1\n0 10\n1 2",
"7 57\n0 25\n3 10\n2 4\n5 20\n3 22\n2 23\n1 9",
"1 0\n1 0",
"5 21600\n4 14\n3 22\n1 0\n0 10\n1 2",
"7 85\n0 25\n3 10\n2 4\n5 20\n3 22\n2 23\n1 9",
"1 0\n1 1",
"7 85\n0 25\n3 10\n2 4\n5 20\n3 22\n2 23\n1 18",
"0 0\n1 1",
"7 99\n0 25\n3 10\n2 4\n5 20\n3 22\n2 23\n1 18",
"0 1\n1 1",
"7 99\n0 25\n3 10\n2 4\n2 20\n3 22\n2 23\n1 18",
"0 1\n2 1",
"7 99\n0 25\n3 10\n2 4\n2 20\n3 22\n2 23\n1 2",
"0 1\n4 1",
"0 1\n4 2",
"7 149\n0 25\n3 10\n2 4\n2 8\n3 22\n2 23\n1 2",
"0 2\n4 1",
"7 149\n0 25\n3 10\n2 4\n2 9\n3 22\n2 23\n1 2",
"0 2\n4 2",
"7 149\n1 25\n3 10\n2 4\n2 9\n3 22\n2 23\n1 2",
"0 2\n3 2",
"7 149\n1 25\n3 10\n3 4\n2 9\n3 22\n2 23\n1 2",
"0 2\n6 2",
"7 149\n1 25\n3 10\n3 4\n2 9\n3 11\n2 23\n1 2",
"0 0\n6 2",
"7 149\n1 25\n3 10\n3 4\n2 9\n3 11\n2 23\n1 0",
"0 0\n6 0",
"7 149\n1 48\n3 10\n3 4\n2 9\n3 11\n2 23\n1 0",
"1 0\n6 0",
"7 149\n1 48\n3 10\n4 4\n2 9\n3 11\n2 23\n1 0",
"1 0\n9 0",
"7 149\n1 48\n3 10\n4 4\n2 9\n0 11\n2 23\n1 0",
"1 0\n7 0",
"7 149\n1 48\n3 10\n4 4\n1 9\n0 11\n2 23\n1 0",
"1 1\n7 0",
"7 149\n0 48\n3 10\n4 4\n1 9\n0 11\n2 23\n1 0",
"1 1\n7 -1",
"7 61\n0 48\n3 10\n4 4\n1 9\n0 11\n2 23\n1 0",
"1 1\n7 -2",
"0 1\n7 -2",
"0 1\n7 0",
"0 1\n11 0",
"0 1\n9 0",
"0 1\n10 0",
"0 1\n10 1",
"0 1\n10 2",
"0 2\n10 2",
"0 2\n10 0",
"0 2\n2 0",
"1 0\n0 3",
"5 21600\n2 14\n3 22\n1 3\n1 4\n1 9",
"3 0\n2 0\n3 2\n0 3",
"7 57\n0 25\n3 10\n2 4\n9 15\n3 22\n2 14\n1 15",
"1 5\n0 0",
"5 21600\n2 14\n2 22\n1 3\n0 10\n1 9",
"3 5\n2 0\n0 2\n0 3",
"7 57\n0 11\n3 10\n2 4\n5 15\n3 22\n2 14\n1 9",
"5 21600\n2 14\n3 6\n1 3\n0 10\n1 3",
"2 5\n2 0\n3 2\n1 3",
"7 57\n0 25\n3 19\n3 4\n5 15\n3 22\n2 14\n1 9",
"1 3\n2 -1",
"5 21600\n2 14\n4 22\n1 3\n0 10\n1 2",
"7 57\n0 25\n5 10\n3 4\n5 20\n3 22\n2 14\n1 9",
"5 21600\n2 14\n0 22\n1 1\n0 10\n1 2",
"0 0\n1 -1",
"7 57\n0 25\n3 10\n2 4\n5 1\n3 22\n2 23\n1 9",
"1 0\n0 0",
"5 21600\n0 14\n3 22\n1 0\n0 10\n1 2",
"7 85\n0 25\n3 10\n2 4\n5 20\n3 22\n4 23\n1 9",
"1 -1\n1 1",
"7 85\n0 25\n3 10\n2 4\n5 20\n3 22\n1 23\n1 18",
"0 -1\n1 1",
"7 99\n0 25\n3 10\n2 4\n5 1\n3 22\n2 23\n1 18",
"1 0\n0 1",
"7 99\n0 25\n3 10\n2 4\n2 23\n3 22\n2 23\n1 18",
"0 1\n0 1",
"7 99\n0 25\n3 10\n2 4\n2 20\n3 22\n3 23\n1 2",
"0 1\n1 2",
"7 149\n0 25\n3 10\n2 4\n2 32\n3 22\n2 23\n1 2",
"0 1\n8 2",
"7 149\n0 25\n3 10\n2 4\n2 8\n3 23\n2 23\n1 2"
],
"outputs": [
"0",
"5",
"2",
"3",
"1\n",
"5\n",
"3\n",
"0\n",
"4\n",
"2\n",
"6\n",
"7\n",
"1\n",
"1\n",
"5\n",
"1\n",
"3\n",
"1\n",
"5\n",
"3\n",
"1\n",
"5\n",
"3\n",
"5\n",
"3\n",
"0\n",
"5\n",
"3\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"0\n",
"4\n",
"0\n",
"4\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"4\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"4\n",
"0\n",
"4\n",
"0\n",
"5\n",
"0\n",
"4\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"5\n",
"0\n",
"3\n",
"1\n",
"5\n",
"1\n",
"3\n",
"5\n",
"1\n",
"3\n",
"1\n",
"5\n",
"3\n",
"5\n",
"0\n",
"3\n",
"0\n",
"5\n",
"3\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"3\n",
"0\n",
"4\n",
"0\n",
"4\n"
]
}
|
There are N stores called Store 1, Store 2, \cdots, Store N. Takahashi, who is at his house at time 0, is planning to visit some of these stores.
It takes Takahashi one unit of time to travel from his house to one of the stores, or between any two stores.
If Takahashi reaches Store i at time t, he can do shopping there after standing in a queue for a_i \times t + b_i units of time. (We assume that it takes no time other than waiting.)
All the stores close at time T + 0.5. If Takahashi is standing in a queue for some store then, he cannot do shopping there.
Takahashi does not do shopping more than once in the same store.
Find the maximum number of times he can do shopping before time T + 0.5.
Constraints
* All values in input are integers.
* 1 \leq N \leq 2 \times 10^5
* 0 \leq a_i \leq 10^9
* 0 \leq b_i \leq 10^9
* 0 \leq T \leq 10^9
Input
Input is given from Standard Input in the following format:
N T
a_1 b_1
a_2 b_2
\vdots
a_N b_N
Output
Print the answer.
Examples
Input
3 7
2 0
3 2
0 3
Output
2
Input
1 3
0 3
Output
0
Input
5 21600
2 14
3 22
1 3
1 10
1 9
Output
5
Input
7 57
0 25
3 10
2 4
5 15
3 22
2 14
1 15
Output
3
|
{
"inputs": [
"6\n1 3\n2 3\n3 3\n4 -3\n5 -1\n6 -100\n",
"3\n-5 9\n0 1\n5 -1\n",
"14\n-916171372 999999988\n-892307487 999999987\n-882212312 999999986\n-700694118 999998986\n-490374058 999997986\n-179890370 999996986\n-153268251 999995986\n-143722350 -999994986\n822181362 -999995986\n888153520 -999996986\n913366887 -999997986\n971641961 -999998986\n982052281 -999999986\n989641415 -999999987\n",
"2\n-1 1\n1 -1\n",
"2\n-156937950 -374833246\n958300153 463070159\n",
"1\n-772620876 2105125\n",
"2\n-1000000000 -1000000000\n1000000000 1000000000\n",
"10\n-957843473 999999990\n-892079437 3\n-660108218 2\n-38604909 1\n117904913 -1\n161630686 -2\n300782495 -3\n503931515 -4\n624182611 -5\n946997174 -999999990\n",
"10\n-904213434 999999991\n-800146111 999999990\n-64167773 999998990\n40786982 999997990\n57739924 999996990\n140713247 -999995990\n242293931 -999996990\n470153869 -999997990\n688427965 -999998990\n979253150 -999999990\n",
"20\n-991228878 999999990\n-966272577 999999989\n-832645426 999999988\n-595404692 999999987\n-593256652 999999986\n-403204913 999999985\n-331750739 999999984\n-254714125 999999983\n-252716873 999999982\n-242309489 999999981\n-99999163 999999980\n53963197 1\n102558090 -1\n208915316 -2\n327993195 -999999980\n338364526 -999999981\n353909346 -999999982\n699191947 -999999983\n748932019 -999999984\n807201175 -999999985\n",
"2\n-1000000000 1\n1000000000 -1\n",
"2\n635254031 797637946\n855431510 75159864\n",
"20\n-993032259 588930376\n-992093161 915475807\n-916464883 -313099768\n-777812700 -790244010\n-559998666 152323291\n-552926767 745694067\n-489434665 332658987\n-310676193 687524020\n-238620668 88387668\n-183633372 294074811\n-89656750 233743240\n-39938323 194724339\n15621290 -244257473\n118853137 -823979220\n215181269 961240622\n224560970 967953108\n297709949 665893756\n314124971 127542046\n317622290 -269656857\n710505266 635433994\n",
"3\n-881879811 207649703\n458744977 -751771616\n589655887 -175300397\n",
"2\n-1000000000 7\n1000000000 -6\n",
"1\n-780061535 64785965\n",
"10\n-904213434 999999991\n-800146111 999999990\n-64167773 3\n40786982 2\n57739924 1\n140713247 -1\n242293931 -2\n470153869 -3\n688427965 -4\n979253150 -999999990\n",
"2\n-1 1000000000\n1 -1000000000\n",
"2\n-1 1000000000\n0 -1000000000\n",
"4\n-925572098 -981226339\n-79539996 -599059823\n221011621 -813670952\n769702162 -909895529\n",
"10\n-774675771 179630170\n-743176829 190325067\n-718170081 850285922\n-672683474 -389325596\n-612117485 -338760201\n-200797120 -278253406\n-134576842 748798831\n301079085 755005057\n945958360 -883545251\n955629379 -312997434\n",
"2\n-1000000000 1000000000\n1000000000 -1000000000\n",
"1\n-554798529 -923175217\n",
"20\n-990544325 999999983\n-982730292 999999982\n-954108391 999999981\n-843979328 999999980\n-842201083 999998980\n-841368019 999997980\n-713774935 999996980\n-526274553 999995980\n-414200681 999994980\n-380902854 999993980\n-356598408 -999991980\n82002495 -999992980\n337411348 -999993980\n431155182 -999994980\n495442299 -999995980\n500857279 -999996980\n501941044 -999997980\n666074520 -999998980\n766795088 -999999980\n889713230 -999999981\n",
"20\n-977812598 999999995\n-859749238 999999994\n-795105479 999999993\n-755580921 999999992\n-703290711 999999991\n-684916878 999999990\n-671093572 999999989\n-598373289 999999988\n-430900427 999999987\n-409406663 999999986\n-186156927 999999985\n137241693 999999984\n174675082 999999983\n233164672 999999982\n263947075 999999981\n281714302 999999980\n501584746 -1\n638491974 -2\n654696707 -999999980\n795033851 -999999981\n",
"2\n-912376737 -339403417\n389839726 -135372297\n",
"5\n-99999163 999999980\n53963197 1\n102558090 -1\n208915316 -2\n327993195 -999999980\n",
"14\n-916171372 999999988\n-892307487 999999987\n-882212312 999999986\n-700694118 999998986\n-490374058 999997986\n-179890370 999996986\n-153268251 999995986\n-143722350 -999994986\n822181362 -1073366343\n888153520 -999996986\n913366887 -999997986\n971641961 -999998986\n982052281 -999999986\n989641415 -999999987\n",
"2\n-2 1\n1 -1\n",
"2\n-297445480 -374833246\n958300153 463070159\n",
"10\n-957843473 999999990\n-892079437 3\n-660108218 2\n-38604909 1\n117904913 -1\n161630686 -2\n508404423 -3\n503931515 -4\n624182611 -5\n946997174 -999999990\n",
"10\n-904213434 999999991\n-800146111 999999990\n-64167773 999998990\n40786982 999997990\n57739924 999996990\n140713247 -999995990\n242293931 -999996990\n470153869 -999997990\n688427965 -999998990\n979253150 -905164443\n",
"20\n-993032259 588930376\n-992093161 915475807\n-916464883 -313099768\n-777812700 -790244010\n-559998666 152323291\n-552926767 745694067\n-489434665 332658987\n-310676193 687524020\n-238620668 88387668\n-183633372 294074811\n-89656750 233743240\n-39938323 194724339\n15626029 -244257473\n118853137 -823979220\n215181269 961240622\n224560970 967953108\n297709949 665893756\n314124971 127542046\n317622290 -269656857\n710505266 635433994\n",
"3\n-881879811 207649703\n857695456 -751771616\n589655887 -175300397\n",
"2\n-771342052 7\n1000000000 -6\n",
"2\n-1 1000000000\n2 -1000000000\n",
"2\n-1 1000100000\n0 -1000000000\n",
"10\n-774675771 179630170\n-743176829 190325067\n-718170081 850285922\n-672683474 -389325596\n-612117485 -345878652\n-200797120 -278253406\n-134576842 748798831\n301079085 755005057\n945958360 -883545251\n955629379 -312997434\n",
"2\n-153034748 1000000000\n1000000000 -1000000000\n",
"20\n-990544325 999999983\n-982730292 999999982\n-954108391 999999981\n-843979328 999999980\n-842201083 999998980\n-841368019 999997980\n-713774935 999996980\n-526274553 999995980\n-414200681 999994980\n-380902854 999993980\n-53630737 -999991980\n82002495 -999992980\n337411348 -999993980\n431155182 -999994980\n495442299 -999995980\n500857279 -999996980\n501941044 -999997980\n666074520 -999998980\n766795088 -999999980\n889713230 -999999981\n",
"20\n-977812598 999999995\n-859749238 999999994\n-795105479 305814143\n-755580921 999999992\n-703290711 999999991\n-684916878 999999990\n-671093572 999999989\n-598373289 999999988\n-430900427 999999987\n-409406663 999999986\n-186156927 999999985\n137241693 999999984\n174675082 999999983\n233164672 999999982\n263947075 999999981\n281714302 999999980\n501584746 -1\n638491974 -2\n654696707 -999999980\n795033851 -999999981\n",
"5\n-99999163 432879381\n53963197 1\n102558090 -1\n208915316 -2\n327993195 -999999980\n",
"6\n1 3\n2 3\n3 3\n4 -2\n5 -1\n6 -100\n",
"3\n-5 9\n0 1\n6 -1\n",
"2\n-2 2\n1 -1\n",
"3\n-881879811 207649703\n857695456 -840825921\n589655887 -175300397\n",
"2\n-771342052 7\n1000000000 -8\n",
"2\n-1 1000000000\n2 -1885034862\n",
"2\n-1 1000100000\n0 -1164784485\n",
"2\n-153034748 1000000000\n1010000000 -1000000000\n",
"20\n-990544325 999999983\n-982730292 999999982\n-954108391 999999981\n-843979328 999999980\n-842201083 999998980\n-841368019 999997980\n-713774935 999996980\n-526274553 999995980\n-414200681 999994980\n-380902854 703210509\n-53630737 -999991980\n82002495 -999992980\n337411348 -999993980\n431155182 -999994980\n495442299 -999995980\n500857279 -999996980\n501941044 -999997980\n666074520 -999998980\n766795088 -999999980\n889713230 -999999981\n",
"20\n-993032259 588930376\n-992093161 915475807\n-916464883 -313099768\n-777812700 -790244010\n-559998666 152323291\n-315862644 745694067\n-489434665 332658987\n-310676193 687524020\n-238620668 88387668\n-183633372 294074811\n-89656750 233743240\n-39938323 194724339\n15626029 -244257473\n118853137 -823979220\n215181269 961240622\n224560970 967953108\n297709949 665893756\n314124971 127542046\n405780822 -269656857\n710505266 635433994\n",
"3\n-881879811 229141260\n857695456 -840825921\n589655887 -175300397\n",
"2\n-771342052 7\n1000000000 -15\n",
"2\n-1 1000000000\n2 -861263255\n",
"1\n-772620876 1636394\n",
"1\n-780061535 35487013\n",
"4\n-925572098 -981226339\n-79539996 -357444363\n221011621 -813670952\n769702162 -909895529\n",
"1\n-880211986 -923175217\n",
"2\n-912376737 -339403417\n389839726 -223356035\n",
"14\n-916171372 999999988\n-892307487 999999987\n-882212312 999999986\n-700694118 1906510073\n-490374058 999997986\n-179890370 999996986\n-153268251 999995986\n-143722350 -999994986\n822181362 -1073366343\n888153520 -999996986\n913366887 -999997986\n971641961 -999998986\n982052281 -999999986\n989641415 -999999987\n",
"2\n-297445480 -374833246\n1299014805 463070159\n",
"1\n-512779913 1636394\n",
"10\n-957843473 999999990\n-892079437 3\n-660108218 2\n-38604909 1\n117904913 -1\n161630686 -2\n237389805 -3\n503931515 -4\n624182611 -5\n946997174 -999999990\n",
"10\n-904213434 1410395458\n-800146111 999999990\n-64167773 999998990\n40786982 999997990\n57739924 999996990\n140713247 -999995990\n242293931 -999996990\n470153869 -999997990\n688427965 -999998990\n979253150 -905164443\n",
"20\n-993032259 588930376\n-992093161 915475807\n-916464883 -313099768\n-777812700 -790244010\n-559998666 152323291\n-315862644 745694067\n-489434665 332658987\n-310676193 687524020\n-238620668 88387668\n-183633372 294074811\n-89656750 233743240\n-39938323 194724339\n15626029 -244257473\n118853137 -823979220\n215181269 961240622\n224560970 967953108\n297709949 665893756\n314124971 127542046\n317622290 -269656857\n710505266 635433994\n",
"1\n-1045168328 35487013\n",
"4\n-925572098 -981226339\n-79539996 -357444363\n221011621 -813670952\n1189200486 -909895529\n",
"10\n-774675771 179630170\n-743176829 190325067\n-718170081 850285922\n-672683474 -389325596\n-612117485 -345878652\n-200797120 -278253406\n-134576842 748798831\n301079085 755005057\n724081931 -883545251\n955629379 -312997434\n",
"2\n-912376737 -339403417\n287841096 -223356035\n",
"5\n-99999163 432879381\n53963197 1\n102558090 -1\n79792713 -2\n327993195 -999999980\n",
"14\n-916171372 999999988\n-892307487 999999987\n-882212312 1296065011\n-700694118 1906510073\n-490374058 999997986\n-179890370 999996986\n-153268251 999995986\n-143722350 -999994986\n822181362 -1073366343\n888153520 -999996986\n913366887 -999997986\n971641961 -999998986\n982052281 -999999986\n989641415 -999999987\n",
"1\n-215402061 1636394\n",
"10\n-957843473 999999990\n-892079437 3\n-660108218 2\n-38604909 1\n117904913 -1\n161630686 -2\n237389805 -3\n503931515 -4\n440713792 -5\n946997174 -999999990\n",
"1\n-695223893 35487013\n"
],
"outputs": [
"0.0291262135922\n",
"0.9999999999945\n",
"0.0047729720452\n",
"1.0000000000018\n",
"-1\n",
"-1\n",
"-1\n",
"0.9524203330262\n",
"0.0414868071184\n",
"0.2025572568487\n",
"1000000000.00000000000000000000\n",
"-1\n",
"0.0088049563420\n",
"1.3973264523610\n",
"153846153.84615385532379150391\n",
"-1\n",
"0.8896996393940\n",
"0.0000000010000\n",
"0.0000000005000\n",
"-1\n",
"0.0366942435911\n",
"0.9999999999945\n",
"-1\n",
"0.0121523083092\n",
"0.1864912062293\n",
"-1\n",
"0.2025572568482\n",
"0.00477297204519581183\n",
"1.50000000000000000000\n",
"-1\n",
"0.95242033302420336938\n",
"0.04148680711869298654\n",
"0.00880495634198667429\n",
"1.81315052370646778712\n",
"136257080.92307692766189575195\n",
"0.00000000150000000000\n",
"0.00000000049997500125\n",
"0.03669424359124098117\n",
"0.57651737400000002687\n",
"0.16363720723319477579\n",
"0.18649120622982412465\n",
"0.27403000320657006084\n",
"0.02912621359223301065\n",
"1.10000000000000008882\n",
"1.00000000000000000000\n",
"1.65914707712842357523\n",
"118089470.13333334028720855713\n",
"-0.00000000212776153499\n",
"-0.00000000046946531601\n",
"0.58151737400000003131\n",
"0.18028614746568147331\n",
"0.06155769294046074119\n",
"1.62582114469546512581\n",
"80515547.81818181276321411133\n",
"0.00000000161180853484\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"0.00477297204519581183\n",
"-1\n",
"-1\n",
"0.95242033302420336938\n",
"0.04148680711869298654\n",
"0.00880495634198667429\n",
"-1\n",
"-1\n",
"0.03669424359124098117\n",
"-1\n",
"0.27403000320657006084\n",
"0.00477297204519581183\n",
"-1\n",
"0.95242033302420336938\n",
"-1\n"
]
}
|
Recently the construction of Berland collider has been completed. Collider can be represented as a long narrow tunnel that contains n particles. We associate with collider 1-dimensional coordinate system, going from left to right. For each particle we know its coordinate and velocity at the moment of start of the collider. The velocities of the particles don't change after the launch of the collider. Berland scientists think that the big bang will happen at the first collision of particles, whose velocities differs in directions. Help them to determine how much time elapses after the launch of the collider before the big bang happens.
Input
The first line contains single integer n (1 ≤ n ≤ 5·105) — amount of particles in the collider. Next n lines contain description of particles. Each particle is described by two integers xi, vi ( - 109 ≤ xi, vi ≤ 109, vi ≠ 0) — coordinate and velocity respectively. All the coordinates are distinct. The particles are listed in order of increasing of coordinates. All the coordinates are in meters, and all the velocities — in meters per second. The negative velocity means that after the start of collider the particle will move to the left, and the positive — that the particle will move to the right.
Output
If there will be no big bang, output -1. Otherwise output one number — how much time in seconds elapses after the launch of the collider before the big bang happens. Your answer must have a relative or absolute error less than 10 - 9.
Examples
Input
3
-5 9
0 1
5 -1
Output
1.00000000000000000000
Input
6
1 3
2 3
3 3
4 -3
5 -1
6 -100
Output
0.02912621359223301065
|
{
"inputs": [
"5 229 8419\n1795 95\n4873 720\n3149 81\n6101 2325\n3674 629\n\nSAMPLE",
"5 438 8419\n1795 95\n4873 720\n3149 81\n6101 2325\n3674 629\n\nSAMPLE",
"5 438 8419\n1795 21\n4873 720\n3149 81\n6101 2325\n3674 629\n\nELPMAS",
"5 438 8419\n1795 21\n4873 720\n3149 81\n6101 2325\n3674 795\n\nSLPMAE",
"5 438 8419\n1795 21\n4873 720\n868 81\n6101 2325\n3674 795\n\nSLPMAE",
"5 438 8419\n1795 21\n4873 720\n868 81\n6101 2325\n4262 795\n\nEAMPLS",
"5 438 8419\n1795 21\n4873 720\n868 81\n6101 2325\n2027 795\n\nEAMPLS",
"5 438 8419\n1795 21\n4873 720\n868 81\n6101 2325\n2027 1259\n\nEAMPLS",
"5 438 8419\n1795 21\n673 720\n868 81\n6101 2325\n2027 1259\n\nEAMPLS",
"5 438 8419\n1795 21\n788 720\n868 81\n5717 2325\n2027 1259\n\nEAMPLS",
"5 438 8419\n3322 21\n788 720\n868 81\n5717 2325\n2027 1259\n\nEAMPLS",
"5 858 8419\n3322 21\n788 1921\n868 151\n7295 2325\n2027 1259\n\nEASPLM",
"5 948 8419\n3322 21\n788 1921\n868 204\n7295 2325\n3479 1259\n\nEASPLM",
"5 948 8419\n3322 21\n788 589\n868 204\n7295 2325\n3479 1259\n\nEASPLM",
"5 948 14243\n3322 21\n788 589\n868 200\n7295 2325\n3479 1259\n\nEASPLM",
"5 1875 14243\n3322 21\n788 589\n868 200\n7295 2325\n3479 1259\n\nEASPLM",
"5 1875 14243\n3322 21\n788 589\n868 200\n7295 2325\n925 1259\n\nEATPLM",
"5 1875 14243\n3322 21\n788 589\n868 119\n7295 2325\n216 1259\n\nEAPTLM",
"5 1875 14243\n572 21\n788 589\n868 119\n7295 2325\n76 1259\n\nEAPTLM",
"5 1875 14243\n572 21\n788 589\n1461 119\n7295 2325\n76 2508\n\nDAPTLM",
"5 1875 27053\n572 21\n788 1124\n1461 119\n7295 2325\n76 2508\n\nDAPTLM",
"5 1875 31573\n572 10\n788 100\n1461 119\n7295 2325\n76 2508\n\nMLTPAD",
"5 1875 31573\n572 10\n788 100\n1087 155\n7295 2325\n109 2508\n\nMLTPAD",
"5 1875 31573\n572 10\n788 110\n472 155\n7295 3261\n109 2508\n\nMLTPAD",
"5 229 8419\n2815 95\n4873 720\n3149 81\n6101 2325\n3674 629\n\nSAMPLE",
"5 438 8419\n1795 21\n4873 720\n3149 81\n6101 1806\n3674 629\n\nELPMAS",
"5 438 8419\n1795 21\n4873 720\n3149 81\n9045 2325\n3674 795\n\nSLPMAE",
"5 438 8419\n1795 21\n4873 720\n868 81\n6101 2325\n2617 795\n\nEAMPLS",
"5 438 8419\n209 21\n4873 720\n868 81\n6101 2325\n4262 795\n\nEAMPLS",
"5 438 8419\n1795 21\n4873 720\n868 81\n1727 2325\n2027 795\n\nEAMPLS",
"5 438 8419\n1795 21\n4873 720\n868 81\n6101 2325\n2790 1259\n\nEAMPLS",
"5 438 13855\n1795 21\n673 720\n868 81\n6101 2325\n2027 1259\n\nEAMPLS",
"5 438 7562\n1795 21\n788 720\n868 81\n5717 2325\n2027 1259\n\nEAMPLS",
"5 438 11919\n3322 21\n788 720\n868 151\n5717 2325\n2027 1259\n\nEAMPLS",
"5 438 8419\n3322 21\n788 1305\n868 151\n5717 2325\n889 1259\n\nEAMPLS",
"5 438 8193\n3322 21\n788 1921\n868 151\n5717 2325\n2027 1259\n\nEASPLM",
"5 948 8419\n3322 21\n788 1921\n868 204\n7295 2657\n2027 1259\n\nEASPLM",
"5 948 11109\n3322 21\n788 589\n868 200\n7295 2325\n3479 1259\n\nEASPLM",
"5 948 14243\n3322 21\n1312 589\n868 200\n7295 2325\n3479 1259\n\nEASPLM",
"5 1875 14243\n3322 21\n788 589\n868 200\n7295 1906\n3479 1259\n\nEASPLM",
"5 1875 14243\n3322 38\n788 589\n868 200\n7295 2325\n925 1259\n\nEATPLM",
"3 1875 14243\n3322 21\n788 589\n868 119\n7295 2325\n216 1259\n\nEAPTLM",
"5 1875 8967\n572 21\n788 589\n868 119\n7295 2325\n76 1259\n\nEAPTLM",
"5 1875 14243\n572 21\n1448 589\n1461 119\n7295 2325\n76 1259\n\nDAPTLM",
"5 1875 27053\n572 5\n788 1124\n1461 119\n7295 2325\n80 2508\n\nDAPTLM",
"5 1875 31573\n572 10\n788 100\n1087 155\n7295 3459\n76 2508\n\nMLTPAD",
"5 229 8419\n4828 95\n4873 720\n3149 81\n6101 2325\n3674 629\n\nSAMPLE",
"5 438 8419\n1795 95\n8847 720\n3149 81\n6101 613\n3674 629\n\nSAMPLE",
"5 438 8419\n1795 21\n4873 720\n3149 139\n6101 1806\n3674 629\n\nELPMAS",
"5 137 8419\n1795 21\n4873 720\n3149 81\n9045 2325\n3674 795\n\nSLPMAE",
"4 438 8419\n1795 21\n4873 720\n868 81\n6101 2325\n2617 795\n\nEAMPLS",
"5 438 13250\n1795 21\n4873 720\n868 81\n1727 2325\n2027 795\n\nEAMPLS",
"5 438 8419\n1795 21\n4873 720\n868 81\n6101 2325\n4719 1259\n\nEAMPLS",
"4 438 13855\n1795 21\n673 720\n868 81\n6101 2325\n2027 1259\n\nEAMPLS",
"5 438 8419\n3322 33\n788 1305\n868 151\n5717 2325\n889 1259\n\nEAMPLS",
"5 438 8193\n3322 21\n788 1921\n868 151\n5717 2325\n2027 382\n\nEASPLM",
"5 948 2123\n3322 34\n788 589\n868 204\n7295 2325\n3479 1259\n\nEASPLM",
"5 948 14243\n3322 21\n1843 589\n868 200\n7295 2325\n3479 1259\n\nEASPLM",
"5 1875 14243\n3322 21\n788 589\n1479 200\n7295 2325\n4033 1259\n\nEATPLM",
"3 1811 14243\n3322 21\n788 589\n868 119\n7295 2325\n216 1259\n\nEAPTLM",
"5 1875 14243\n572 21\n788 1124\n1461 119\n7295 2579\n76 2508\n\nCAPTLM",
"5 1875 27053\n572 10\n788 265\n1461 119\n7295 1156\n76 2508\n\nDAPTLM",
"3 1875 31573\n572 10\n788 110\n1461 119\n7295 2325\n76 2508\n\nMLTPAD",
"5 1875 31573\n390 10\n788 100\n2030 155\n7295 2325\n76 2258\n\nMLTPAD",
"5 1875 31573\n572 10\n788 110\n1087 155\n7295 2325\n123 2508\n\nMLTPAC",
"5 1875 31573\n572 10\n1331 110\n472 155\n7295 4239\n109 2508\n\nMLTPAD",
"5 438 8419\n1795 95\n8847 720\n3149 128\n6101 613\n3674 629\n\nSAMPLE",
"5 588 8419\n1795 21\n4873 720\n3149 139\n6101 1806\n3674 629\n\nELPMAS",
"4 438 8419\n1795 21\n4873 720\n868 81\n6101 4339\n2617 795\n\nEAMPLS",
"5 438 8419\n1795 21\n4873 720\n868 81\n9984 2325\n4719 1259\n\nEAMPLS",
"4 438 13855\n386 21\n673 720\n868 81\n6101 2325\n2027 1259\n\nEAMPLS",
"5 591 8419\n1795 21\n788 720\n868 81\n6101 1395\n2027 1259\n\nEAMPMS",
"5 438 11919\n3322 32\n788 720\n868 124\n5717 2325\n2027 1259\n\nEAMPLS",
"5 438 7219\n3322 33\n788 1305\n868 151\n5717 2325\n889 1259\n\nEAMPLS",
"5 858 8419\n3322 21\n195 805\n868 151\n7295 2325\n18 1259\n\nEASPLM",
"5 1875 14243\n3322 9\n788 589\n868 200\n5910 1906\n3479 1259\n\nEASPLM",
"5 1875 14243\n3322 21\n788 589\n868 155\n7295 2325\n925 1396\n\nMLTPAE",
"3 1811 27330\n3322 21\n788 589\n868 119\n7295 2325\n216 1259\n\nEAPTLM",
"5 1875 18072\n175 21\n788 589\n1461 119\n10723 2325\n76 2508\n\nDAPTLM",
"5 1875 14243\n572 21\n788 1124\n1461 119\n7295 2579\n38 2508\n\nCAPTLM",
"5 1875 23758\n572 5\n788 1124\n1461 119\n7295 2325\n80 2508\n\nDTPALM",
"5 1875 31573\n572 15\n788 101\n1087 155\n7295 2325\n117 2508\n\nMLTPAD",
"5 204 8419\n4828 95\n3961 720\n3149 81\n6101 2325\n3674 629\n\nSAMPLE",
"5 438 8419\n1795 95\n8847 1088\n3149 128\n6101 613\n3674 629\n\nSAMPLE",
"5 588 8419\n1795 21\n4873 720\n3149 139\n6101 1806\n3674 1126\n\nELPMAS",
"5 438 7562\n1795 21\n788 720\n1399 118\n5717 2325\n2027 1188\n\nEAMPLS",
"5 438 8193\n3322 21\n788 1921\n521 151\n440 2325\n2027 382\n\nEASPLM",
"5 948 14243\n3322 21\n1843 589\n868 200\n7295 2325\n3479 475\n\nEARPLM",
"5 2234 14243\n3322 21\n788 589\n1479 200\n7295 2325\n4033 1259\n\nEASPLM",
"5 3623 18072\n175 21\n788 589\n1461 119\n10723 2325\n76 2508\n\nDAPTLM",
"5 1875 27053\n572 10\n788 100\n2090 119\n7196 2325\n76 3737\n\nMLTPAD",
"5 438 8419\n1795 95\n2867 1088\n3149 128\n6101 613\n3674 629\n\nSAMPLE",
"5 588 8419\n1795 21\n1490 720\n3149 139\n6101 1806\n3674 1126\n\nELPMAS",
"5 591 10163\n1093 21\n788 720\n868 81\n6101 1395\n2027 1259\n\nEAMPMS",
"5 438 11919\n3379 32\n788 720\n868 124\n5717 2325\n2027 1259\n\nEAPMLS",
"5 948 14243\n3322 21\n1843 589\n868 200\n7295 1595\n3479 475\n\nEARPLM",
"5 1875 14243\n572 21\n788 1124\n1461 119\n7295 2579\n38 3657\n\nBAPTLM",
"5 1875 27053\n572 4\n788 1257\n845 119\n7295 2325\n76 2794\n\nMLTPAD",
"5 1875 31573\n572 10\n788 010\n1087 284\n7295 2325\n123 385\n\nMLTPAC",
"5 1875 31573\n572 10\n73 110\n102 43\n7295 3261\n109 3804\n\nNLTPAD",
"5 204 8419\n4828 95\n2698 720\n3149 75\n6101 2325\n3674 629\n\nSAMPLE"
],
"outputs": [
"2626\n",
"2417\n",
"2565\n",
"2399\n",
"2237\n",
"2825\n",
"1586\n",
"820\n",
"490\n",
"483\n",
"441\n",
"1642\n",
"232\n",
"1075\n",
"5698\n",
"5200\n",
"7367\n",
"7676\n",
"7718\n",
"7009\n",
"19819\n",
"24339\n",
"24306\n",
"22434\n",
"2626\n",
"3077\n",
"3526\n",
"1544\n",
"2867\n",
"2927\n",
"931\n",
"5919\n",
"106\n",
"3941\n",
"1579\n",
"215\n",
"1310\n",
"2564\n",
"5174\n",
"6038\n",
"7333\n",
"12326\n",
"3095\n",
"7556\n",
"19815\n",
"22071\n",
"2816\n",
"5015\n",
"3042\n",
"3827\n",
"3134\n",
"7758\n",
"2818\n",
"7770\n",
"1555\n",
"792\n",
"746\n",
"5041\n",
"5522\n",
"12390\n",
"6501\n",
"22157\n",
"29698\n",
"24589\n",
"24292\n",
"20478\n",
"4991\n",
"2892\n",
"1162\n",
"4499\n",
"7812\n",
"2343\n",
"3919\n",
"1178\n",
"3651\n",
"6772\n",
"7230\n",
"25477\n",
"10838\n",
"6539\n",
"16520\n",
"24298\n",
"2841\n",
"4623\n",
"2430\n",
"177\n",
"5386\n",
"6397\n",
"5163\n",
"9799\n",
"18590\n",
"4152\n",
"1032\n",
"4087\n",
"3938\n",
"7857\n",
"5390\n",
"19533\n",
"25048\n",
"21138\n",
"1774\n"
]
}
|
Protection of the Indian border and safe transport of items from one point to another along the border are the paramount jobs for the Indian army. However they need some information about the protection status along the length of the border. The border can be viewed as the real x-axis. Along the axis, Indian army has N checkpoints for lookout.
We know that each checkpoint is located at an integer location xi. Each checkpoint must have a fleet of armed men which are responsible for guarding the neighboring areas of the checkpoint and provide military assistance of all kinds. The size of the fleet is based on the location of the checkpoint and how active the region is for terrorist activities.
Given the number of armed men assigned at the i^th checkpoint, as pi, this information is available for all checkpoints.
With the skills of the armed men, it is known that if for the i^th checkpoint, the length on the x axis that they can defend is a closed interval [xi-pi, xi+pi].
Now, your task is to transport some military items from position S to the end position E on the x-axis.
Input:
First line of the input contains 3 integers N, S and E. N is the number of checkpoints that the Indian Army has on the border.
Then N lines follow. i^th line contains 2 integers, xi and pi.
Output:
Print the total distance of the x-axisfrom S to E, that is not protected by the armed forces.
Constraints:
1 ≤ N ≤ 10^5
1 ≤ xi, pi ≤ 10^18
xi + pi ≤ 10^18
1 ≤ S ≤ E ≤ 10^18
SAMPLE INPUT
5 229 8419
1795 95
4873 720
3149 81
6101 2325
3674 629
SAMPLE OUTPUT
2626
|
{
"inputs": [
"3 6 1 2 1\n",
"5 10 1 2 5\n",
"10000 1 999999999 1000000000 1\n",
"9103 555078149 86703 93382 8235\n",
"9102 808807765 95894 96529 2021\n",
"39 407 62 63 2\n",
"8367 515267305 49370 57124 723\n",
"59 770 86 94 2\n",
"39 252 51 98 26\n",
"10000 1 1 2 1\n",
"59 96 75 98 9\n",
"1 1 1 2 1\n",
"10000 1000000000 999999999 1000000000 3\n",
"9538 765513348 52584 86675 8268\n",
"9274 783669740 44989 60995 6973\n",
"87 422 7 90 3\n",
"1 1 1 1000000000 1\n",
"1 1000000000 1 1000000000 1\n",
"10000 1000000000 1 2 1\n",
"10000 1000000000 1 1000000000 10000\n",
"39 221 55 94 1\n",
"8811 929128198 57528 84457 6629\n",
"10000 1000000000 1 2 10000\n",
"6592 724149457 54877 85492 6302\n",
"9750 980765213 40044 94985 4226\n",
"1 1000000000 1 2 1\n",
"10000 1000000000 999999999 1000000000 10000\n",
"10000 1 1 1000000000 1\n",
"87 237 3 21 40\n",
"9999 1000000 10 20 3\n",
"10000 1000000000 999999999 1000000000 1\n",
"18 518 99 100 4\n",
"10000 1 999999999 1000000000 10000\n",
"5884 943590784 42695 98774 3117\n",
"10000 1000000000 1 1000000000 1\n",
"10000 1 1 2 10000\n",
"8861 990217735 49933 64765 6526\n",
"10000 1 1 1000000000 10000\n",
"11 81 31 90 1\n",
"1 1000000000 999999999 1000000000 1\n",
"15 563 38 51 5\n",
"1 1 999999999 1000000000 1\n",
"10000 1 999999999 1000000000 2\n",
"9103 494293183 86703 93382 8235\n",
"9102 808807765 95894 96529 2766\n",
"39 392 62 63 2\n",
"8367 221036323 49370 57124 723\n",
"59 901 86 94 2\n",
"39 252 51 170 26\n",
"59 167 75 98 9\n",
"2 1 1 2 1\n",
"10000 1000000100 999999999 1000000000 3\n",
"9538 765513348 29678 86675 8268\n",
"9274 1318627196 44989 60995 6973\n",
"1 1 1 1000000001 1\n",
"10000 1000000100 1 2 1\n",
"10000 1000000000 1 1100000000 10000\n",
"39 259 55 94 1\n",
"10000 1000000000 1 2 10001\n",
"9750 823945396 40044 94985 4226\n",
"87 230 3 21 40\n",
"9999 1000100 10 20 3\n",
"18 518 84 100 4\n",
"10000 1 999999999 1000001000 10000\n",
"5884 256358708 42695 98774 3117\n",
"10000 1 1 4 10000\n",
"11 81 35 90 1\n",
"2 1000000000 999999999 1000000000 1\n",
"1 1 127322332 1000000000 1\n",
"4 10 1 2 5\n",
"10000 0 999999999 1000000000 2\n",
"12555 808807765 95894 96529 2766\n",
"39 392 62 63 4\n",
"59 901 86 94 3\n",
"39 491 51 170 26\n",
"9538 765513348 51248 86675 8268\n",
"39 259 55 94 2\n",
"9750 1401028803 40044 94985 4226\n",
"17625 1000100 10 20 3\n",
"11000 1 999999999 1000001000 10000\n",
"5884 256358708 42695 148765 3117\n",
"10000 2 1 4 10000\n",
"11 81 67 90 1\n",
"2 1000010000 999999999 1000000000 1\n",
"1 1 127322332 1000010000 1\n",
"19700 808807765 95894 96529 2766\n",
"39 392 1 63 4\n",
"59 901 40 94 3\n",
"16122 1401028803 40044 94985 4226\n",
"10000 1000000000 999999999 1100000100 10001\n",
"87 230 6 21 39\n",
"17625 1000101 10 20 3\n",
"11 94 67 90 1\n",
"2 1000010000 299020616 1000000000 1\n",
"2 1 127322332 1000010000 1\n",
"32 392 1 63 4\n",
"88 901 40 94 3\n",
"39 491 51 262 36\n",
"10000 1000000000 999999999 1000000100 10001\n",
"87 216 6 21 39\n",
"17625 1000101 1 20 3\n",
"11010 1 999999999 1000011000 10000\n",
"32 262 1 63 4\n",
"88 554 40 94 3\n",
"39 491 47 262 36\n",
"150 216 6 21 39\n",
"10000 1000000000 999999999 1100000000 10000\n",
"10000 1000000000 2 1100000000 10000\n",
"10000 1000000000 999999999 1100000000 10001\n",
"87 230 3 21 39\n",
"2 10 1 2 5\n",
"39 491 51 170 36\n",
"10000 1000000000 2 1100000000 11000\n",
"11010 1 999999999 1000001000 10000\n",
"10000 2 1 4 10001\n",
"2 0 127322332 1000010000 1\n",
"10000 0000000000 999999999 1000000100 10001\n",
"11010 1 999999999 1000011000 10001\n",
"30 262 1 63 4\n"
],
"outputs": [
"4.714285714285714285714285713\n",
"5\n",
"1.000000000999900000999850006E-9\n",
"6168.789328312547849224303937\n",
"8423.267636612606874076300656\n",
"6.559266296872100983346448887\n",
"10310.34922876281976242409477\n",
"8.926948158882814043870627756\n",
"3.534433693796243597040409787\n",
"0.9999250037498125093745312735\n",
"1.231565133042965555280826217\n",
"0.5\n",
"1.000000000999700060987552535\n",
"11295.64974048123987308997568\n",
"14946.94023718163097645119191\n",
"49.25730515791865485117018862\n",
"1E-9\n",
"1\n",
"999925003.7498125093745312735\n",
"1\n",
"3.960801226758673567184205482\n",
"13306.28781071827525114599897\n",
"500000000\n",
"10543.92135458822279837889309\n",
"18012.22666724895290095881322\n",
"500000000\n",
"1\n",
"0.00001999860004799864007519713613\n",
"33.85714285714285714285714287\n",
"99977.50112494375281235938205\n",
"1.000000000999900000999850006\n",
"5.221816347124117053481331990\n",
"1E-9\n",
"14275.99910461026578760447058\n",
"19998.60004799864007519713613\n",
"0.5\n",
"17403.19260373231992827503108\n",
"1E-9\n",
"2.333198380566801619433198380\n",
"1\n",
"13.42112114555365714750630543\n",
"1E-9\n",
"1.0000000009998e-09\n",
"5493.263458201885\n",
"8420.488380765162\n",
"6.317524295758878\n",
"4422.87267260557\n",
"10.44568868980963\n",
"2.5746130030959753\n",
"2.142410179355992\n",
"0.7\n",
"1.0000001009997002\n",
"14561.895257009057\n",
"25150.18876923127\n",
"9.99999999e-10\n",
"999925103.7423129\n",
"0.9090909090909091\n",
"4.641843971631205\n",
"500000000.0\n",
"15132.155012708632\n",
"32.857142857142854\n",
"99987.49887505625\n",
"5.954579439252337\n",
"9.99999000001e-10\n",
"3878.5634068539657\n",
"0.25\n",
"2.1\n",
"1.0000000005\n",
"1e-09\n",
"5.0\n",
"0.0\n",
"8423.267636612607\n",
"6.312472020771779\n",
"10.430196968949005\n",
"5.01640866873065\n",
"11434.879235837898\n",
"4.57907215417217\n",
"25730.570408170137\n",
"99997.23385243809\n",
"9.999995005003747e-10\n",
"3043.706399835316\n",
"0.5\n",
"1.1765531062124248\n",
"1.000010000500005\n",
"9.99990000099999e-10\n",
"8427.438245039408\n",
"90.90514905149051\n",
"21.476665208778204\n",
"27705.954130089995\n",
"0.9090908264462885\n",
"23.837535014005603\n",
"99997.33383967321\n",
"1.365382617086024\n",
"1.7390332369417616\n",
"2.2629327896492804e-09\n",
"75.46438746438747\n",
"21.818420641939344\n",
"3.7797020141635245\n",
"0.99999990000001\n",
"22.386554621848738\n",
"998405.6975146572\n",
"9.999945005453717e-10\n",
"50.43793243793244\n",
"13.41554387972741\n",
"3.8736480215180045\n",
"24.979591836734695\n",
"0.9090909090909091\n",
"0.9090909090909091\n",
"0.9090909090909091\n",
"32.857142857142854\n",
"5.0\n",
"5.01640866873065\n",
"0.9090909090909091\n",
"9.999995005003747e-10\n",
"0.5\n",
"0.0\n",
"0.0\n",
"9.999945005453717e-10\n",
"50.43793243793244\n"
]
}
|
On vacations n pupils decided to go on excursion and gather all together. They need to overcome the path with the length l meters. Each of the pupils will go with the speed equal to v1. To get to the excursion quickly, it was decided to rent a bus, which has seats for k people (it means that it can't fit more than k people at the same time) and the speed equal to v2. In order to avoid seasick, each of the pupils want to get into the bus no more than once.
Determine the minimum time required for all n pupils to reach the place of excursion. Consider that the embarkation and disembarkation of passengers, as well as the reversal of the bus, take place immediately and this time can be neglected.
Input
The first line of the input contains five positive integers n, l, v1, v2 and k (1 ≤ n ≤ 10 000, 1 ≤ l ≤ 109, 1 ≤ v1 < v2 ≤ 109, 1 ≤ k ≤ n) — the number of pupils, the distance from meeting to the place of excursion, the speed of each pupil, the speed of bus and the number of seats in the bus.
Output
Print the real number — the minimum time in which all pupils can reach the place of excursion. Your answer will be considered correct if its absolute or relative error won't exceed 10 - 6.
Examples
Input
5 10 1 2 5
Output
5.0000000000
Input
3 6 1 2 1
Output
4.7142857143
Note
In the first sample we should immediately put all five pupils to the bus. The speed of the bus equals 2 and the distance is equal to 10, so the pupils will reach the place of excursion in time 10 / 2 = 5.
|
{
"inputs": [
"5\n1 2 3 4 5\n",
"10\n635370 154890 909382 220996 276501 716105 538714 140162 171960 271264\n",
"1\n1\n",
"10\n371054 506438 397130 1 766759 208409 769264 549213 641270 771837\n",
"1\n1000000\n",
"1\n2\n",
"2\n3 2\n",
"50\n110876 835020 859879 999908 712969 788264 287153 921820 330355 499311 209594 484829 296329 940051 174081 931503 1 780512 390075 97866 124255 950067 697612 244256 782385 789882 37608 82153 399889 598867 416717 377988 535636 511221 792568 683271 131077 290194 496712 330720 587436 563481 645817 942562 654093 980561 382937 48293 582608 116156\n",
"2\n2 3\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 70997 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 490879 394582 493952 619247 633202 612928 50907 276653 407819 489945 153173\n",
"10\n635370 154890 909382 220996 276501 716105 526532 140162 171960 271264\n",
"10\n371054 506438 397130 1 766759 208409 769264 549213 641270 722331\n",
"1\n1000100\n",
"1\n3\n",
"50\n110876 835020 859879 999908 712969 788264 287153 921820 330355 499311 209594 484829 296329 940051 174081 931503 1 780512 390075 97866 124255 950067 697612 244256 782385 789882 37608 82153 399889 598867 416717 377988 535636 511221 792568 683271 131077 290194 513355 330720 587436 563481 645817 942562 654093 980561 382937 48293 582608 116156\n",
"2\n2 6\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 70997 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 633202 612928 50907 276653 407819 489945 153173\n",
"5\n1 2 3 4 8\n",
"10\n635370 154890 909382 220996 276501 716105 526532 192444 171960 271264\n",
"1\n1000101\n",
"2\n2 4\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 50629 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 633202 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 3 4 8\n",
"10\n635370 154890 909382 220996 276501 716105 526532 192444 171960 203955\n",
"1\n1000001\n",
"2\n1 4\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 50629 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 4 4 8\n",
"10\n635370 154890 909382 220996 276501 716105 526532 227874 171960 203955\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 50629 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 4 4 13\n",
"10\n635370 154890 909382 220996 54937 716105 526532 227874 171960 203955\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 50629 393786 382994 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 1 4 13\n",
"10\n635370 154890 909382 220996 54937 532701 526532 227874 171960 203955\n",
"50\n474421 421097 217233 144863 27075 733996 281778 863492 184707 956857 288561 50629 393786 382994 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 1 4 24\n",
"10\n635370 154890 909382 220996 54937 532701 526532 227874 319886 203955\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 50629 393786 382994 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 1 7 24\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 50629 393786 401832 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 1 7 31\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 23392 393786 401832 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 629056 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 955109 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 955109 619247 903971 150498 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 148782 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 955109 619247 903971 150498 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 148782 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 955109 619247 903971 257126 50907 276653 407819 489945 153173\n",
"10\n635370 154890 909382 220996 268988 716105 538714 140162 171960 271264\n",
"1\n4\n",
"10\n371054 902890 397130 1 766759 208409 769264 549213 641270 771837\n",
"1\n1001000\n",
"1\n5\n",
"2\n2 2\n",
"2\n3 3\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 70997 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 587959 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 490879 394582 493952 619247 633202 612928 50907 276653 407819 489945 153173\n",
"5\n1 2 3 5 5\n",
"10\n635370 154890 909382 220996 276501 716105 526532 186905 171960 271264\n",
"10\n371054 506438 397130 1 766759 208409 769264 857536 641270 722331\n",
"1\n1000111\n",
"50\n110876 835020 859879 999908 712969 788264 287153 921820 330355 499311 209594 484829 296329 940051 174081 931503 1 780512 390075 97866 238666 950067 697612 244256 782385 789882 37608 82153 399889 598867 416717 377988 535636 511221 792568 683271 131077 290194 513355 330720 587436 563481 645817 942562 654093 980561 382937 48293 582608 116156\n",
"2\n3 4\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 70997 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 420847 394582 493952 619247 633202 612928 50907 276653 407819 489945 153173\n",
"10\n635370 4815 909382 220996 276501 716105 526532 192444 171960 271264\n",
"1\n1000011\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 50629 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 247808 421423 544173 394582 493952 619247 633202 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 3 4 6\n",
"10\n635370 154890 909382 220996 276501 318336 526532 192444 171960 203955\n",
"1\n0000011\n",
"2\n1 6\n",
"50\n474421 421097 199933 156339 27075 733996 281778 863492 184707 956857 288561 50629 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 4 4 6\n",
"10\n635370 154890 909382 165257 276501 716105 526532 227874 171960 203955\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 50629 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 563344 903971 612928 50907 276653 407819 489945 153173\n",
"5\n1 2 4 4 13\n",
"10\n635370 154890 909382 220996 54937 785632 526532 227874 171960 203955\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 50629 393786 382994 663642 131184 637 273801 799870 295017 255335 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 1 1 4 13\n",
"10\n635370 154890 909382 190266 54937 532701 526532 227874 171960 203955\n",
"50\n474421 421097 217233 144863 27075 733996 281778 863492 184707 956857 288561 50629 393786 382994 663642 131184 637 273801 799870 371858 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 1 8 24\n",
"10\n635370 154890 909382 220996 54937 532701 526532 324858 319886 203955\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 50629 393786 382994 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 83900\n",
"5\n2 2 1 7 35\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 50629 393786 401832 663642 77358 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"5\n2 2 1 10 31\n",
"50\n474421 421097 217233 275519 27075 733996 20674 863492 184707 956857 288561 23392 393786 401832 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 311979 401832 663642 131184 637 273801 799870 295017 392338 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 241424 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 102013 930684 375703 838048 154915 138503 629056 196556 893619 19263 787927 684541 320265 841090 421423 230474 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 629056 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 493952 619247 905741 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 502142 684541 320265 841090 421423 544173 394582 493952 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 79 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 955109 619247 903971 612928 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 184707 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 161336 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 955109 619247 903971 150498 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 148782 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 13849 893619 19263 787927 684541 320265 841090 421423 544173 394582 955109 619247 903971 150498 50907 276653 407819 489945 153173\n",
"50\n474421 421097 217233 144863 27075 733996 20674 863492 50098 956857 288561 27195 393786 401832 663642 131184 637 273801 799870 295017 461916 842567 198250 297705 153526 930684 375703 838048 154915 138503 243117 196556 893619 19263 787927 684541 320265 841090 421423 544173 394582 955109 619247 903971 257126 50907 276653 407819 489945 153173\n",
"1\n7\n",
"10\n371054 902890 397130 1 766759 208409 769264 549213 641270 890064\n",
"1\n1001001\n",
"1\n8\n",
"2\n4 2\n",
"50\n474421 421097 217233 156339 27075 733996 281778 863492 184707 956857 288561 70997 393786 337382 663642 131184 637 273801 799870 295017 392338 842567 161819 297705 102013 930684 587959 838048 154915 138503 629056 256591 893619 19263 787927 684541 320265 841090 648302 490879 394582 493952 619247 633202 612928 50907 276653 407819 489945 153173\n"
],
"outputs": [
"-1\n",
"1\n",
"-1\n",
"-1\n",
"1\n",
"1\n",
"1\n",
"-1\n",
"1\n",
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"-1\n",
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"-1\n",
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"-1\n",
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"-1\n",
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"1\n",
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"1\n",
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"1\n",
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"-1\n",
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]
}
|
A magic island Geraldion, where Gerald lives, has its own currency system. It uses banknotes of several values. But the problem is, the system is not perfect and sometimes it happens that Geraldionians cannot express a certain sum of money with any set of banknotes. Of course, they can use any number of banknotes of each value. Such sum is called unfortunate. Gerald wondered: what is the minimum unfortunate sum?
Input
The first line contains number n (1 ≤ n ≤ 1000) — the number of values of the banknotes that used in Geraldion.
The second line contains n distinct space-separated numbers a1, a2, ..., an (1 ≤ ai ≤ 106) — the values of the banknotes.
Output
Print a single line — the minimum unfortunate sum. If there are no unfortunate sums, print - 1.
Examples
Input
5
1 2 3 4 5
Output
-1
|
{
"inputs": [
"1 8\n2 8 81\n",
"2 30\n20 30 80\n3 9 85\n",
"4 319\n63 79 89\n79 97 91\n75 87 88\n75 90 83\n",
"2 98\n77 86 82\n17 21 91\n",
"50 1872\n45 85 93\n37 67 97\n62 77 83\n50 71 81\n59 62 84\n52 82 96\n67 73 96\n59 92 99\n33 66 96\n18 43 94\n4 82 96\n15 29 93\n47 87 84\n33 67 83\n78 99 88\n48 93 84\n19 74 98\n14 47 99\n23 87 88\n5 20 86\n12 39 94\n6 52 93\n14 89 94\n54 71 85\n43 52 97\n24 85 82\n11 13 95\n44 77 95\n63 100 84\n31 88 80\n18 96 90\n1 41 83\n65 87 91\n29 65 98\n23 73 83\n22 48 96\n19 62 89\n23 94 83\n47 92 97\n49 99 86\n16 94 80\n24 38 85\n85 88 96\n18 71 83\n26 64 95\n64 76 96\n48 72 80\n12 22 97\n1 68 90\n40 56 87\n",
"49 1595\n35 59 98\n19 20 89\n44 73 99\n9 85 93\n24 98 97\n37 73 98\n46 49 98\n50 89 99\n15 25 97\n37 96 96\n2 22 98\n11 83 87\n23 83 94\n8 45 99\n53 98 99\n4 96 96\n43 58 92\n53 74 94\n27 58 93\n15 98 96\n9 10 91\n35 90 95\n23 86 99\n30 99 92\n71 93 91\n18 28 99\n25 43 92\n33 40 98\n37 60 99\n36 62 91\n20 50 94\n57 97 94\n63 75 99\n73 91 96\n37 44 98\n29 63 96\n12 71 98\n4 47 97\n12 32 87\n2 68 98\n24 97 99\n21 74 93\n49 90 97\n6 70 96\n16 40 91\n35 81 99\n74 89 89\n3 28 99\n19 94 90\n",
"50 2355\n48 91 87\n49 89 98\n25 74 83\n30 86 88\n45 50 84\n19 39 86\n58 60 91\n13 84 89\n56 61 94\n1 50 94\n27 68 85\n66 75 93\n37 54 89\n79 89 94\n59 65 83\n2 3 85\n35 57 91\n19 80 96\n17 87 84\n2 61 90\n19 68 99\n32 51 95\n27 69 94\n22 58 90\n48 83 94\n15 27 97\n41 94 92\n37 39 86\n32 79 80\n16 37 87\n37 38 83\n41 59 87\n2 92 85\n23 45 80\n68 99 88\n56 67 81\n57 94 95\n4 63 99\n26 39 88\n66 67 96\n69 99 84\n22 92 84\n24 88 93\n17 35 84\n46 77 96\n34 57 87\n65 89 96\n10 31 96\n22 66 87\n50 93 85\n",
"49 1959\n29 38 99\n4 88 83\n3 64 83\n12 85 84\n44 84 88\n40 57 91\n23 63 95\n66 92 87\n10 50 96\n1 8 85\n10 86 85\n64 80 95\n6 38 85\n66 88 90\n19 94 84\n44 83 87\n28 63 87\n59 73 95\n59 80 86\n21 100 97\n58 96 84\n40 67 99\n52 73 90\n1 45 95\n19 32 96\n37 73 80\n3 81 85\n51 65 83\n5 88 85\n36 58 94\n30 59 84\n50 75 99\n24 49 94\n33 71 89\n41 46 92\n35 72 91\n2 43 85\n84 88 95\n15 71 84\n16 30 86\n51 66 84\n55 62 99\n4 91 95\n75 86 89\n7 13 90\n19 23 95\n72 88 82\n61 72 92\n42 91 93\n",
"30 1056\n11 72 80\n40 89 80\n8 35 80\n59 83 80\n33 48 80\n34 74 80\n79 93 80\n41 82 80\n34 38 80\n33 46 80\n31 83 80\n5 79 80\n52 53 80\n3 53 80\n40 43 80\n63 72 80\n20 72 80\n13 78 80\n45 93 80\n56 77 80\n29 95 80\n45 82 80\n53 86 80\n22 49 80\n25 95 80\n9 58 80\n4 61 80\n78 92 80\n70 86 80\n21 96 80\n",
"40 1766\n4 33 90\n23 88 91\n56 79 81\n3 80 94\n53 72 87\n75 79 92\n44 67 97\n18 40 99\n42 76 82\n51 75 83\n23 30 98\n66 86 96\n56 87 94\n26 62 82\n48 100 83\n37 66 97\n6 9 89\n90 100 81\n1 15 91\n22 76 98\n22 56 90\n26 56 93\n7 43 84\n78 79 81\n26 75 90\n28 92 99\n8 78 84\n3 76 87\n37 69 93\n46 83 97\n15 29 92\n18 29 93\n5 83 83\n78 89 88\n21 61 92\n80 83 84\n21 100 94\n1 61 87\n87 93 92\n67 100 98\n",
"45 1686\n66 99 98\n79 98 92\n54 92 97\n65 74 90\n27 54 87\n5 43 97\n1 89 85\n62 73 89\n28 69 89\n34 71 90\n43 71 90\n1 65 97\n56 63 87\n22 46 86\n75 84 87\n16 89 81\n58 83 81\n87 97 82\n12 61 88\n30 35 83\n9 93 89\n63 90 98\n26 50 85\n40 98 91\n21 55 96\n82 88 83\n36 81 91\n36 82 84\n26 88 86\n2 39 97\n21 91 92\n24 60 97\n20 73 89\n9 38 82\n36 81 95\n37 86 82\n63 89 86\n43 71 85\n33 38 90\n34 61 81\n6 8 94\n4 40 87\n7 77 95\n33 60 91\n55 97 93\n",
"5 318\n82 94 97\n22 66 82\n18 34 86\n31 71 87\n14 61 95\n",
"50 3561\n20 38 90\n42 46 85\n28 44 81\n9 94 97\n17 37 85\n25 41 80\n26 43 96\n56 61 88\n42 97 99\n44 66 93\n38 88 94\n59 78 89\n94 98 96\n19 87 84\n44 85 97\n50 82 80\n84 94 84\n49 74 93\n47 77 90\n37 45 84\n68 85 81\n50 78 96\n74 88 94\n57 86 96\n18 67 83\n48 91 93\n64 93 94\n3 16 85\n62 76 82\n51 99 94\n67 84 91\n29 77 88\n22 33 91\n26 68 89\n81 84 98\n38 76 94\n50 95 84\n85 96 96\n27 52 91\n36 81 97\n27 40 83\n34 49 95\n26 94 80\n49 83 94\n59 85 90\n58 82 89\n5 23 86\n44 48 86\n45 76 89\n11 81 98\n",
"48 1568\n13 90 98\n51 69 96\n8 59 89\n33 37 97\n51 84 92\n23 84 96\n39 96 96\n20 50 99\n37 94 99\n15 81 97\n77 91 98\n25 87 95\n26 38 83\n29 62 95\n26 89 94\n21 61 98\n66 70 95\n13 94 99\n46 56 99\n4 98 96\n10 73 99\n13 81 98\n14 36 96\n10 58 99\n69 77 97\n10 16 97\n20 45 97\n35 56 93\n64 88 94\n4 45 97\n15 99 97\n33 39 98\n51 100 97\n58 87 96\n70 98 96\n84 86 97\n47 68 97\n31 64 98\n29 88 95\n10 72 94\n32 86 95\n4 76 92\n52 65 92\n12 91 91\n22 42 95\n94 100 95\n18 96 99\n1 58 97\n",
"48 2407\n31 77 98\n29 32 95\n20 52 81\n65 95 85\n57 94 82\n16 78 99\n49 92 83\n16 61 80\n39 89 88\n3 7 81\n49 79 99\n40 83 85\n21 84 89\n21 65 84\n48 82 90\n46 74 84\n78 84 94\n31 50 91\n71 74 95\n8 90 91\n17 60 97\n92 94 99\n15 90 82\n9 10 94\n19 86 81\n26 86 94\n10 77 95\n46 64 93\n58 73 95\n31 87 95\n52 66 87\n4 60 93\n39 51 99\n47 97 95\n49 81 89\n6 68 89\n9 93 85\n20 25 98\n40 54 97\n19 85 80\n32 60 83\n29 65 83\n16 68 91\n31 37 95\n73 82 92\n51 53 98\n83 99 98\n17 98 89\n",
"29 903\n8 86 80\n28 72 80\n33 90 80\n7 72 80\n9 77 80\n16 26 80\n5 41 80\n46 90 80\n22 68 80\n16 81 80\n60 63 80\n30 79 80\n9 98 80\n13 16 80\n5 12 80\n16 82 80\n32 41 80\n46 83 80\n39 46 80\n38 69 80\n66 99 80\n64 81 80\n19 38 80\n34 37 80\n44 90 80\n55 68 80\n40 53 80\n78 86 80\n25 27 80\n",
"50 1705\n48 64 85\n7 10 82\n21 59 83\n14 91 83\n28 81 81\n24 95 80\n42 97 80\n8 28 80\n36 58 81\n59 65 87\n25 58 88\n1 94 89\n8 86 83\n55 97 81\n28 77 84\n15 30 91\n49 87 80\n73 94 82\n62 83 91\n3 65 82\n57 74 83\n59 75 91\n6 51 82\n21 85 87\n20 45 80\n76 100 86\n3 59 80\n59 98 80\n21 48 83\n89 93 81\n7 22 83\n10 27 81\n71 76 80\n45 75 82\n82 86 80\n4 30 90\n74 95 80\n26 45 82\n5 56 85\n1 33 81\n39 44 87\n12 23 89\n54 85 80\n11 86 86\n7 78 81\n14 79 81\n9 17 81\n42 96 84\n26 70 80\n25 87 93\n",
"50 50\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n",
"50 1686\n39 92 87\n8 21 88\n39 80 92\n28 62 88\n19 68 87\n43 53 99\n35 45 94\n13 80 85\n25 69 98\n56 98 93\n64 84 96\n5 69 86\n29 88 96\n12 92 96\n20 80 83\n80 100 83\n45 100 91\n15 66 94\n19 73 80\n34 74 85\n72 76 87\n21 35 94\n34 52 83\n10 69 87\n11 20 80\n6 44 95\n34 99 89\n30 74 92\n15 100 82\n71 90 84\n62 77 84\n6 66 87\n22 80 99\n63 95 80\n55 73 99\n24 34 83\n27 50 91\n7 44 85\n45 80 93\n72 97 91\n27 55 80\n20 61 87\n45 95 99\n27 71 99\n74 84 85\n15 93 91\n30 59 92\n55 57 80\n45 51 90\n33 43 97\n",
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"1 88\n77 88 96\n",
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"48 1976\n30 97 84\n80 81 84\n41 70 86\n23 57 80\n17 60 85\n36 48 81\n51 87 81\n38 85 81\n31 67 80\n11 40 96\n63 100 83\n4 67 82\n16 67 90\n45 97 80\n60 75 82\n5 95 84\n21 85 83\n4 14 81\n21 85 81\n32 39 80\n25 32 80\n34 79 83\n67 100 81\n28 46 80\n16 19 89\n32 94 80\n45 49 81\n3 37 82\n60 96 81\n32 68 88\n21 36 84\n76 95 81\n87 91 84\n58 60 82\n71 97 81\n9 15 81\n13 24 81\n32 87 83\n24 94 85\n33 56 81\n55 100 88\n11 40 82\n51 60 81\n52 78 84\n33 65 82\n84 99 81\n32 71 81\n67 72 87\n",
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"47 1676\n34 58 88\n8 96 98\n6 69 97\n89 98 97\n31 80 91\n49 62 82\n10 85 93\n39 90 88\n22 37 89\n50 52 91\n42 44 99\n30 89 92\n18 67 86\n4 47 83\n27 64 86\n4 22 95\n41 77 81\n65 96 89\n8 51 82\n53 66 83\n81 86 94\n38 50 95\n14 40 82\n26 56 99\n42 92 96\n32 84 96\n74 85 96\n44 63 95\n43 81 99\n26 60 80\n96 99 94\n42 93 98\n18 85 98\n14 36 88\n6 64 91\n8 92 94\n35 99 85\n39 85 88\n41 79 95\n17 68 99\n17 98 92\n40 81 80\n58 64 99\n1 36 90\n18 42 96\n41 77 95\n7 23 93\n",
"30 1591\n63 80 92\n47 90 96\n23 47 90\n34 40 83\n64 94 91\n48 87 99\n30 78 99\n29 68 88\n2 58 83\n86 96 82\n64 80 95\n68 97 80\n11 75 99\n52 70 87\n32 63 84\n55 76 86\n87 65 83\n71 81 98\n39 89 82\n34 86 99\n56 69 83\n2 17 89\n24 36 80\n22 23 88\n22 28 92\n71 92 85\n74 84 82\n1 44 97\n7 58 95\n18 26 93\n",
"50 1872\n45 85 93\n37 67 97\n62 154 83\n50 71 81\n59 62 84\n52 82 96\n67 73 96\n59 92 145\n33 66 96\n18 43 94\n4 82 96\n15 29 93\n47 87 84\n33 67 83\n78 99 88\n48 93 84\n19 74 98\n14 47 99\n23 87 88\n5 20 86\n12 39 94\n6 52 93\n14 89 94\n54 71 85\n43 52 97\n24 85 82\n11 13 95\n44 77 95\n63 100 84\n31 88 80\n18 96 90\n1 41 83\n65 87 91\n29 65 98\n23 73 83\n22 48 96\n19 62 89\n23 94 83\n47 92 97\n49 99 86\n16 94 80\n24 38 85\n85 88 96\n18 71 83\n26 64 95\n64 76 96\n48 72 80\n12 22 97\n1 68 90\n40 56 87\n",
"50 2355\n48 91 87\n49 89 98\n25 74 83\n30 86 88\n45 50 84\n19 39 86\n58 60 91\n13 84 89\n56 61 94\n1 50 94\n27 68 85\n66 75 93\n37 54 89\n79 89 94\n59 65 83\n2 4 85\n35 57 91\n19 80 96\n17 87 84\n2 61 90\n19 68 99\n32 51 95\n27 69 94\n22 58 90\n48 83 94\n15 27 97\n41 94 92\n37 39 86\n32 79 80\n16 37 87\n37 38 83\n41 59 87\n2 128 85\n23 45 80\n68 99 88\n56 67 81\n57 94 95\n4 63 99\n26 39 88\n66 67 96\n69 99 84\n22 92 84\n24 88 93\n17 35 84\n46 77 96\n34 57 87\n65 89 96\n10 31 96\n22 66 87\n50 93 85\n",
"49 1959\n29 38 99\n4 88 83\n3 64 83\n12 85 84\n44 84 88\n40 57 91\n23 63 95\n66 92 87\n10 50 96\n1 8 85\n10 86 85\n64 80 95\n6 38 85\n66 88 90\n19 94 84\n44 83 87\n28 63 87\n59 73 95\n59 80 86\n21 100 97\n58 96 84\n40 67 99\n52 73 90\n1 45 95\n19 32 96\n37 73 80\n3 81 85\n51 65 83\n5 88 85\n36 58 94\n30 59 84\n50 75 99\n24 49 94\n33 71 89\n41 46 92\n35 72 91\n2 43 85\n84 88 95\n15 71 14\n16 53 86\n51 66 84\n55 62 99\n4 91 95\n75 86 89\n7 13 90\n19 23 95\n72 88 82\n61 72 92\n42 91 93\n",
"30 1056\n11 72 80\n40 89 80\n8 35 80\n59 83 80\n33 48 80\n34 74 80\n79 93 80\n41 82 80\n34 38 80\n33 46 80\n31 83 80\n5 79 15\n52 53 80\n3 53 94\n40 43 80\n63 72 80\n20 72 80\n13 78 80\n45 93 80\n56 77 80\n29 95 80\n45 82 80\n53 86 80\n22 49 80\n25 95 80\n9 58 80\n4 61 80\n78 92 80\n70 86 80\n21 96 80\n",
"40 1766\n4 33 90\n23 88 91\n53 79 81\n3 80 94\n53 72 87\n75 79 92\n44 67 97\n18 40 99\n42 76 82\n51 75 83\n23 30 98\n66 86 96\n56 87 94\n26 62 82\n48 100 83\n37 66 97\n6 9 89\n90 100 81\n1 15 91\n22 76 98\n22 56 90\n26 56 93\n7 43 84\n78 79 81\n26 75 90\n28 92 99\n14 78 84\n3 76 87\n37 69 93\n46 83 97\n15 29 92\n18 29 93\n5 83 83\n78 89 88\n21 61 92\n80 83 84\n21 100 94\n1 61 87\n87 93 92\n67 100 98\n",
"45 1686\n66 99 98\n79 98 92\n54 92 97\n65 74 90\n27 54 87\n5 43 97\n1 89 85\n62 73 89\n28 69 89\n45 71 90\n43 71 90\n1 65 97\n56 63 87\n22 46 86\n75 84 87\n16 89 81\n58 83 81\n87 97 82\n12 61 88\n30 35 83\n9 93 89\n63 90 98\n26 50 85\n40 98 91\n21 55 96\n82 88 83\n36 81 91\n36 82 84\n26 88 86\n2 39 97\n21 91 92\n24 60 97\n20 73 89\n9 38 82\n36 81 95\n37 86 82\n63 89 86\n43 71 85\n33 38 90\n34 43 81\n6 8 94\n4 40 87\n7 77 95\n33 60 91\n55 97 93\n",
"5 318\n82 94 97\n22 66 53\n18 34 86\n31 71 87\n14 57 95\n",
"50 3561\n20 38 90\n42 46 85\n28 44 81\n9 94 97\n17 37 85\n30 41 80\n26 43 96\n56 61 88\n42 97 99\n44 66 93\n41 88 94\n59 78 89\n94 98 96\n19 87 84\n44 85 97\n50 82 80\n84 94 84\n49 74 93\n47 77 90\n37 45 84\n68 85 81\n50 78 96\n74 88 94\n57 86 96\n18 67 83\n48 91 93\n64 93 94\n3 16 85\n62 76 82\n51 99 94\n67 84 91\n29 77 88\n22 33 91\n26 68 89\n81 84 98\n38 76 94\n50 95 84\n85 96 96\n27 52 91\n36 81 97\n27 40 83\n34 49 95\n26 94 80\n49 83 94\n59 85 90\n58 82 89\n5 23 86\n44 48 86\n45 76 89\n11 81 98\n",
"48 2407\n31 77 98\n29 32 95\n20 52 81\n65 95 85\n57 94 82\n16 78 99\n49 92 83\n16 61 80\n39 89 88\n3 7 81\n49 79 99\n40 83 85\n21 84 89\n21 65 84\n48 82 90\n46 74 84\n78 84 94\n31 50 91\n71 74 95\n8 90 91\n17 60 97\n92 94 99\n15 90 82\n9 10 94\n19 86 81\n26 86 94\n15 77 95\n46 64 93\n58 73 95\n31 87 95\n52 66 87\n4 60 93\n39 51 99\n47 97 95\n49 81 89\n6 68 89\n9 93 85\n20 25 98\n51 54 97\n19 85 80\n32 60 83\n29 65 83\n16 68 91\n31 37 95\n73 82 92\n51 53 98\n83 99 98\n17 98 89\n",
"50 50\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n0 2 99\n1 2 94\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n1 2 99\n",
"49 2491\n23 66 96\n73 78 94\n27 57 94\n85 94 83\n11 55 81\n5 10 84\n19 97 90\n28 68 90\n10 31 89\n8 48 93\n57 84 97\n18 56 88\n21 43 95\n42 51 81\n36 89 90\n5 17 87\n23 97 95\n13 33 82\n38 81 86\n8 42 91\n22 26 85\n34 45 83\n70 100 96\n50 97 81\n1 70 98\n12 48 84\n56 89 88\n6 54 92\n36 52 94\n1 2 97\n39 85 92\n74 86 95\n10 20 90\n21 41 98\n35 58 83\n36 83 88\n34 62 99\n21 15 81\n6 23 89\n19 65 82\n16 50 88\n11 82 98\n33 55 88\n55 96 99\n89 91 91\n71 86 83\n40 44 88\n8 63 97\n75 91 94\n",
"46 2431\n4 48 83\n51 57 99\n18 46 97\n50 87 90\n50 81 92\n38 100 84\n49 77 81\n37 63 85\n25 26 93\n13 25 97\n47 80 85\n62 73 80\n39 90 90\n6 93 90\n87 96 96\n19 57 98\n8 43 96\n45 61 91\n23 84 96\n44 63 83\n62 87 80\n63 94 99\n6 7 81\n3 47 91\n6 71 80\n8 81 89\n9 19 97\n26 69 91\n23 35 85\n32 51 85\n1 30 87\n1 24 86\n30 55 87\n13 27 98\n19 24 84\n2 57 93\n48 29 92\n20 100 98\n57 100 96\n51 53 109\n74 93 90\n52 77 96\n9 31 94\n17 28 87\n38 95 98\n17 44 86\n",
"49 3344\n29 57 96\n12 66 89\n25 40 99\n48 98 94\n1 31 82\n51 93 87\n34 56 88\n25 65 97\n38 40 127\n24 25 83\n4 30 83\n84 96 83\n74 88 81\n13 58 85\n55 99 91\n40 99 88\n67 91 80\n6 74 96\n32 79 94\n37 84 99\n14 48 95\n44 57 99\n9 87 94\n33 56 96\n32 86 97\n0 7 84\n56 67 91\n61 77 94\n17 44 95\n48 62 97\n10 84 84\n4 91 83\n63 100 82\n20 94 95\n9 34 84\n54 69 80\n27 72 94\n39 43 80\n39 89 88\n15 83 80\n4 90 81\n18 90 96\n33 64 92\n53 67 98\n37 65 97\n24 54 92\n26 64 98\n30 71 97\n12 60 87\n",
"49 1952\n53 82 82\n50 53 86\n15 24 83\n34 63 81\n39 81 81\n3 37 83\n11 95 80\n37 41 83\n60 78 81\n88 92 81\n3 47 80\n15 45 85\n6 84 83\n63 71 84\n30 98 85\n1 16 81\n38 53 81\n53 70 83\n33 55 85\n1 41 82\n51 79 83\n28 99 82\n31 38 81\n60 62 86\n37 60 81\n29 60 80\n30 59 80\n24 69 81\n8 35 82\n44 89 82\n49 94 85\n22 47 81\n40 84 80\n86 90 10\n45 73 90\n24 27 81\n24 59 86\n68 98 87\n60 80 90\n6 54 91\n78 89 81\n4 24 85\n42 57 85\n13 98 86\n76 82 83\n20 57 86\n50 61 86\n30 85 86\n12 13 82\n",
"50 1630\n61 79 93\n4 21 96\n44 70 98\n9 60 95\n8 85 94\n94 98 96\n3 45 90\n17 36 94\n16 71 95\n41 68 90\n11 84 96\n5 28 99\n25 99 88\n40 54 99\n3 15 98\n33 64 98\n78 87 95\n28 30 99\n17 46 98\n25 77 98\n37 68 99\n10 67 98\n11 65 98\n28 92 99\n34 72 96\n44 89 97\n40 58 98\n73 93 94\n16 45 97\n32 45 98\n10 97 91\n26 30 94\n31 78 91\n24 74 98\n4 41 99\n51 66 97\n27 56 92\n4 58 97\n24 42 98\n44 55 92\n41 97 91\n52 55 92\n30 95 99\n73 98 95\n42 96 89\n51 60 99\n29 58 92\n29 77 93\n73 81 99\n77 89 99\n",
"10 371\n71 80 81\n26 90 97\n54 55 86\n7 17 38\n47 55 17\n27 61 80\n22 30 97\n20 41 82\n18 26 98\n54 100 84\n",
"35 1344\n13 45 78\n45 56 88\n41 69 83\n52 71 89\n95 96 88\n55 91 96\n52 81 94\n13 90 95\n26 98 84\n48 59 99\n39 86 97\n66 87 86\n33 81 96\n64 94 92\n57 68 81\n17 50 91\n54 57 89\n12 66 87\n27 61 90\n21 33 86\n45 90 95\n28 68 90\n19 83 85\n32 62 90\n20 58 94\n59 80 80\n14 93 84\n38 78 84\n40 84 85\n3 61 81\n33 62 85\n12 44 98\n26 85 91\n14 22 84\n15 76 89\n",
"47 1676\n34 58 88\n8 96 98\n6 69 97\n89 98 97\n31 80 91\n49 62 82\n10 85 93\n39 90 88\n22 37 89\n50 52 91\n42 44 99\n30 89 92\n18 67 86\n4 47 83\n27 64 86\n4 22 95\n41 77 81\n65 96 89\n8 51 82\n53 66 83\n81 86 94\n38 50 95\n14 40 82\n26 56 99\n42 92 96\n32 84 96\n74 85 96\n44 63 95\n43 81 99\n26 60 80\n96 99 94\n42 93 98\n18 85 98\n14 36 88\n6 64 91\n8 92 94\n35 99 85\n25 85 88\n41 79 95\n17 68 99\n17 98 92\n40 81 80\n58 64 99\n1 36 90\n18 42 96\n41 77 95\n7 23 93\n",
"30 1591\n63 80 92\n47 90 96\n23 47 90\n34 40 83\n64 94 91\n48 87 99\n30 78 99\n29 68 88\n2 58 83\n86 96 82\n64 80 95\n68 97 80\n11 75 99\n52 70 87\n32 63 84\n55 76 86\n87 65 83\n71 81 98\n39 89 82\n34 86 99\n56 69 83\n2 17 89\n24 36 80\n22 23 126\n22 28 92\n71 92 85\n74 84 82\n1 44 97\n7 58 95\n18 26 93\n",
"50 1872\n45 85 93\n37 67 97\n62 154 83\n50 71 81\n59 62 84\n52 82 96\n67 73 96\n59 92 145\n33 66 96\n18 43 94\n4 82 96\n15 29 93\n47 87 84\n33 67 83\n78 99 88\n48 93 84\n19 74 98\n14 47 99\n23 87 88\n5 20 86\n12 39 94\n6 52 93\n14 89 94\n54 71 85\n43 52 97\n24 85 82\n11 13 38\n44 77 95\n63 100 84\n31 88 80\n18 96 90\n1 41 83\n65 87 91\n29 65 98\n23 73 83\n22 48 96\n19 62 89\n23 94 83\n47 92 97\n49 99 86\n16 94 80\n24 38 85\n85 88 96\n18 71 83\n26 64 95\n64 76 96\n48 72 80\n12 22 97\n1 68 90\n40 56 87\n",
"50 2355\n48 91 87\n49 89 98\n25 74 83\n30 86 88\n45 50 84\n19 39 86\n58 60 91\n13 84 89\n56 61 94\n1 50 94\n27 68 85\n66 75 93\n37 54 89\n79 89 94\n59 65 83\n2 4 85\n35 57 91\n19 80 96\n17 87 84\n2 61 90\n19 68 99\n32 51 95\n27 69 94\n22 58 90\n48 83 94\n15 27 97\n41 94 92\n37 39 86\n32 79 80\n16 37 87\n37 38 83\n41 59 145\n2 128 85\n23 45 80\n68 99 88\n56 67 81\n57 94 95\n4 63 99\n26 39 88\n66 67 96\n69 99 84\n22 92 84\n24 88 93\n17 35 84\n46 77 96\n34 57 87\n65 89 96\n10 31 96\n22 66 87\n50 93 85\n",
"49 1959\n29 38 99\n4 88 83\n3 64 83\n12 85 84\n44 84 88\n40 57 91\n23 63 95\n66 92 87\n10 50 96\n1 8 85\n10 86 85\n64 80 95\n6 38 85\n66 88 90\n19 94 84\n44 83 87\n28 63 87\n59 73 95\n59 80 86\n21 100 97\n58 96 84\n40 67 99\n52 73 90\n1 45 95\n19 32 96\n37 73 80\n3 81 85\n51 65 83\n5 88 85\n36 105 94\n30 59 84\n50 75 99\n24 49 94\n33 71 89\n41 46 92\n35 72 91\n2 43 85\n84 88 95\n15 71 14\n16 53 86\n51 66 84\n55 62 99\n4 91 95\n75 86 89\n7 13 90\n19 23 95\n72 88 82\n61 72 92\n42 91 93\n",
"30 1056\n11 72 80\n40 89 80\n8 35 80\n59 83 80\n33 48 80\n34 74 80\n79 93 80\n41 82 80\n34 38 80\n33 85 80\n31 83 80\n5 79 15\n52 53 80\n3 53 94\n40 43 80\n63 72 80\n20 72 80\n13 78 80\n45 93 80\n56 77 80\n29 95 80\n45 82 80\n53 86 80\n22 49 80\n25 95 80\n9 58 80\n4 61 80\n78 92 80\n70 86 80\n21 96 80\n",
"40 1766\n4 33 90\n23 88 91\n53 79 81\n3 80 94\n53 72 87\n75 79 92\n44 67 97\n18 40 99\n42 76 82\n51 75 83\n23 30 98\n66 86 96\n56 87 94\n26 62 82\n48 100 83\n37 66 97\n6 9 89\n90 100 81\n0 15 91\n22 76 98\n22 56 90\n26 56 93\n7 43 84\n78 79 81\n26 75 90\n28 92 99\n14 78 84\n3 76 87\n37 69 93\n46 83 97\n15 29 92\n18 29 93\n5 83 83\n78 89 88\n21 61 92\n80 83 84\n21 100 94\n1 61 87\n87 93 92\n67 100 98\n",
"45 1686\n66 99 98\n79 98 92\n54 92 97\n65 74 90\n27 54 87\n5 43 97\n1 89 85\n62 73 89\n28 69 89\n45 71 90\n43 71 90\n1 65 97\n56 63 87\n22 46 86\n75 84 87\n16 129 81\n58 83 81\n87 97 82\n12 61 88\n30 35 83\n9 93 89\n63 90 98\n26 50 85\n40 98 91\n21 55 96\n82 88 83\n36 81 91\n36 82 84\n26 88 86\n2 39 97\n21 91 92\n24 60 97\n20 73 89\n9 38 82\n36 81 95\n37 86 82\n63 89 86\n43 71 85\n33 38 90\n34 43 81\n6 8 94\n4 40 87\n7 77 95\n33 60 91\n55 97 93\n",
"5 318\n82 94 97\n22 66 53\n18 34 86\n31 71 87\n14 57 58\n"
],
"outputs": [
"3.140000000\n",
"31.400000000\n",
"314.159265358\n",
"113.238048780\n",
"3431.473428359\n",
"1645.203067662\n",
"1881.705309654\n",
"1892.204605665\n",
"157713.051258640\n",
"1556.594340817\n",
"4951.041735762\n",
"185.070909438\n",
"2277.940000000\n",
"3099.044268005\n",
"1868.433644398\n",
"97375.561080652\n",
"11833.916905054\n",
"65.940474627\n",
"109887.704460502\n",
"1672.810000000\n",
"77.440000000\n",
"1538.000000000\n",
"1710.610000000\n",
"99849.074567181\n",
"2996.615458522\n",
"853.758957539\n",
"6119.656442952\n",
"542.054472685\n",
"4864.102213996\n",
"3343.345692954\n",
"2750.005780871\n",
"2482.339684472\n",
"1266.050072603\n",
"7286648.0144888312",
"15103188.157444097\n",
"9723361.7464834694",
"183.870204081",
"3482.329953486",
"1524.918623648",
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"1901.625840247",
"810191.652147333",
"1562.286491262",
"4707.341100615",
"197.832538387",
"2281.939999997",
"1873.184130767",
"52.634964742",
"122353.218675203",
"1672.090000000",
"1537.620000000",
"1707.249999998",
"100510.110947990",
"3042.705901708",
"6117.691002107",
"596.401033540",
"4090.351287117",
"2559.024228191",
"2801.828023209",
"1301.740933980",
"3167.535947515",
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"690418.060488296",
"1559.377639949",
"5439.989227042",
"197.632535821",
"2284.759999998",
"1883.856068694",
"53.242876736",
"1661.259999999",
"1533.380000000",
"1706.689999997",
"3029.750759051",
"6113.398858616",
"669.126758080",
"2563.028957121",
"2579.742285020",
"1301.360907731",
"3193.948264212",
"1876.819930082",
"2008.492096558",
"694256.597541530",
"1558.280320166",
"5466.989685852",
"213.563017905"
]
}
|
You're trying to set the record on your favorite video game. The game consists of N levels, which must be completed sequentially in order to beat the game. You usually complete each level as fast as possible, but sometimes finish a level slower. Specifically, you will complete the i-th level in either Fi seconds or Si seconds, where Fi < Si, and there's a Pi percent chance of completing it in Fi seconds. After completing a level, you may decide to either continue the game and play the next level, or reset the game and start again from the first level. Both the decision and the action are instant.
Your goal is to complete all the levels sequentially in at most R total seconds. You want to minimize the expected amount of time playing before achieving that goal. If you continue and reset optimally, how much total time can you expect to spend playing?
Input
The first line of input contains integers N and R <image>, the number of levels and number of seconds you want to complete the game in, respectively. N lines follow. The ith such line contains integers Fi, Si, Pi (1 ≤ Fi < Si ≤ 100, 80 ≤ Pi ≤ 99), the fast time for level i, the slow time for level i, and the probability (as a percentage) of completing level i with the fast time.
Output
Print the total expected time. Your answer must be correct within an absolute or relative error of 10 - 9.
Formally, let your answer be a, and the jury's answer be b. Your answer will be considered correct, if <image>.
Examples
Input
1 8
2 8 81
Output
3.14
Input
2 30
20 30 80
3 9 85
Output
31.4
Input
4 319
63 79 89
79 97 91
75 87 88
75 90 83
Output
314.159265358
Note
In the first example, you never need to reset. There's an 81% chance of completing the level in 2 seconds and a 19% chance of needing 8 seconds, both of which are within the goal time. The expected time is 0.81·2 + 0.19·8 = 3.14.
In the second example, you should reset after the first level if you complete it slowly. On average it will take 0.25 slow attempts before your first fast attempt. Then it doesn't matter whether you complete the second level fast or slow. The expected time is 0.25·30 + 20 + 0.85·3 + 0.15·9 = 31.4.
|
{
"inputs": [
"1\n0 10 0 10\n",
"2\n12 3 4 7\n1 15 9 1\n",
"2\n5 4 8 8\n4 12 14 0\n",
"10\n31181 6 72281 7\n65255 10 17867 2\n96212 8 32852 10\n69668 6 37236 1\n6031 7 61541 0\n12286 4 40227 2\n30573 9 36317 3\n97429 6 35399 9\n20907 5 19251 8\n86446 8 56301 10\n",
"10\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n",
"10\n3 86311 1 17635\n6 34036 8 37167\n4 53806 6 25588\n3 91425 4 86666\n6 50210 10 7332\n4 59721 10 697\n0 15949 2 66047\n0 68146 10 70354\n2 1075 0 23359\n5 48622 9 70531\n",
"2\n252323306 923185060 41887968 12082849\n956989832 311441362 23412620 77648740\n",
"10\n7 4 5 3\n6 7 10 1\n1 6 3 7\n3 4 6 0\n9 7 3 9\n9 1 10 10\n5 10 7 6\n8 5 1 9\n1 8 8 4\n7 5 9 4\n",
"4\n632771442 501825496 853869326 796417562\n250298560 151058732 702922596 492637085\n688226592 702784823 444110577 613300642\n809656720 636217627 270335668 655753596\n",
"10\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n",
"1\n618436682 429762104 387908221 774440069\n",
"2\n161177104 219082322 609600790 834825669\n28637550 764143871 832346520 978676472\n",
"1\n0 0 0 0\n",
"3\n90031019 712505278 263580537 367435742\n66829732 915548158 31385852 432626559\n510612253 671761432 753952282 230959195\n",
"7\n479456257 682467462 202838061 802929167\n133179116 541657110 703996842 253385760\n559317856 865639323 321812660 580155067\n723036605 467995973 911771109 838534160\n732332969 59715289 216696388 60573917\n515702466 655741352 105418444 651954316\n884987644 907866122 399463262 952777963\n",
"10\n31181 6 33890 7\n65255 10 17867 2\n96212 8 32852 10\n69668 6 37236 1\n6031 7 61541 0\n12286 4 40227 2\n30573 9 36317 3\n97429 6 35399 9\n20907 5 19251 8\n86446 8 56301 10\n",
"10\n1000000000 0 1100000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n",
"10\n3 86311 1 17635\n6 34036 8 37167\n4 53806 6 25588\n3 91425 4 86666\n6 13217 10 7332\n4 59721 10 697\n0 15949 2 66047\n0 68146 10 70354\n2 1075 0 23359\n5 48622 9 70531\n",
"2\n252323306 923185060 28480032 12082849\n956989832 311441362 23412620 77648740\n",
"10\n7 4 5 3\n6 7 10 1\n1 6 3 7\n3 4 6 0\n9 8 3 9\n9 1 10 10\n5 10 7 6\n8 5 1 9\n1 8 8 4\n7 5 9 4\n",
"4\n376789650 501825496 853869326 796417562\n250298560 151058732 702922596 492637085\n688226592 702784823 444110577 613300642\n809656720 636217627 270335668 655753596\n",
"10\n0 1000000000 0 1000000000\n0 1000001000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n",
"1\n356241850 429762104 387908221 774440069\n",
"1\n0 0 -1 0\n",
"3\n24066193 712505278 263580537 367435742\n66829732 915548158 31385852 432626559\n510612253 671761432 753952282 230959195\n",
"7\n479456257 682467462 202838061 802929167\n133179116 541657110 703996842 253385760\n829210948 865639323 321812660 580155067\n723036605 467995973 911771109 838534160\n732332969 59715289 216696388 60573917\n515702466 655741352 105418444 651954316\n884987644 907866122 399463262 952777963\n",
"1\n0 10 0 19\n",
"2\n5 4 0 8\n4 12 14 0\n",
"10\n31181 6 33890 7\n65255 10 17867 2\n96212 8 32852 10\n69668 6 37236 1\n6031 7 61541 0\n12286 4 40227 2\n30573 9 36317 1\n97429 6 35399 9\n20907 5 19251 8\n86446 8 56301 10\n",
"10\n1000000000 0 1100000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000001000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n",
"10\n3 86311 1 17635\n6 34036 8 37167\n1 53806 6 25588\n3 91425 4 86666\n6 13217 10 7332\n4 59721 10 697\n0 15949 2 66047\n0 68146 10 70354\n2 1075 0 23359\n5 48622 9 70531\n",
"2\n252323306 34213620 28480032 12082849\n956989832 311441362 23412620 77648740\n",
"10\n7 4 5 3\n6 7 10 1\n1 6 3 7\n3 4 6 0\n9 8 3 9\n9 1 10 10\n5 10 7 6\n8 5 1 9\n1 8 8 4\n7 5 9 1\n",
"4\n376789650 501825496 853869326 796417562\n250298560 151058732 702922596 492637085\n688226592 702784823 496307711 613300642\n809656720 636217627 270335668 655753596\n",
"3\n24066193 712505278 312128103 367435742\n66829732 915548158 31385852 432626559\n510612253 671761432 753952282 230959195\n",
"2\n12 1 1 7\n1 15 9 1\n",
"2\n5 4 0 2\n4 12 14 0\n",
"10\n31181 6 33890 7\n65255 10 17867 2\n96212 8 32852 10\n37797 6 37236 1\n6031 7 61541 0\n12286 4 40227 2\n30573 9 36317 1\n97429 6 35399 9\n20907 5 19251 8\n86446 8 56301 10\n",
"2\n252323306 34213620 28480032 4961058\n956989832 311441362 23412620 77648740\n",
"7\n479456257 926507357 202838061 802929167\n133179116 541657110 703996842 253385760\n829210948 865639323 321812660 580155067\n723036605 611918584 911771109 838534160\n732332969 59715289 216696388 60573917\n515702466 655741352 105418444 651954316\n884987644 907866122 399463262 952777963\n",
"1\n0 10 1 11\n",
"2\n12 1 1 5\n1 15 9 1\n",
"2\n5 4 0 3\n4 12 14 0\n",
"10\n31181 6 33890 7\n65255 10 17867 1\n96212 8 32852 10\n37797 6 37236 1\n6031 7 61541 0\n12286 4 40227 2\n30573 9 36317 1\n97429 6 35399 9\n20907 5 19251 8\n86446 8 56301 10\n",
"10\n3 86311 1 17635\n6 34036 11 37167\n1 53806 6 25588\n3 91425 4 86666\n6 13217 10 7332\n4 59721 10 697\n0 15949 2 66047\n0 68146 19 70354\n2 1075 0 23359\n5 48622 9 70531\n",
"2\n252323306 34213620 28480032 4961058\n956989832 311441362 39788809 77648740\n",
"10\n0 1000000000 0 1000000000\n0 1000001000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 1 1000000000\n0 1000000000 0 1000000000\n1 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000010\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n",
"3\n24066193 712505278 312128103 367435742\n66829732 915548158 31385852 432626559\n510612253 671761432 1306198318 291186445\n",
"10\n1000000000 0 1100000000 0\n1000000000 0 1000000011 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000001000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 1 1000000000 0\n",
"2\n12 3 1 7\n1 15 9 1\n",
"10\n0 1000000000 0 1000000000\n0 1000001000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000010\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n",
"1\n465051040 429762104 387908221 774440069\n",
"1\n0 -1 -1 0\n",
"7\n479456257 682467462 202838061 802929167\n133179116 541657110 703996842 253385760\n829210948 865639323 321812660 580155067\n723036605 611918584 911771109 838534160\n732332969 59715289 216696388 60573917\n515702466 655741352 105418444 651954316\n884987644 907866122 399463262 952777963\n",
"1\n0 10 0 11\n",
"10\n1000000000 0 1100000000 0\n1000000000 0 1000000010 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000001000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n",
"10\n3 86311 1 17635\n6 34036 11 37167\n1 53806 6 25588\n3 91425 4 86666\n6 13217 10 7332\n4 59721 10 697\n0 15949 2 66047\n0 68146 10 70354\n2 1075 0 23359\n5 48622 9 70531\n",
"10\n7 4 5 6\n6 7 10 1\n1 6 3 7\n3 4 6 0\n9 8 3 9\n9 1 10 10\n5 10 7 6\n8 5 1 9\n1 8 8 4\n7 5 9 1\n",
"4\n376789650 501825496 853869326 796417562\n250298560 151058732 702922596 492637085\n688226592 702784823 496307711 613300642\n809656720 636217627 181447617 655753596\n",
"10\n0 1000000000 0 1000000000\n0 1000001000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n1 1000000000 0 1000000000\n0 1000000000 0 1000000000\n0 1000000000 0 1000000010\n0 1000000000 0 1000000000\n0 1000000000 0 1000000000\n",
"1\n309156041 429762104 387908221 774440069\n",
"1\n0 -1 -1 1\n",
"3\n24066193 712505278 312128103 367435742\n66829732 915548158 31385852 432626559\n510612253 671761432 1306198318 230959195\n",
"10\n1000000000 0 1100000000 0\n1000000000 0 1000000011 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000001000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n1000000000 0 1000000000 0\n",
"10\n7 1 5 6\n6 7 10 1\n1 6 3 7\n3 4 6 0\n9 8 3 9\n9 1 10 10\n5 10 7 6\n8 5 1 9\n1 8 8 4\n7 5 9 1\n",
"4\n376789650 501825496 853869326 796417562\n250298560 84495039 702922596 492637085\n688226592 702784823 496307711 613300642\n809656720 636217627 181447617 655753596\n",
"1\n309156041 429762104 545314858 774440069\n",
"7\n479456257 926507357 202838061 802929167\n133179116 541657110 703996842 253385760\n829210948 865639323 321812660 580155067\n723036605 611918584 911771109 838534160\n732332969 59715289 216696388 60573917\n515702466 790149208 105418444 651954316\n884987644 907866122 399463262 952777963\n",
"2\n12 1 2 5\n1 15 9 1\n",
"2\n5 4 0 3\n4 5 14 0\n",
"10\n31181 6 33890 7\n65255 10 12781 1\n96212 8 32852 10\n37797 6 37236 1\n6031 7 61541 0\n12286 4 40227 2\n30573 9 36317 1\n97429 6 35399 9\n20907 5 19251 8\n86446 8 56301 10\n",
"10\n3 86311 1 17635\n6 34036 11 37167\n1 53806 6 25588\n3 91425 4 86666\n6 13217 10 7332\n4 59721 10 697\n0 15949 2 66047\n0 68146 19 70354\n2 1075 0 23359\n5 48622 9 114409\n"
],
"outputs": [
"-10",
"1",
"4",
"418488",
"10000000000",
"-382702",
"45134543",
"5",
"-104771122",
"-10000000000",
"-41853883",
"0",
"0",
"-535068510",
"-253460781",
"418488\n",
"10000000000\n",
"-353667\n",
"45134543\n",
"5\n",
"-104771122\n",
"-10000000000\n",
"-41853883\n",
"0\n",
"-535068510\n",
"-253460781\n",
"-10\n",
"1\n",
"418490\n",
"10000001000\n",
"-353670\n",
"934105983\n",
"8\n",
"-52573988\n",
"-486520944\n",
"2\n",
"7\n",
"409536\n",
"941227774\n",
"-434258188\n",
"-9\n",
"4\n",
"6\n",
"409537\n",
"-353658\n",
"957603963\n",
"-9999999999\n",
"-546748194\n",
"10000000999\n",
"0\n",
"-10000000000\n",
"-41853883\n",
"0\n",
"-253460781\n",
"-10\n",
"10000001000\n",
"-353667\n",
"5\n",
"-52573988\n",
"-10000000000\n",
"-41853883\n",
"0\n",
"-486520944\n",
"10000001000\n",
"5\n",
"-52573988\n",
"0\n",
"-434258188\n",
"4\n",
"6\n",
"409537\n",
"-353658\n"
]
}
|
Alice and Bonnie are sisters, but they don't like each other very much. So when some old family photos were found in the attic, they started to argue about who should receive which photos. In the end, they decided that they would take turns picking photos. Alice goes first.
There are n stacks of photos. Each stack contains exactly two photos. In each turn, a player may take only a photo from the top of one of the stacks.
Each photo is described by two non-negative integers a and b, indicating that it is worth a units of happiness to Alice and b units of happiness to Bonnie. Values of a and b might differ for different photos.
It's allowed to pass instead of taking a photo. The game ends when all photos are taken or both players pass consecutively.
The players don't act to maximize their own happiness. Instead, each player acts to maximize the amount by which her happiness exceeds her sister's. Assuming both players play optimal, find the difference between Alice's and Bonnie's happiness. That is, if there's a perfectly-played game such that Alice has x happiness and Bonnie has y happiness at the end, you should print x - y.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 100 000) — the number of two-photo stacks. Then follow n lines, each describing one of the stacks. A stack is described by four space-separated non-negative integers a1, b1, a2 and b2, each not exceeding 109. a1 and b1 describe the top photo in the stack, while a2 and b2 describe the bottom photo in the stack.
Output
Output a single integer: the difference between Alice's and Bonnie's happiness if both play optimally.
Examples
Input
2
12 3 4 7
1 15 9 1
Output
1
Input
2
5 4 8 8
4 12 14 0
Output
4
Input
1
0 10 0 10
Output
-10
|
{
"inputs": [
"2\n4 1\n1 2 5\n3 1 2\n3 4 3\n7 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 2\n4 7 3\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 10\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 4\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 10\n1 2 9\n3 9\n3 2 6\n2 1 15\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 4\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 10\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 5\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"2\n4 1\n1 2 5\n3 1 2\n3 4 3\n7 2\n1 2 5\n1 3 4\n1 4 3\n2 5 1\n2 6 2\n4 7 3\n",
"2\n4 1\n1 2 5\n3 1 2\n3 4 3\n7 2\n1 2 5\n1 3 8\n1 4 3\n2 5 1\n2 6 2\n4 7 3\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 9\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 4\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n7 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 2\n4 7 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n7 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 0\n4 7 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n5 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 0\n4 7 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n5 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 0\n4 1 3\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 10\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 4\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 2\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 10\n1 2 9\n3 9\n3 2 6\n2 1 15\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 4\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 5\n5 6 1\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 10\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 5\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 1\n2 3 9\n2 4 7\n5 6 1\n",
"2\n4 1\n1 2 5\n3 1 2\n3 4 3\n7 2\n1 2 5\n1 3 8\n2 4 3\n2 5 1\n2 6 2\n4 7 3\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 17\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 9\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 4\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"2\n4 1\n1 2 2\n3 1 2\n1 4 5\n1 2\n1 2 5\n1 3 4\n1 2 0\n2 5 1\n2 6 0\n4 1 3\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 10\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 5\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 2\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 5\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 9\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 4\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"2\n4 1\n1 2 2\n3 1 1\n3 4 3\n7 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 0\n4 7 6\n",
"2\n4 1\n1 2 5\n3 1 3\n3 4 0\n7 2\n1 2 5\n1 3 8\n2 4 3\n2 5 2\n2 6 2\n4 7 3\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 5\n3 6 5\n1 2 5\n2 6\n1 2 0\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 9\n1 2 9\n3 9\n3 2 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 4\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"2\n4 1\n1 2 5\n3 1 3\n3 4 0\n7 2\n1 2 5\n1 3 8\n2 4 3\n2 5 4\n2 6 2\n4 7 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n5 2\n1 2 5\n1 3 12\n1 4 2\n2 5 1\n2 6 0\n4 7 2\n",
"2\n4 1\n1 2 5\n3 1 3\n3 4 0\n7 2\n1 2 5\n1 3 8\n2 4 3\n2 5 4\n2 6 2\n4 7 6\n",
"2\n4 1\n1 2 1\n3 1 2\n3 4 5\n1 2\n1 2 3\n1 3 4\n1 1 2\n2 5 1\n2 6 0\n4 1 3\n",
"10\n9 3\n7 4 10\n6 8 1\n1 3 6\n2 4 10\n2 9 1\n5 4 9\n3 6 5\n1 2 5\n2 6\n1 2 2\n2 4\n1 2 8\n7 7\n4 3 2\n6 5 1\n3 2 3\n3 5 7\n7 1 10\n1 2 9\n3 9\n3 1 6\n2 1 8\n7 10\n1 5 9\n3 4 2\n1 3 6\n7 3 9\n3 6 3\n1 2 3\n6 3\n2 1 5\n4 2 10\n3 5 2\n3 1 5\n2 6 5\n1 2\n9 8\n4 7 7\n4 6 2\n2 9 9\n2 3 5\n5 3 3\n8 2 2\n2 1 1\n1 4 4\n7 4\n7 1 2\n1 2 8\n2 5 2\n2 3 9\n2 4 7\n5 6 1\n",
"2\n4 1\n1 2 5\n3 1 3\n3 4 3\n7 2\n1 2 5\n1 3 8\n1 4 3\n2 5 1\n2 6 2\n4 7 3\n",
"2\n4 1\n1 2 5\n3 1 3\n3 4 3\n7 2\n1 2 5\n1 3 8\n1 4 3\n2 5 2\n2 6 2\n4 7 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n5 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n1 2 5\n1 3 4\n1 4 0\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n1 2 5\n1 3 4\n1 2 0\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 1\n3 4 3\n7 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 6 0\n4 7 3\n",
"2\n4 1\n1 2 5\n3 1 3\n3 4 3\n7 2\n1 2 5\n1 3 8\n2 4 3\n2 5 2\n2 6 2\n4 7 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n5 2\n1 2 5\n1 3 7\n1 4 2\n2 5 1\n2 6 0\n4 7 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n5 2\n1 2 5\n1 3 4\n1 4 2\n2 5 1\n2 10 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n1 2 7\n1 3 4\n1 4 2\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n1 2 5\n1 3 4\n1 0 0\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n5 2\n1 2 5\n1 3 7\n1 4 2\n2 5 1\n2 6 0\n4 7 2\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n1 2 7\n1 3 4\n1 1 2\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n0 2 5\n1 3 4\n1 0 0\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 0\n3 1 2\n1 4 5\n1 2\n1 2 5\n1 3 4\n1 2 0\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n1 2 3\n1 3 4\n1 1 2\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 5\n1 2\n0 2 5\n1 2 4\n1 0 0\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 0\n3 1 2\n1 4 5\n1 2\n1 2 3\n1 3 4\n1 2 0\n2 5 1\n2 6 0\n4 1 3\n",
"2\n4 1\n1 2 2\n3 1 2\n3 4 3\n5 2\n1 2 5\n1 3 12\n1 4 3\n2 5 1\n2 6 0\n4 7 2\n"
],
"outputs": [
"8\n14\n",
"47\n2\n8\n32\n14\n32\n26\n0\n33\n29\n",
"47\n2\n8\n32\n21\n32\n26\n0\n33\n29\n",
"47\n2\n8\n32\n14\n32\n27\n0\n33\n29\n",
"8\n14\n",
"8\n18\n",
"47\n2\n8\n31\n14\n32\n26\n0\n33\n29\n",
"5\n14\n",
"5\n13\n",
"5\n10\n",
"7\n10\n",
"7\n0\n",
"47\n2\n8\n32\n14\n32\n26\n0\n34\n29\n",
"47\n2\n8\n32\n21\n32\n26\n0\n33\n27\n",
"47\n2\n8\n32\n14\n32\n27\n0\n33\n28\n",
"8\n19\n",
"55\n2\n8\n31\n14\n32\n26\n0\n33\n29\n",
"5\n0\n",
"47\n2\n8\n32\n14\n32\n27\n0\n34\n29\n",
"43\n2\n8\n31\n14\n32\n26\n0\n33\n29\n",
"5\n16\n",
"5\n19\n",
"43\n0\n8\n31\n14\n32\n26\n0\n33\n29\n",
"5\n20\n",
"5\n18\n",
"5\n23\n",
"6\n0\n",
"47\n2\n8\n32\n14\n32\n27\n0\n33\n29\n",
"8\n18\n",
"8\n18\n",
"5\n10\n",
"7\n0\n",
"7\n0\n",
"5\n13\n",
"8\n19\n",
"5\n13\n",
"5\n10\n",
"7\n0\n",
"7\n0\n",
"5\n13\n",
"7\n0\n",
"7\n0\n",
"5\n0\n",
"7\n0\n",
"7\n0\n",
"5\n0\n",
"5\n18\n"
]
}
|
You are given a weighted tree consisting of n vertices. Recall that a tree is a connected graph without cycles. Vertices u_i and v_i are connected by an edge with weight w_i.
Let's define the k-coloring of the tree as an assignment of exactly k colors to each vertex, so that each color is used no more than two times. You can assume that you have infinitely many colors available. We say that an edge is saturated in the given k-coloring if its endpoints share at least one color (i.e. there exists a color that is assigned to both endpoints).
Let's also define the value of a k-coloring as the sum of weights of saturated edges.
Please calculate the maximum possible value of a k-coloring of the given tree.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 5 ⋅ 10^5) – the number of queries.
The first line of each query contains two integers n and k (1 ≤ n, k ≤ 5 ⋅ 10^5) — the number of vertices in the tree and the number of colors to assign to each vertex, respectively.
Each of the next n - 1 lines describes an edge of the tree. Edge i is denoted by three integers u_i, v_i and w_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i, 1 ≤ w_i ≤ 10^5) — the labels of vertices it connects and the weight of the edge. It is guaranteed that the given edges form a tree.
It is guaranteed that sum of all n over all queries does not exceed 5 ⋅ 10^5.
Output
For each query print one integer — the maximum value of a k-coloring of the given tree.
Example
Input
2
4 1
1 2 5
3 1 2
3 4 3
7 2
1 2 5
1 3 4
1 4 2
2 5 1
2 6 2
4 7 3
Output
8
14
Note
The tree corresponding to the first query in the example:
<image>
One of the possible k-colorings in the first example: (1), (1), (2), (2), then the 1-st and the 3-rd edges are saturated and the sum of their weights is 8.
The tree corresponding to the second query in the example:
<image>
One of the possible k-colorings in the second example: (1, 2), (1, 3), (2, 4), (5, 6), (7, 8), (3, 4), (5, 6), then the 1-st, 2-nd, 5-th and 6-th edges are saturated and the sum of their weights is 14.
|
{
"inputs": [
"3 4\n2 2 1 3\n2 2 3 1\n\nSAMPLE",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"3 4\n2 2 1 3\n2 2 3 1\n\nSAMPLD",
"6 4\n2 2 1 3\n2 2 3 1\n\nSAMPLD",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 2860 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"3 4\n1 2 1 3\n2 2 3 1\n\nSAMPLD",
"6 4\n2 2 1 3\n2 3 3 1\n\nSAMPLD",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 28771 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 2860 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 95107 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"5 4\n1 2 1 3\n2 2 3 1\n\nSAMPLD",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 28771 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 2860 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 19828 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 95107 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 55334 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 28771 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 71327 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 2860 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 19828 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"3 2\n1 2 1 3\n2 1 1 1\n\nSAMPLE",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 95107 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 55334 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 61591 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 28771 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 71327 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 33181 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 2860 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 19828 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
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"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 38836 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"4 4\n1 2 1 3\n2 2 3 1\n\nSAMPLD",
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"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 4682 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 295 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"9 4\n4 2 1 3\n2 2 3 1\n\nSAMPLD",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 6383 95649 7061 57746 55403 1291 74784 62036 27277 24443 83242 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 2860 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 27536 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 38836 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 5771 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"4 4\n1 2 1 3\n2 2 3 2\n\nSAMPLD",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 289 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 95107 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 82393 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
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"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 4682 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 295 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 900 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"9 4\n4 2 1 3\n4 2 3 1\n\nSAMPLD",
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"9 4\n2 4 1 3\n1 6 3 1\n\nSAMPKD",
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"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 1578 6751 83149 67385 55181 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 48144 50589 70956 28019 35659 61552 26640 46269 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 95107 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 55334 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 17283 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 2386 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 12819 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 54564 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 61591 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 8192 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"15 4\n2 4 1 3\n1 6 3 1\n\nSAMPKD",
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"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 41970 39397 58255 82537 3650 28876 93078 72976 12227 11120 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 28556 48144 50589 70956 28019 35659 61552 26640 46269 2435 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 5904 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 4682 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3959 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 91449 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 96639 29499 44042 64988 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 35770 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 95456 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 17860 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 8425 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 295 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 27796 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 34803 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2009 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 900 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 7555 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732",
"100000 344\n9489 61424 27955 42780 24866 60662 35985 72602 7178 66039 20165 80878 65110 53338 89723 12426 82120 81954 27954 39397 58255 82537 3650 28876 93078 72976 12227 6751 83149 67385 30224 11174 57709 8346 76772 99593 37316 51065 36529 82364 8508 25414 90342 74569 42932 78768 50589 70956 28019 35659 36941 26640 15700 2434 47399 19824 35143 19360 92825 83873 1542 60698 14062 31689 3625 52999 62758 20553 90008 98356 49904 19558 24667 55606 28819 44251 34123 46986 32164 46794 72379 92492 70242 70819 37582 55567 97229 73952 7909 10408 73308 20879 3363 8275 66890 45383 46780 2618 88802 72673 86700 11258 64985 11954 3530 5184 94988 90014 74122 2789 27535 814 36555 50526 6438 65927 40060 33973 5748 3411 2516 42385 31516 84276 3341 90488 29125 71651 61191 35696 81982 17307 25609 79364 56155 29049 8188 81250 15343 85324 28341 58896 87729 20248 37305 70364 8152 8929 86572 32338 91959 63464 73495 69363 65183 35506 17041 85273 95253 18297 12286 87972 90232 29499 44042 38836 82848 46694 87332 77412 63362 20928 74400 51968 91877 7308 63451 44135 81213 45168 20718 17532 8998 42045 50911 5640 4743 98965 31335 57303 1574 83052 62222 24155 38985 28339 65540 43582 38352 66139 56691 56547 96464 46202 70916 39159 61482 63713 62049 17432 74879 13281 38124 77283 61604 74468 50297 71154 62882 69718 60751 30499 92323 88128 5358 24425 7762 56589 94460 26911 14751 60479 10569 86708 69630 3618 53913 82583 89940 94953 42919 58543 58116 26563 56507 52057 72669 8706 39303 94613 56073 17556 18298 97850 44866 51338 42616 28012 75627 80569 20511 23892 28026 76153 21027 71253 1736 25667 28651 85232 91247 33174 36096 47180 95700 34642 31321 22271 53722 65981 94641 66794 75869 42967 34922 85602 30294 63429 17626 89065 32433 19193 98019 29326 86889 13067 73688 20151 83598 14348 9734 60353 40291 57013 1946 59612 38731 60564 88412 37561 17317 1312 40492 6541 2046 85277 44397 24058 46511 26274 47209 31257 26106 22810 32824 71610 26053 37499 42864 85318 29123 31611 64491 30826 17238 40602 91027 13985 95813 35148 9800 23894 23438 39331 \n51712 68577 33412 86503 61390 63789 61543 54121 35999 9479 98415 37108 34850 8807 90782 65393 95201 58678 54913 76936 16336 21463 44060 57445 3826 21133 3401 95649 7061 57746 55403 1291 74784 62036 27277 24443 81362 89135 15523 80723 34105 27962 32413 31364 5594 68930 22704 83794 9301 83977 54254 25357 10152 23435 51437 31990 92871 1476 40512 81034 58570 15667 95235 12605 12150 98663 80209 87817 21487 84055 76784 40882 49312 34906 49023 23751 27859 72727 86013 81639 87332 34221 95973 62029 88137 88231 48273 83144 79539 51210 28990 76422 32606 12939 79159 85133 92632 34076 59094 17592 58404 61158 38328 53404 17016 61668 86879 1775 71477 13472 14127 98014 55190 72801 75619 21229 9952 48440 9081 57639 41786 41773 21554 94436 56099 35417 76588 60575 97094 39514 39273 7210 75793 68766 50922 30304 23029 71796 49250 98833 21077 22003 92914 717 10278 61511 94981 47362 55615 48790 33142 27891 98998 61974 52259 7342 55259 31599 87284 16376 73450 52916 84444 43526 2869 28099 74819 64523 12192 3251 19398 32979 20963 56825 37963 67402 69380 70345 10892 31397 75482 78650 60639 18912 68978 35834 72271 32248 16989 2292 11404 4065 86003 13311 69773 81352 48504 22166 94231 43545 86733 85333 58701 34954 71238 24434 68720 71825 44995 38427 93745 49444 51062 96514 31590 68892 26737 81587 89791 44997 68538 9775 73044 93621 33865 23403 79086 27674 95618 36468 86982 34101 78946 22966 47083 29898 14987 93714 48250 25181 12847 61405 7635 32164 26607 94027 2139 30300 83375 77843 5067 98128 6426 79696 88735 34025 50488 32323 37055 12663 13829 13857 260 35537 25887 70050 6624 45581 38716 85970 95047 27734 29964 22371 18962 75484 88711 43445 88092 76402 12440 46987 56627 65296 33055 73843 22950 83760 61560 54189 49507 29176 55087 72855 42999 83767 8573 5748 9020 5771 53127 49660 62970 63286 18364 91927 30686 5992 56881 98796 27087 59357 24306 81779 68467 60761 41156 47560 58755 59898 23914 17706 12573 14144 8352 42016 85054 97308 51097 69686 69507 3551 14022 45212 84496 70561 59912 1742 67885 48149 40763 64131 76087 23732"
],
"outputs": [
"4\n",
"17377022\n",
"17378902\n",
"4\n",
"8\n",
"17370581\n",
"17364886\n",
"3\n",
"9\n",
"17370227\n",
"17321747\n",
"7\n",
"17378651\n",
"17337567\n",
"17369201\n",
"2\n",
"17343371\n",
"17397837\n",
"17360949\n",
"17396522\n",
"17413709\n",
"17352997\n",
"17372136\n",
"17354743\n",
"17368709\n",
"5\n",
"17380354\n",
"17311628\n",
"17351989\n",
"17352182\n",
"17407606\n",
"17350300\n",
"17386037\n",
"17419907\n",
"17309814\n",
"17373288\n",
"10\n",
"17357725\n",
"17366925\n",
"6\n",
"17285782\n",
"17342135\n",
"17342792\n",
"17364896\n",
"17396222\n",
"17389232\n",
"17280511\n",
"17344290\n",
"12\n",
"17365417\n",
"17285679\n",
"17334485\n",
"17357053\n",
"17365546\n",
"17408857\n",
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|
After setting up the area and his toys. Chandu is up for playing his very first game. His first game is played on a N X N board with some initial stones placed on each cell. He can move each stone in all four direction i.e up,down, left or right. His target of the game is to move all stones to any one of the four corners in minimum moves (different stones can be moved to different corners).
Chandu seeks you again for his help. Your task is to write a program that tell the minimum number of moves given a particular state of board.
NOTE: One cell may contain more than one stones.
Input:
First line of input contains two integers N and K. Where, N X N is the size of the board and k is the no of stones present on the board. Then, two lines(x[] and y[]) follow each containing K integers where i\;th integer of first line and i\;th integer of second line represent the x-coordinate and y-coordinate of i\;th stone respectively. in short, (x[i], y[i]) is where i\;th stone is placed at.
Output:
Print the minimum number of moves required to move all stone to the corners.
Constraints:
1 ≤ N ≤ 10^6
1 ≤ k ≤ 10^5
SAMPLE INPUT
3 4
2 2 1 3
2 2 3 1
SAMPLE OUTPUT
4
Explanation
For the two stones lying on the 2,2 cell you can place any of them on any of the two unfilled corner in 2 moves each.
|
{
"inputs": [
"3\n0 0 1\n0 0 1\n1 1 0\n",
"4\n0 1 1 1\n1 0 1 1\n1 1 0 1\n1 1 1 0\n",
"3\n0 0 0\n0 0 1\n0 1 0\n",
"4\n0 0 1 0\n0 0 0 1\n1 0 0 0\n0 1 0 0\n",
"4\n0 0 0 1\n0 0 0 0\n0 0 0 1\n1 0 1 0\n",
"10\n0 0 0 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n",
"4\n0 0 1 0\n0 0 0 1\n1 0 0 0\n0 0 0 0\n",
"10\n0 0 1 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n",
"4\n0 0 1 0\n0 1 0 1\n1 0 0 0\n0 0 0 0\n",
"10\n0 0 1 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n",
"4\n0 0 1 0\n0 1 0 1\n1 0 0 0\n0 0 0 1\n",
"10\n0 0 1 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n",
"4\n-1 0 1 0\n0 1 0 1\n1 0 0 0\n0 0 0 1\n",
"10\n0 0 1 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 0 0\n0 0 0 0 0 0 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n",
"4\n-1 0 1 0\n0 2 0 1\n1 0 0 0\n0 0 0 1\n",
"10\n0 0 1 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 0 0\n0 0 0 0 0 0 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0 0 0\n",
"4\n-2 0 1 0\n0 2 0 1\n1 0 0 0\n0 0 0 1\n",
"10\n0 0 1 0 0 0 1 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 0 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0 0 0\n",
"4\n-2 0 1 0\n0 3 0 1\n1 0 0 0\n0 0 0 1\n",
"10\n0 0 1 0 0 0 1 0 0 0\n0 0 0 0 1 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 0 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 -1 0 0 0 0 0 0\n",
"4\n-2 0 1 0\n0 0 0 1\n1 0 0 0\n0 0 0 1\n",
"10\n0 0 1 0 0 0 1 0 0 0\n0 0 0 0 1 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 0 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"4\n-2 0 1 0\n0 0 0 1\n1 0 0 1\n0 0 0 1\n",
"10\n0 1 1 0 0 0 1 0 0 0\n0 0 0 0 1 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 0 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
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"10\n0 1 1 0 0 -1 1 0 0 0\n0 0 0 0 1 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"10\n0 1 1 0 0 -1 1 0 0 0\n0 0 0 0 1 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"10\n0 1 1 0 0 -1 1 0 0 0\n0 0 0 0 1 0 0 0 0 0\n0 0 0 1 0 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"10\n0 1 1 0 0 -1 1 0 0 0\n0 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"10\n0 1 1 0 0 -1 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n1 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"10\n0 1 1 0 0 -1 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0\n0 0 1 0 0 0 0 0 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"10\n0 1 1 0 0 -1 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0\n0 0 1 0 0 0 0 -1 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0\n0 0 1 0 0 0 0 -1 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 0 0 -2 0 0 0 0 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0\n0 0 1 0 0 0 0 -1 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 0 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 0 0 0 0\n0 0 1 0 0 0 0 -1 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 1 0 0 0\n0 0 1 0 0 0 0 -1 0 0\n0 0 -1 0 0 0 1 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 1 0 0 0\n0 0 1 0 0 0 0 -1 0 0\n0 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 1 0 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 0 1 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 1 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 0\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 1 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 1\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 0 -1 0 0\n",
"10\n0 1 1 0 0 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 1 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 1\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 -1 -1 0 0\n",
"10\n0 1 1 0 -1 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 1 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 1\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 -1 -1 0 0\n",
"10\n0 1 1 0 -1 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 1 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 2\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 -1 -1 0 0\n",
"10\n0 1 1 0 -1 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 2 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 0 0 0 2\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 -1 -1 0 0\n",
"10\n0 1 1 0 -1 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 2 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 0 0 0 1 -1 0 0 1\n2 0 0 0 0 0 1 0 0 2\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 -1 -1 0 0\n",
"10\n0 1 1 0 -1 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 2 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 -1 0 0 1 -1 0 0 1\n2 0 0 0 0 0 1 0 0 2\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 0 -2 0 0 -1 -1 0 0\n",
"10\n0 1 1 0 -1 -2 1 0 0 0\n1 0 0 0 1 0 0 0 0 0\n0 0 1 2 1 0 1 1 0 0\n0 0 1 0 0 0 0 -1 0 0\n-1 0 -1 0 0 0 0 0 1 0\n0 0 -1 0 0 1 -1 0 0 1\n2 0 0 0 0 0 1 0 0 2\n0 -1 0 0 0 0 0 0 0 0\n0 0 0 0 0 -1 0 0 0 0\n0 1 1 -2 0 0 -1 -1 0 0\n"
],
"outputs": [
"1\n",
"12\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
}
|
There are n points marked on the plane. The points are situated in such a way that they form a regular polygon (marked points are its vertices, and they are numbered in counter-clockwise order). You can draw n - 1 segments, each connecting any two marked points, in such a way that all points have to be connected with each other (directly or indirectly).
But there are some restrictions. Firstly, some pairs of points cannot be connected directly and have to be connected undirectly. Secondly, the segments you draw must not intersect in any point apart from the marked points (that is, if any two segments intersect and their intersection is not a marked point, then the picture you have drawn is invalid).
How many ways are there to connect all vertices with n - 1 segments? Two ways are considered different iff there exist some pair of points such that a segment is drawn between them in the first way of connection, but it is not drawn between these points in the second one. Since the answer might be large, output it modulo 109 + 7.
Input
The first line contains one number n (3 ≤ n ≤ 500) — the number of marked points.
Then n lines follow, each containing n elements. ai, j (j-th element of line i) is equal to 1 iff you can connect points i and j directly (otherwise ai, j = 0). It is guaranteed that for any pair of points ai, j = aj, i, and for any point ai, i = 0.
Output
Print the number of ways to connect points modulo 109 + 7.
Examples
Input
3
0 0 1
0 0 1
1 1 0
Output
1
Input
4
0 1 1 1
1 0 1 1
1 1 0 1
1 1 1 0
Output
12
Input
3
0 0 0
0 0 1
0 1 0
Output
0
|
{
"inputs": [
"8 3\n2 0\n7 0\n8 3\n",
"8 2\n2 0\n7 0\n",
"99999999 20\n3 100000000\n14 100000000\n22 100000000\n24 100000000\n31 100000000\n41 100000000\n46 100000000\n84 100000000\n94 100000000\n98 100000000\n99999912 100000000\n99999915 100000000\n99999916 100000000\n99999923 100000000\n99999935 100000000\n99999937 100000000\n99999954 100000000\n99999955 100000000\n99999979 100000000\n99999982 100000000\n",
"1 1\n1 2\n",
"10 10\n1 0\n2 0\n3 0\n4 0\n5 1\n6 2\n7 3\n8 2\n9 3\n10 4\n",
"3 2\n1 0\n3 0\n",
"100000000 1\n9783835 100000000\n",
"8 3\n2 0\n7 3\n8 0\n",
"9 2\n1 1\n9 3\n",
"50 10\n5 17\n7 15\n10 4\n15 11\n18 13\n21 15\n31 5\n34 13\n40 15\n49 16\n",
"1 1\n1 10\n",
"100000000 2\n1 2\n2 1\n",
"1 1\n1 100\n",
"10 1\n5 5\n",
"10000000 1\n10000000 0\n",
"100 2\n1 100\n2 1\n",
"100000000 1\n100000000 100000000\n",
"50 10\n1 42\n7 36\n16 40\n21 40\n26 39\n30 41\n32 41\n36 40\n44 37\n50 41\n",
"1 1\n1 5\n",
"100000000 2\n1 100000000\n100000000 100000000\n",
"9 2\n1 8\n9 11\n",
"100 50\n1 53\n3 51\n4 50\n6 48\n9 45\n12 48\n14 46\n16 48\n17 47\n19 49\n20 48\n22 46\n23 45\n24 44\n26 46\n27 47\n29 49\n32 52\n33 53\n35 55\n37 53\n40 50\n41 51\n43 53\n47 57\n50 60\n51 59\n52 60\n57 65\n59 63\n60 62\n61 61\n62 60\n64 62\n68 66\n70 64\n71 63\n73 65\n77 69\n79 67\n81 65\n83 63\n86 66\n88 68\n89 69\n91 67\n94 64\n95 63\n98 60\n100 58\n",
"100000000 2\n50000000 100000000\n50000001 100000000\n",
"100000000 1\n1 100000000\n",
"10 1\n4 16160172\n",
"10000 2\n3270 897970\n8270 899508\n",
"190877881 20\n3 100000000\n14 100000000\n22 100000000\n24 100000000\n31 100000000\n41 100000000\n46 100000000\n84 100000000\n94 100000000\n98 100000000\n99999912 100000000\n99999915 100000000\n99999916 100000000\n99999923 100000000\n99999935 100000000\n99999937 100000000\n99999954 100000000\n99999955 100000000\n99999979 100000000\n99999982 100000000\n",
"100000000 1\n5314198 100000000\n",
"8 3\n2 0\n7 0\n8 0\n",
"50 10\n5 17\n7 15\n10 4\n15 11\n18 13\n21 15\n39 5\n34 13\n40 15\n49 16\n",
"110000000 2\n1 2\n2 1\n",
"1 1\n1 000\n",
"10 1\n5 1\n",
"10000000 1\n10000000 1\n",
"100000001 1\n100000000 100000000\n",
"100000000 2\n1 100000000\n100000000 101000000\n",
"100000100 2\n50000000 100000000\n50000001 100000000\n",
"100000000 1\n1 110000000\n",
"10 1\n4 29243766\n",
"10001 2\n3270 897970\n8270 899508\n",
"110000000 2\n1 2\n2 2\n",
"101000100 2\n50000000 100000000\n50000001 100000000\n",
"14 1\n4 29243766\n",
"110000001 2\n1 2\n2 2\n",
"101000100 2\n50000000 100000000\n65663031 100010010\n",
"3 2\n2 0\n3 0\n",
"100000010 1\n9783835 100000000\n",
"10 1\n10 5\n",
"1 1\n1 7\n",
"100000000 2\n1 100000000\n100000000 100010000\n",
"100000000 2\n50000000 100000000\n50000001 100000001\n",
"100000000 1\n1 101000000\n",
"10 1\n4 7454604\n",
"101000000 1\n5314198 100000000\n",
"10 1\n5 29243766\n",
"10001 2\n4345 897970\n8270 899508\n",
"110000101 2\n1 2\n3 2\n",
"100010010 1\n9783835 100000000\n",
"10 1\n10 9\n",
"100000100 1\n1 101000000\n",
"10 1\n4 286960\n",
"101001000 1\n5314198 100000000\n",
"10001 2\n5719 897970\n8270 899508\n",
"101000100 2\n53809896 100000000\n93795066 100010010\n",
"4 1\n1 0\n",
"100010010 1\n9783835 100000100\n",
"10 1\n5 286960\n",
"100010010 1\n13722255 100000100\n",
"101101000 1\n100000000 100001000\n",
"000 2\n1 100\n2 1\n",
"100 2\n1 100\n4 1\n",
"10001 2\n3270 897970\n8270 1605287\n",
"100 2\n1 100\n4 0\n",
"101000100 2\n50000000 100000000\n50000001 100010000\n",
"110000001 2\n1 2\n3 2\n",
"101000100 2\n50000000 100000000\n50000001 100010010\n",
"1 1\n1 0\n",
"10 10\n1 0\n2 0\n3 0\n4 0\n5 1\n6 4\n7 3\n8 2\n9 3\n10 4\n",
"6 3\n2 0\n7 3\n8 0\n",
"9 2\n1 1\n9 4\n",
"101000000 1\n100000000 100000000\n",
"100 50\n1 53\n3 51\n4 50\n6 48\n9 45\n12 48\n14 46\n16 48\n17 47\n19 49\n20 48\n22 46\n23 45\n24 44\n26 46\n27 47\n29 49\n32 52\n33 53\n35 55\n37 53\n40 50\n41 51\n43 53\n47 57\n50 60\n51 40\n52 60\n57 65\n59 63\n60 62\n61 61\n62 60\n64 62\n68 66\n70 64\n71 63\n73 65\n77 69\n79 67\n81 65\n83 63\n86 66\n88 68\n89 69\n91 67\n94 64\n95 63\n98 60\n100 58\n",
"10000 2\n3270 897970\n8270 484536\n",
"8 3\n2 0\n7 0\n8 5\n",
"190877881 20\n3 100000000\n14 100000000\n22 100000000\n24 100000000\n31 100000000\n41 100100000\n46 100000000\n84 100000000\n94 100000000\n98 100000000\n99999912 100000000\n99999915 100000000\n99999916 100000000\n99999923 100000000\n99999935 100000000\n99999937 100000000\n99999954 100000000\n99999955 100000000\n99999979 100000000\n99999982 100000000\n",
"35 10\n5 17\n7 15\n10 4\n15 11\n18 13\n21 15\n39 5\n34 13\n40 15\n49 16\n",
"1 1\n1 001\n",
"001 2\n1 100\n2 1\n",
"100000100 2\n50000000 100000100\n50000001 100000000\n",
"101000100 2\n50000000 100010000\n50000001 100000000\n",
"10001 2\n6280 897970\n8270 1605287\n",
"101000100 2\n50000000 100000000\n93795066 100010010\n",
"101000100 2\n50000000 100000000\n65663031 100000010\n",
"2 1\n1 0\n",
"4 2\n2 0\n3 0\n",
"101100000 1\n100000000 100000000\n",
"100 50\n1 53\n3 51\n4 50\n6 48\n9 45\n12 48\n14 46\n16 48\n17 47\n19 49\n20 48\n22 46\n23 45\n24 44\n26 46\n27 47\n29 49\n32 52\n33 53\n35 55\n37 53\n40 50\n41 51\n43 53\n47 57\n50 60\n51 40\n52 60\n57 65\n59 63\n60 62\n61 61\n62 60\n64 62\n57 66\n70 64\n71 63\n73 65\n77 69\n79 67\n81 65\n83 63\n86 66\n88 68\n89 69\n91 67\n94 64\n95 63\n98 60\n100 58\n",
"100000000 2\n50000000 100000000\n50000001 100000101\n",
"10000 2\n1812 897970\n8270 484536\n",
"190877881 20\n3 100000000\n14 100000000\n22 100000000\n24 100000000\n31 100000000\n41 100100000\n46 100000000\n84 100000000\n94 100000000\n98 100000000\n99999912 100000000\n99999915 100000000\n99999916 100000000\n99999923 100000000\n12733231 100000000\n99999937 100000000\n99999954 100000000\n99999955 100000000\n99999979 100000000\n99999982 100000000\n",
"35 10\n5 17\n7 15\n10 4\n15 11\n18 13\n14 15\n39 5\n34 13\n40 15\n49 16\n",
"100000100 2\n50000000 100000100\n85471826 100000000\n",
"10 1\n6 29243766\n",
"001000100 2\n50000000 100010000\n50000001 100000000\n",
"10001 2\n6280 1571461\n8270 1605287\n",
"101000100 2\n50000000 000000000\n65663031 100000010\n",
"101101000 1\n100000000 100000000\n",
"100 50\n1 53\n3 51\n4 50\n6 48\n9 45\n12 48\n14 46\n16 48\n17 47\n19 49\n20 48\n22 46\n23 45\n24 44\n26 46\n27 47\n29 49\n32 59\n33 53\n35 55\n37 53\n40 50\n41 51\n43 53\n47 57\n50 60\n51 40\n52 60\n57 65\n59 63\n60 62\n61 61\n62 60\n64 62\n57 66\n70 64\n71 63\n73 65\n77 69\n79 67\n81 65\n83 63\n86 66\n88 68\n89 69\n91 67\n94 64\n95 63\n98 60\n100 58\n",
"10010 2\n1812 897970\n8270 484536\n",
"190877881 20\n3 100000000\n14 100000000\n22 100000000\n24 100000000\n31 100000000\n41 100100000\n46 000000000\n84 100000000\n94 100000000\n98 100000000\n99999912 100000000\n99999915 100000000\n99999916 100000000\n99999923 100000000\n12733231 100000000\n99999937 100000000\n99999954 100000000\n99999955 100000000\n99999979 100000000\n99999982 100000000\n",
"35 10\n5 17\n7 15\n10 4\n22 11\n18 13\n14 15\n39 5\n34 13\n40 15\n49 16\n",
"100000100 2\n50000000 100000100\n54463944 100000000\n",
"10001 2\n7513 1571461\n8270 1605287\n",
"100 50\n1 53\n3 51\n4 50\n6 48\n9 45\n12 48\n14 46\n16 48\n17 47\n19 49\n20 48\n22 46\n23 45\n24 44\n26 46\n27 47\n29 49\n32 59\n33 53\n35 55\n37 53\n40 50\n41 51\n43 53\n47 57\n50 60\n51 40\n78 60\n57 65\n59 63\n60 62\n61 61\n62 60\n64 62\n57 66\n70 64\n71 63\n73 65\n77 69\n79 67\n81 65\n83 63\n86 66\n88 68\n89 69\n91 67\n94 64\n95 63\n98 60\n100 58\n",
"10011 2\n1812 897970\n8270 484536\n",
"190877881 20\n3 100000000\n14 100000000\n22 100000000\n24 100000000\n31 100000000\n41 100100000\n46 000000000\n84 100000000\n94 100000000\n98 100000000\n99999912 100000000\n99999915 100000000\n99999916 100000000\n99999923 100000000\n23060190 100000000\n99999937 100000000\n99999954 100000000\n99999955 100000000\n99999979 100000000\n99999982 100000000\n",
"35 10\n5 17\n7 15\n10 4\n22 11\n17 13\n14 15\n39 5\n34 13\n40 15\n49 16\n",
"100000100 2\n50000000 100000100\n54463944 101000000\n"
],
"outputs": [
"IMPOSSIBLE",
"2",
"149999907",
"2",
"4",
"1",
"190216165",
"IMPOSSIBLE",
"6",
"IMPOSSIBLE",
"10",
"99999999",
"100",
"10",
"9999999",
"IMPOSSIBLE",
"199999999",
"42",
"5",
"149999999",
"13",
"69",
"149999999",
"199999999",
"16160178",
"901239",
"190877899\n",
"194685802\n",
"2\n",
"IMPOSSIBLE\n",
"109999999\n",
"0\n",
"6\n",
"10000000\n",
"199999999\n",
"150499999\n",
"150000099\n",
"209999999\n",
"29243772\n",
"901239\n",
"110000000\n",
"151000099\n",
"29243776\n",
"110000001\n",
"149999999\n",
"1\n",
"190216175\n",
"14\n",
"7\n",
"150004999\n",
"150000000\n",
"200999999\n",
"7454610\n",
"195685802\n",
"29243771\n",
"902314\n",
"110000100\n",
"190226175\n",
"18\n",
"201000099\n",
"286966\n",
"195686802\n",
"903688\n",
"153809895\n",
"3\n",
"190226275\n",
"286965\n",
"186287855\n",
"200000999\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"110000000\n",
"IMPOSSIBLE\n",
"0\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"6\n",
"199999999\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"1\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"149999999\n",
"149999999\n",
"1\n",
"1\n",
"199999999\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"150000099\n",
"29243771\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"199999999\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"150000099\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"IMPOSSIBLE\n",
"150000099\n"
]
}
|
A tourist hiked along the mountain range. The hike lasted for n days, during each day the tourist noted height above the sea level. On the i-th day height was equal to some integer hi. The tourist pick smooth enough route for his hike, meaning that the between any two consecutive days height changes by at most 1, i.e. for all i's from 1 to n - 1 the inequality |hi - hi + 1| ≤ 1 holds.
At the end of the route the tourist rafted down a mountain river and some notes in the journal were washed away. Moreover, the numbers in the notes could have been distorted. Now the tourist wonders what could be the maximum height during his hike. Help him restore the maximum possible value of the maximum height throughout the hike or determine that the notes were so much distorted that they do not represent any possible height values that meet limits |hi - hi + 1| ≤ 1.
Input
The first line contains two space-separated numbers, n and m (1 ≤ n ≤ 108, 1 ≤ m ≤ 105) — the number of days of the hike and the number of notes left in the journal.
Next m lines contain two space-separated integers di and hdi (1 ≤ di ≤ n, 0 ≤ hdi ≤ 108) — the number of the day when the i-th note was made and height on the di-th day. It is guaranteed that the notes are given in the chronological order, i.e. for all i from 1 to m - 1 the following condition holds: di < di + 1.
Output
If the notes aren't contradictory, print a single integer — the maximum possible height value throughout the whole route.
If the notes do not correspond to any set of heights, print a single word 'IMPOSSIBLE' (without the quotes).
Examples
Input
8 2
2 0
7 0
Output
2
Input
8 3
2 0
7 0
8 3
Output
IMPOSSIBLE
Note
For the first sample, an example of a correct height sequence with a maximum of 2: (0, 0, 1, 2, 1, 1, 0, 1).
In the second sample the inequality between h7 and h8 does not hold, thus the information is inconsistent.
|
{
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"4\n-1 0 010 60\n-1 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 50\n0 40 50 70\n7 40 100 113\n50 74 100 80\n0 70 50 120\n77 80 100 120\n0",
"4\n0 0 100 25\n0 33 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 67 50 134\n50 40 110 60\n50 60 100 80\n0 132 50 120\n50 80 101 164\n0",
"4\n-1 0 010 60\n-1 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 50\n0 40 50 70\n7 40 100 113\n50 74 100 80\n0 70 51 120\n77 80 100 120\n0",
"4\n0 0 100 25\n0 33 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 67 50 134\n50 40 100 60\n50 60 100 80\n0 132 50 120\n50 80 101 164\n0",
"4\n-1 0 010 60\n-1 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 1 100 50\n0 40 50 70\n7 40 100 113\n50 74 100 80\n0 70 51 120\n77 80 100 120\n0",
"4\n0 0 100 25\n0 33 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 67 50 134\n50 40 100 60\n50 60 100 80\n0 132 50 235\n50 80 101 164\n0",
"4\n-1 0 010 60\n-1 43 50 90\n50 60 100 90\n0 90 100 120\n6\n0 1 100 50\n0 40 50 70\n7 40 100 113\n50 74 100 80\n0 70 51 120\n77 80 100 120\n0",
"4\n0 0 100 25\n0 33 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 67 50 134\n50 18 100 60\n50 60 100 80\n0 132 50 235\n50 80 101 164\n0",
"4\n-1 0 010 60\n-1 43 50 90\n50 60 100 90\n0 90 100 120\n6\n0 1 100 50\n-1 40 50 70\n7 40 100 113\n50 74 100 80\n0 70 51 120\n77 80 100 120\n0",
"4\n0 0 100 25\n0 33 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 67 50 134\n50 18 100 60\n50 60 100 80\n0 132 50 235\n50 80 111 164\n0",
"4\n-1 0 010 60\n-1 43 50 90\n50 60 100 90\n0 90 100 120\n6\n0 1 100 50\n-1 40 50 70\n7 40 100 113\n50 74 100 80\n1 70 51 120\n77 80 100 120\n0",
"4\n0 0 100 25\n0 33 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 67 50 5\n50 18 100 60\n50 60 100 80\n0 132 50 235\n50 80 111 164\n0",
"4\n0 0 100 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 28 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0",
"4\n0 0 100 60\n0 60 79 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 67 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n61 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 40 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n77 80 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 100 40\n0 67 50 70\n50 30 100 60\n50 60 100 80\n0 70 50 120\n50 80 101 120\n0",
"4\n0 0 100 60\n0 20 65 90\n50 89 100 90\n0 90 100 120\n6\n0 0 100 40\n0 67 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 101 120\n0",
"4\n0 0 100 60\n0 60 50 90\n50 60 100 90\n0 90 000 120\n6\n0 1 100 40\n0 40 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n4 60 100 90\n0 90 100 120\n6\n0 0 100 58\n0 67 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0",
"4\n-1 0 100 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 110 40\n0 40 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n77 80 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n54 89 100 90\n0 90 100 120\n6\n0 0 100 40\n0 67 50 70\n50 40 110 60\n50 60 100 80\n0 70 50 120\n50 80 101 120\n0",
"4\n0 0 100 60\n0 60 50 90\n58 60 100 90\n0 90 000 120\n6\n0 0 100 40\n0 69 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0",
"4\n-1 0 110 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 40 50 98\n50 40 100 60\n50 60 100 80\n0 70 50 120\n77 80 100 120\n0",
"4\n0 1 100 60\n0 60 50 90\n50 89 100 90\n0 90 101 120\n6\n-1 0 100 40\n0 67 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n50 80 100 120\n0",
"4\n0 0 100 21\n0 60 50 90\n82 89 100 90\n0 90 100 120\n6\n0 0 100 40\n0 67 50 70\n50 40 110 60\n50 60 100 80\n0 70 50 120\n50 80 101 120\n0",
"4\n-1 0 110 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 -1 100 40\n0 40 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n106 80 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 100 55\n0 67 50 70\n50 40 100 60\n50 60 100 73\n0 70 50 120\n50 80 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 58\n-1 67 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 150\n50 80 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n50 89 100 90\n0 90 100 120\n6\n-1 0 100 10\n0 67 50 70\n50 40 100 60\n50 60 100 80\n0 70 84 120\n50 80 100 120\n0",
"4\n0 -1 100 60\n0 60 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 100 40\n-1 67 50 70\n50 40 110 60\n50 60 100 80\n0 70 50 120\n50 80 101 120\n0",
"4\n-1 0 010 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 -1 100 40\n0 40 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 120\n77 24 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n97 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 40 50 70\n50 40 100 60\n50 60 100 90\n1 70 50 120\n50 80 100 120\n0",
"4\n0 0 100 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 58\n-1 67 50 70\n50 40 100 60\n50 60 100 80\n0 9 50 120\n50 80 101 120\n0",
"4\n0 0 100 60\n0 60 50 90\n50 89 100 90\n0 109 100 120\n6\n-1 0 100 40\n0 67 50 70\n50 40 100 60\n50 60 100 80\n1 70 84 120\n50 80 100 120\n0",
"4\n0 0 101 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 58\n0 67 50 70\n50 40 100 60\n50 60 100 80\n0 70 50 177\n50 80 101 227\n0",
"4\n-1 0 010 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 -1 110 40\n0 40 50 70\n50 40 100 113\n50 60 100 80\n0 70 50 120\n77 80 100 120\n0",
"4\n0 0 100 17\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 58\n-1 67 50 70\n50 40 100 60\n50 60 100 80\n0 9 50 120\n50 80 110 120\n0",
"4\n-1 0 010 60\n0 60 50 90\n50 60 100 90\n0 90 100 120\n6\n0 -1 100 50\n0 40 60 70\n50 40 100 113\n50 60 100 80\n0 70 50 120\n77 80 100 120\n0",
"4\n0 0 100 60\n0 60 91 90\n50 60 100 90\n0 90 100 120\n6\n0 0 100 58\n-1 67 50 70\n24 40 100 60\n50 60 100 80\n0 9 50 120\n50 80 110 120\n0",
"4\n0 0 100 14\n0 76 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 67 50 70\n50 40 100 60\n50 60 100 80\n0 132 50 120\n50 80 101 120\n0",
"4\n-1 0 010 60\n-1 60 50 90\n46 60 100 90\n0 90 100 120\n6\n0 -1 100 50\n0 40 50 70\n50 40 100 113\n50 60 100 80\n0 70 50 120\n77 80 100 120\n0",
"4\n0 0 101 60\n0 60 50 90\n97 60 100 90\n0 90 100 120\n6\n0 0 100 40\n0 28 50 70\n50 40 100 60\n50 60 100 90\n1 70 50 120\n81 80 100 120\n0",
"4\n0 0 100 14\n0 76 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 67 50 93\n50 40 110 60\n50 60 100 80\n0 132 50 120\n50 80 101 164\n0",
"4\n0 0 101 60\n0 60 50 90\n97 60 100 90\n0 90 100 239\n6\n0 0 100 40\n0 28 50 70\n50 40 100 60\n50 60 100 90\n0 70 50 120\n128 80 100 120\n0",
"4\n-1 0 010 60\n-1 60 50 90\n50 60 101 90\n0 90 100 120\n6\n0 -1 100 50\n0 40 50 70\n7 40 100 113\n50 74 100 80\n0 70 50 120\n77 80 100 120\n0",
"4\n0 0 100 25\n0 33 50 90\n50 89 100 90\n0 90 100 120\n6\n0 0 000 40\n0 122 50 70\n50 40 110 60\n50 60 100 80\n0 132 50 120\n50 80 101 164\n0"
],
"outputs": [
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n5\n6\n3\n4\n",
"1\n2\n3\n4\n\n1\n3\n4\n5\n2\n6\n",
"1\n2\n3\n4\n\n1\n2\n5\n4\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n3\n5\n4\n6\n",
"1\n2\n3\n4\n",
"1\n2\n4\n3\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n5\n4\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n2\n1\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n",
"1\n2\n3\n4\n\n1\n2\n4\n5\n3\n6\n"
]
}
|
Yanagi is a high school student, and she is called "Hime" by her boyfriend who is a ninja fanboy. She likes picture books very much, so she often writes picture books by herself. She always asks you to make her picture book as an assistant. Today, you got asked to help her with making a comic.
She sometimes reads her picture books for children in kindergartens. Since Yanagi wants to let the children read, she wants to insert numbers to frames in order. Of course, such a task should be done by the assistant, you.
You want to do the task easily and fast, so you decide to write a program to output the order of reading frames based on the positions of the frames.
Write a program to print the number of order for each frame.
The comics in this problem satisfy the following rules.
The each comic is drawn on a sheet of rectangle paper. You can assume that the top side of the paper is on the x-axis. And you can assume that the right-hand side of the paper is on the y-axis. The positive direction of the x-axis is leftward. The positive direction of the y-axis is down direction. The paper is large enough to include all frames of the comic. In other words, no area in a frame is out of the paper.
The area of each frame is at least one. All sides of each frame are parallel to the x-axis or the y-axis. The frames can't overlap one another. However the frames may share the line of side.
You must decide the order to read K , where K is a set of frames, with the following steps.
Step 1:You must choose an unread frame at the right-most position in K.
If you find such frames multiple, you must choose the frame at the top position among them.
If you can't find any unread frames, you stop reading K.
The frame you chose is "Starting Frame".
In step 1, you assume that the position of a frame is the top-right point of the frame.
Step 2:You should draw a line from the right-bottom point of "Starting Frame" to leftward horizontally.
If the line touch the right-hand side of other frame, you should stop drawing.
If the line is on the side of other frame, you should not stop drawing.
If the line touch the edge of paper, you should stop drawing.
Step 3:The set of the unread frames which are above the line ( they may be the bottom-side on the line ) drawn at Step 2 is L.
And you should read L.
Step 4: Go back to Step 1.
Constraints
0 < n < 10
(x0i != x1i) and (y0i != y1i)
0 ≤ x0i , y0i , x1i , y1i ≤ 500
Input
The input consists of multiple datasets. The last dataset is followed by a line containing one zero. You don't have to process this data.
Each datasets is in the following format.
n
x01 y01 x11 y11
x02 y02 x12 y12
....
x0n y0n x1n y1n
All numbers of the datasets are integer. They are separated by a space. The first line of a dataset contains one integer. n is the number of frames of the comic. x0i , y0i , x1i , y1i are two non-neighboring points of i th frame in the line.
Output
Print n lines for each dataset. Print the number of order for ith frame in the ith line. And you should print blank line between the datasets.
Output format:
num1
num2
...
numi
...
numn
Example
Input
4
0 0 100 60
0 60 50 90
50 60 100 90
0 90 100 120
6
0 0 100 40
0 40 50 70
50 40 100 60
50 60 100 80
0 70 50 120
50 80 100 120
0
Output
1
2
3
4
1
2
4
5
3
6
|
{
"inputs": [
"10 3 5 2\n5 50\n7 60\n8 100\n2 2 5\n3\n1 3\n3\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 99\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 49 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 36\n84 58\n76 58\n1036 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 16 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 256\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 9 48\n3\n2 7 6\n2 12 16\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 49 42\n22 1\n306 25\n75 8\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 36\n84 47\n76 58\n1036 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 16 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 256\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 9 48\n3\n2 7 6\n2 12 16\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 85\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 172\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 12\n380 14\n449 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 61\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 49 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 39\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 36\n84 58\n76 58\n1036 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 16 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 256\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 9 48\n3\n2 7 6\n3 12 16\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 41\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n89 83\n25 85\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 35\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 63\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 10\n3\n2 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 13 49 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 39\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n3 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 36\n84 58\n76 58\n1036 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 16 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 6 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 256\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 9 48\n3\n2 7 6\n3 12 16\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 53\n294 58\n64 22\n380 14\n300 41\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 27\n78 46\n21 20\n60 74\n101 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 47\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 127\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 47\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 13 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n3 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 0\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 25\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 10 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 21\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 1\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 72\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 47\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 127\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 47\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 13 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 2\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n3 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 8\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 248\n1 28\n1 0\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 49 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 39\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n3 2 11\n0\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 0\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n161 46\n91 3\n39 87\n100 55\n294 58\n64 44\n380 22\n449 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n245 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 10 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 21\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 264\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 16\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 1\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 53\n294 58\n64 22\n380 14\n300 41\n143 79\n15 24\n2 40\n90 53\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n51 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 15\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 53\n143 79\n15 24\n2 40\n90 54\n323 21\n240 4\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 318\n3\n1 128\n1 340\n1 233\n1 198\n2 25 18\n1 108\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 32\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"919 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 8\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n24 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 248\n1 28\n1 0\n2 24 17\n3\n2 17 14\n2 2 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 53\n143 79\n15 24\n2 40\n90 54\n323 21\n240 4\n147 99\n289 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n5 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 318\n3\n1 128\n1 173\n1 233\n1 198\n2 25 18\n1 108\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 32\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"10 3 5 2\n5 50\n14 60\n8 100\n2 2 5\n3\n1 3\n3\n3\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 42\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 36\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 39\n1 570\n1 494\n2 11 25\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 27\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 99\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 47\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 63\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 27\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 342\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n449 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 12\n380 14\n449 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 21\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 589\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 13 37 42\n22 2\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 27\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n101 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 127\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 47\n3\n3\n3\n2 23 15\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 39\n84 47\n76 58\n1036 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 16 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 256\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 9 48\n3\n2 7 6\n2 12 16\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n3 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 27\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 342\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n2 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 0\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 233\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n449 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n245 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 248\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 -1\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 172\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 9\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 21\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 1\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 39\n84 47\n76 58\n978 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 16 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 256\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 9 48\n3\n2 7 6\n2 12 16\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 3\n89 83\n25 85\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n2\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 35\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n254 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 63\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 233\n1 198\n2 25 18\n1 108\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n161 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n449 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n245 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 8\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 248\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 172\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 239\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 9\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 49 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 39\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n3 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n3\n2 1 0\n2 1 0\n2 10 0\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 53\n294 58\n64 22\n380 14\n300 41\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n51 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 27\n78 46\n21 20\n60 74\n101 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 61\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 39\n84 47\n76 58\n978 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 16 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 256\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 8 48\n3\n2 7 6\n2 12 16\n",
"1444 13 37 42\n22 1\n306 25\n75 9\n132 1\n89 83\n25 85\n352 71\n646 37\n740 92\n88 19\n408 92\n208 93\n136 25\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 25\n2 2 11\n3\n1 456\n3\n1 840\n2 3 2\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 680\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 3\n2\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 233\n1 198\n2 25 18\n1 108\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 32\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n161 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 22\n449 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n245 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 16\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 10 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 21\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 253\n1 60\n3\n3\n3\n1 1190\n1 32\n1 570\n1 494\n2 11 16\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 1\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 53\n294 58\n64 22\n380 14\n300 41\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n51 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 15\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 39\n84 47\n76 58\n978 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 31 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 256\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 8 48\n3\n2 7 6\n2 12 16\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 318\n3\n1 128\n1 340\n1 233\n1 198\n2 25 18\n1 108\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 32\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 8\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n24 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 248\n1 28\n1 0\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n324 13\n220 17\n93 39\n84 47\n76 58\n978 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 31 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 147\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 8 48\n3\n2 7 6\n2 12 16\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 4\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 318\n3\n1 128\n1 340\n1 233\n1 198\n2 25 18\n1 108\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 32\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"919 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 8\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n24 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 248\n1 28\n1 0\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 10 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 21\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 264\n1 60\n3\n3\n3\n1 1190\n1 32\n0 570\n1 494\n2 11 16\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 4 0\n2 13 0\n3\n3\n3\n2 10 1\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"1444 18 45 31\n476 56\n176 31\n75 47\n810 56\n145 13\n220 17\n93 39\n84 47\n76 58\n978 79\n828 13\n138 20\n750 78\n90 3\n333 28\n442 97\n348 16\n130 36\n3\n1 144\n1 72\n1 210\n2 8 43\n1 95\n1 468\n1 580\n1 24\n2 16 93\n2 31 0\n2 14 1\n3\n1 260\n2 1 51\n2 5 5\n3\n1 48\n1 220\n1 504\n2 8 10\n1 925\n3\n3\n1 180\n1 156\n2 14 0\n2 11 5\n1 143\n3\n1 120\n1 147\n2 5 1\n2 1 2\n2 8 0\n3\n1 627\n2 9 9\n1 256\n1 360\n3\n2 8 48\n3\n2 7 6\n2 12 16\n",
"1444 13 10 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 21\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 264\n1 60\n3\n3\n3\n1 1190\n1 32\n0 570\n1 494\n2 11 16\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 299\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 7 0\n2 13 0\n3\n3\n3\n2 10 1\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 53\n143 79\n15 24\n2 40\n90 54\n323 21\n240 4\n147 99\n289 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 318\n3\n1 128\n1 340\n1 233\n1 198\n2 25 18\n1 108\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 32\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"919 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 8\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n24 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 248\n1 28\n1 0\n2 24 17\n3\n2 17 14\n2 2 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 48\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"1444 13 10 42\n22 1\n306 25\n75 9\n132 3\n651 83\n25 43\n352 71\n1220 37\n740 92\n88 19\n408 92\n208 93\n136 21\n2 11 59\n1 12\n2 5 21\n2 13 20\n1 66\n1 264\n1 60\n3\n3\n3\n1 1190\n1 32\n0 570\n1 494\n2 11 16\n2 2 10\n3\n1 456\n3\n1 840\n2 3 0\n3\n1 108\n2 13 4\n1 986\n3\n1 36\n1 265\n3\n1 780\n1 588\n2 2 8\n1 1308\n1 135\n3\n1 56\n3\n1 108\n2 7 0\n2 13 0\n3\n3\n3\n2 10 1\n3\n2 1 0\n2 1 0\n2 10 4\n3\n",
"484 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 53\n143 79\n15 24\n2 40\n90 54\n323 21\n240 4\n147 99\n289 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 318\n3\n1 128\n1 173\n1 233\n1 198\n2 25 18\n1 108\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 32\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"919 30 46 77\n18 74\n105 26\n242 24\n22 81\n78 46\n21 20\n60 74\n160 46\n91 3\n39 22\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 8\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n24 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 248\n1 28\n1 0\n2 24 17\n3\n2 17 14\n2 2 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 48\n2 13 8\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 27\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 99\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 128\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n187 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 18\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n",
"484 30 46 67\n51 74\n105 26\n242 24\n22 81\n48 46\n21 11\n60 74\n160 46\n91 3\n39 87\n100 55\n294 58\n64 22\n380 14\n300 33\n143 79\n15 24\n2 40\n90 54\n323 21\n240 6\n147 99\n311 16\n25 30\n88 32\n130 28\n49 98\n45 25\n14 41\n260 74\n1 144\n1 266\n3\n2 16 19\n1 121\n1 270\n1 28\n1 3\n2 24 17\n3\n2 17 14\n2 12 56\n3\n1 80\n1 126\n1 6\n2 19 0\n1 160\n3\n1 128\n1 340\n1 130\n1 198\n2 25 18\n1 80\n3\n1 45\n1 126\n1 30\n1 63\n3\n3\n1 52\n3\n3\n3\n3\n2 18 37\n2 13 4\n3\n2 25 7\n2 10 38\n3\n3\n3\n2 23 15\n"
],
"outputs": [
"55\n100\n50\n",
"0\n99\n98\n81\n74\n74\n61\n55\n54\n46\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n37\n8\n7\n0\n93\n6\n1\n0\n0\n0\n0\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n",
"0\n99\n98\n81\n74\n74\n61\n55\n54\n46\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n37\n8\n7\n0\n93\n6\n",
"0\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n74\n60\n55\n54\n46\n46\n33\n28\n26\n24\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n37\n8\n6\n0\n93\n6\n1\n0\n0\n0\n0\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n",
"92\n85\n62\n71\n37\n8\n7\n0\n93\n6\n",
"92\n62\n43\n71\n37\n9\n8\n0\n93\n6\n",
"0\n99\n98\n81\n74\n74\n63\n55\n54\n46\n46\n33\n28\n26\n24\n",
"92\n62\n43\n71\n37\n9\n8\n0\n93\n7\n",
"46\n172\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n63\n61\n55\n54\n46\n46\n33\n28\n26\n24\n",
"92\n44\n43\n71\n37\n8\n7\n0\n93\n6\n1\n0\n0\n0\n0\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n7\n",
"0\n99\n98\n81\n74\n74\n61\n55\n54\n46\n41\n28\n26\n24\n21\n",
"92\n85\n0\n71\n62\n37\n8\n7\n93\n6\n",
"0\n99\n98\n81\n74\n74\n60\n55\n54\n35\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n37\n9\n8\n93\n7\n",
"92\n44\n43\n71\n37\n7\n5\n0\n93\n17\n1\n0\n0\n0\n0\n",
"0\n79\n78\n56\n31\n28\n16\n8\n7\n7\n",
"0\n99\n98\n81\n74\n74\n61\n54\n53\n46\n41\n28\n26\n24\n21\n",
"0\n99\n98\n74\n74\n60\n55\n54\n46\n46\n33\n28\n27\n26\n24\n",
"0\n99\n98\n81\n74\n61\n55\n54\n47\n46\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n67\n37\n9\n0\n93\n6\n",
"0\n99\n98\n81\n74\n74\n55\n54\n54\n46\n46\n33\n28\n26\n24\n",
"92\n62\n43\n",
"0\n99\n98\n81\n74\n72\n61\n55\n54\n47\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n67\n37\n9\n0\n93\n15\n",
"46\n74\n21\n99\n98\n60\n55\n54\n46\n33\n28\n26\n24\n16\n14\n",
"92\n44\n43\n71\n37\n8\n7\n0\n93\n17\n1\n0\n0\n0\n0\n",
"0\n99\n98\n81\n74\n74\n63\n55\n54\n46\n46\n40\n33\n28\n26\n",
"43\n0\n0\n",
"0\n99\n98\n81\n74\n74\n61\n53\n53\n46\n41\n28\n26\n24\n21\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n53\n46\n28\n26\n24\n21\n",
"46\n74\n58\n99\n98\n60\n55\n54\n46\n33\n28\n24\n21\n16\n14\n",
"46\n99\n98\n81\n74\n60\n55\n54\n53\n46\n28\n26\n24\n21\n18\n",
"50\n100\n55\n",
"92\n43\n41\n71\n37\n8\n7\n0\n93\n6\n",
"46\n99\n98\n81\n74\n74\n60\n55\n46\n36\n33\n28\n26\n24\n21\n",
"92\n62\n43\n93\n71\n37\n19\n8\n1\n7\n",
"92\n62\n43\n71\n37\n8\n7\n0\n93\n6\n",
"92\n62\n43\n71\n37\n8\n7\n0\n93\n6\n",
"0\n99\n98\n81\n74\n74\n60\n55\n54\n46\n46\n33\n28\n26\n24\n",
"0\n99\n98\n81\n74\n74\n61\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n37\n8\n7\n0\n93\n6\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n74\n63\n55\n54\n46\n46\n33\n28\n26\n24\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n37\n9\n8\n0\n93\n7\n",
"0\n99\n98\n81\n74\n74\n63\n55\n54\n46\n46\n33\n28\n26\n24\n",
"92\n62\n43\n71\n37\n9\n8\n0\n93\n7\n",
"92\n62\n43\n71\n37\n8\n7\n0\n93\n6\n",
"92\n62\n43\n71\n37\n8\n7\n0\n93\n6\n",
"0\n99\n98\n81\n74\n74\n60\n55\n54\n46\n46\n33\n28\n26\n24\n",
"0\n99\n98\n81\n74\n74\n61\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n",
"92\n62\n43\n71\n37\n9\n8\n0\n93\n6\n",
"92\n62\n43\n71\n37\n8\n7\n0\n93\n6\n",
"0\n99\n98\n81\n74\n74\n63\n55\n54\n46\n46\n33\n28\n26\n24\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n74\n63\n55\n54\n46\n46\n33\n28\n26\n24\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n37\n9\n8\n0\n93\n7\n",
"46\n172\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"92\n62\n43\n71\n37\n9\n8\n0\n93\n7\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n",
"92\n85\n0\n71\n62\n37\n8\n7\n93\n6\n",
"0\n99\n98\n81\n74\n74\n60\n55\n54\n35\n33\n28\n26\n24\n21\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n74\n63\n55\n54\n46\n46\n33\n28\n26\n24\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"46\n172\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"92\n44\n43\n71\n37\n7\n5\n0\n93\n17\n1\n0\n0\n0\n0\n",
"0\n99\n98\n81\n74\n74\n61\n54\n53\n46\n41\n28\n26\n24\n21\n",
"0\n99\n98\n74\n74\n60\n55\n54\n46\n46\n33\n28\n27\n26\n24\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n",
"92\n85\n0\n71\n62\n37\n8\n7\n93\n6\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n74\n63\n55\n54\n46\n46\n33\n28\n26\n24\n",
"92\n62\n43\n",
"0\n99\n98\n81\n74\n74\n61\n54\n53\n46\n41\n28\n26\n24\n21\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"46\n74\n21\n99\n98\n60\n55\n54\n46\n33\n28\n26\n24\n16\n14\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n",
"46\n74\n21\n99\n98\n60\n55\n54\n46\n33\n28\n26\n24\n16\n14\n",
"43\n0\n0\n",
"0\n79\n78\n56\n31\n28\n17\n16\n8\n",
"43\n0\n0\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n53\n46\n28\n26\n24\n21\n",
"46\n74\n58\n99\n98\n60\n55\n54\n46\n33\n28\n24\n21\n16\n14\n",
"43\n0\n0\n",
"46\n99\n98\n81\n74\n74\n60\n55\n54\n53\n46\n28\n26\n24\n21\n",
"46\n74\n58\n99\n98\n60\n55\n54\n46\n33\n28\n24\n21\n16\n14\n",
"0\n99\n98\n81\n74\n74\n61\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n74\n61\n55\n54\n46\n33\n28\n26\n24\n21\n",
"0\n99\n98\n81\n74\n74\n60\n55\n54\n46\n33\n28\n26\n24\n21\n"
]
}
|
Rainbow built h cells in a row that are numbered from 1 to h from left to right. There are n cells with treasure. We call each of these n cells "Treasure Cell". The i-th "Treasure Cell" is the ai-th cell and the value of treasure in it is ci dollars.
Then, Freda went in the first cell. For now, she can go just k cells forward, or return to the first cell. That means Freda was able to reach the 1st, (k + 1)-th, (2·k + 1)-th, (3·k + 1)-th cells and so on.
Then Rainbow gave Freda m operations. Each operation is one of the following three types:
1. Add another method x: she can also go just x cells forward at any moment. For example, initially she has only one method k. If at some moment she has methods a1, a2, ..., ar then she can reach all the cells with number in form <image>, where vi — some non-negative integer.
2. Reduce the value of the treasure in the x-th "Treasure Cell" by y dollars. In other words, to apply assignment cx = cx - y.
3. Ask the value of the most valuable treasure among the cells Freda can reach. If Freda cannot reach any cell with the treasure then consider the value of the most valuable treasure equal to 0, and do nothing. Otherwise take the most valuable treasure away. If several "Treasure Cells" have the most valuable treasure, take the "Treasure Cell" with the minimum number (not necessarily with the minimum number of cell). After that the total number of cells with a treasure is decreased by one.
As a programmer, you are asked by Freda to write a program to answer each query.
Input
The first line of the input contains four integers: h (1 ≤ h ≤ 1018), n, m (1 ≤ n, m ≤ 105) and k (1 ≤ k ≤ 104).
Each of the next n lines contains two integers: ai (1 ≤ ai ≤ h), ci (1 ≤ ci ≤ 109). That means the i-th "Treasure Cell" is the ai-th cell and cost of the treasure in that cell is ci dollars. All the ai are distinct.
Each of the next m lines is in one of the three following formats:
* "1 x" — an operation of type 1, 1 ≤ x ≤ h;
* "2 x y" — an operation of type 2, 1 ≤ x ≤ n, 0 ≤ y < cx;
* "3" — an operation of type 3.
There are at most 20 operations of type 1. It's guaranteed that at any moment treasure in each cell has positive value. It's guaranteed that all operations is correct (no operation can decrease the value of the taken tresure).
Please, do not use the %lld specifier to read 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Output
For each operation of type 3, output an integer indicates the value (in dollars) of the most valuable treasure among the "Treasure Cells" Freda can reach. If there is no such treasure, output 0.
Examples
Input
10 3 5 2
5 50
7 60
8 100
2 2 5
3
1 3
3
3
Output
55
100
50
Note
In the sample, there are 10 cells and 3 "Treasure Cells". The first "Treasure Cell" is cell 5, having 50 dollars tresure in it. The second "Treasure Cell" is cell 7, having 60 dollars tresure in it. The third "Treasure Cell" is cell 8, having 100 dollars tresure in it.
At first, Freda can only reach cell 1, 3, 5, 7 and 9. In the first operation, we reduce the value in the second "Treasure Cell" from 60 to 55. Then the most valuable treasure among the "Treasure Cells" she can reach is max(50, 55) = 55. After the third operation, she can also go 3 cells forward each step, being able to reach cell 1, 3, 4, 5, 6, 7, 8, 9, 10. So the most valuable tresure is 100.
Noticed that she took the 55 dollars and 100 dollars treasure away, so the last answer is 50.
|
{
"inputs": [
"2 10\n1 2\n1 9\n8 7",
"2 10\n1 2\n1 9\n6 7",
"2 10\n2 2\n1 9\n10 7",
"1 10\n1 2\n1 9\n8 7",
"2 10\n1 2\n1 9\n10 7",
"2 20\n2 2\n1 9\n10 7",
"2 10\n3 2\n1 9\n10 7",
"1 10\n1 2\n0 9\n8 7",
"2 11\n2 2\n1 9\n10 7",
"2 13\n3 2\n1 9\n10 7",
"1 10\n1 0\n0 9\n8 7",
"2 14\n2 2\n1 9\n10 7",
"2 13\n3 2\n1 18\n10 7",
"1 13\n1 0\n0 9\n8 7",
"1 14\n2 2\n1 9\n10 7",
"2 13\n3 2\n1 18\n17 7",
"1 11\n2 2\n1 9\n10 7",
"1 11\n2 2\n1 9\n0 7",
"1 17\n2 2\n1 9\n0 7",
"1 17\n2 2\n1 15\n0 7",
"1 17\n2 2\n1 15\n-1 7",
"1 17\n4 2\n1 15\n-1 7",
"1 17\n4 2\n0 15\n-1 7",
"1 17\n4 2\n-1 15\n-1 7",
"1 24\n4 2\n-1 15\n-1 7",
"1 24\n4 4\n-1 15\n-1 7",
"1 24\n4 8\n-1 15\n-1 7",
"2 24\n4 8\n-1 15\n-1 7",
"2 24\n4 8\n-1 3\n-1 7",
"2 24\n4 9\n-1 3\n-1 7",
"2 24\n4 9\n-1 3\n-2 7",
"2 45\n4 9\n-1 3\n-2 7",
"2 45\n4 9\n-1 4\n-2 7",
"2 45\n4 15\n-1 4\n-2 7",
"2 45\n4 10\n-1 4\n-2 7",
"2 10\n1 2\n1 8\n8 7",
"2 10\n2 2\n1 9\n3 7",
"1 10\n1 2\n2 9\n8 7",
"2 20\n3 2\n1 9\n10 7",
"1 10\n2 2\n0 9\n8 7",
"2 11\n2 2\n2 9\n10 7",
"1 10\n1 0\n0 11\n8 7",
"2 14\n2 2\n2 9\n10 7",
"2 13\n4 2\n1 18\n10 7",
"1 8\n1 0\n0 9\n8 7",
"2 13\n3 2\n1 1\n17 7",
"1 11\n2 2\n1 9\n13 7",
"1 9\n2 2\n1 9\n0 7",
"1 17\n2 1\n1 9\n0 7",
"1 17\n1 2\n1 15\n0 7",
"1 17\n2 3\n1 15\n-1 7",
"2 17\n4 2\n1 15\n-1 7",
"1 17\n4 2\n0 15\n-1 13",
"1 17\n4 4\n-1 15\n-1 7",
"1 24\n4 2\n0 15\n-1 7",
"1 24\n4 4\n-1 15\n-2 7",
"1 24\n4 8\n-1 15\n-1 5",
"2 24\n4 8\n-1 6\n-1 7",
"2 24\n4 13\n-1 3\n-1 7",
"2 24\n4 2\n-1 3\n-1 7",
"2 24\n4 9\n-1 3\n-4 7",
"2 88\n4 9\n-1 4\n-2 7",
"2 45\n4 26\n-1 4\n-2 7",
"2 45\n4 10\n-1 4\n-2 9",
"2 10\n1 2\n0 8\n8 7",
"2 10\n3 2\n1 9\n3 7",
"1 10\n0 2\n0 9\n8 7",
"2 20\n3 2\n1 15\n10 7",
"2 11\n2 2\n2 14\n10 7",
"1 10\n1 0\n0 11\n6 7",
"2 13\n8 2\n1 18\n10 7",
"2 13\n3 2\n1 1\n17 0",
"1 11\n2 2\n1 9\n13 9",
"1 9\n2 0\n1 9\n0 7",
"1 17\n2 1\n1 9\n1 7",
"1 17\n1 2\n1 15\n-1 7",
"1 17\n2 3\n0 15\n-1 7",
"2 17\n4 2\n0 15\n-1 7",
"1 17\n8 2\n0 15\n-1 7",
"1 17\n4 4\n0 15\n-1 7",
"1 43\n4 2\n0 15\n-1 7",
"1 24\n4 4\n0 15\n-2 7",
"1 38\n4 8\n-1 15\n-1 5",
"2 24\n4 8\n-1 6\n-1 0",
"2 24\n3 13\n-1 3\n-1 7",
"2 48\n4 2\n-1 3\n-1 7",
"2 24\n4 9\n-1 3\n-4 2",
"2 175\n4 9\n-1 4\n-2 7",
"2 45\n4 26\n-1 4\n-2 9",
"2 10\n1 2\n0 8\n5 7",
"2 10\n3 2\n1 9\n3 4",
"2 20\n3 3\n1 15\n10 7",
"2 11\n3 2\n2 14\n10 7",
"2 13\n8 4\n1 18\n10 7",
"2 13\n6 2\n1 1\n17 0",
"1 11\n2 2\n1 9\n9 9",
"1 17\n2 1\n1 9\n1 0",
"1 17\n1 2\n1 29\n-1 7",
"2 17\n4 2\n0 13\n-1 7",
"1 17\n8 2\n0 15\n-1 8",
"1 17\n1 4\n0 15\n-1 7"
],
"outputs": [
"2\n1",
"2\n1\n",
"1\n0\n",
"1\n",
"2\n1\n",
"1\n0\n",
"1\n0\n",
"1\n",
"1\n0\n",
"1\n0\n",
"1\n",
"1\n0\n",
"1\n0\n",
"1\n",
"1\n",
"1\n0\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"2\n1\n",
"1\n0\n",
"1\n",
"1\n0\n",
"1\n",
"1\n0\n",
"1\n",
"1\n0\n",
"1\n0\n",
"1\n",
"1\n0\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n0\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"2\n1\n",
"1\n0\n",
"1\n",
"1\n0\n",
"1\n0\n",
"1\n",
"1\n0\n",
"1\n0\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n0\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"2\n1\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n0\n",
"1\n",
"1\n",
"1\n",
"1\n0\n",
"1\n",
"1\n"
]
}
|
H: Colorful Tree
Story
Yamiuchi (assassination) is a traditional event that is held annually in JAG summer camp. Every team displays a decorated tree in the dark and all teams' trees are compared from the point of view of their colorfulness. In this competition, it is allowed to cut the other teams’ tree to reduce its colorfulness. Despite a team would get a penalty if it were discovered that the team cuts the tree of another team, many teams do this obstruction.
You decided to compete in Yamiuchi and write a program that maximizes the colorfulness of your team’s tree. The program has to calculate maximum scores for all subtrees in case the other teams cut your tree.
Problem Statement
You are given a rooted tree G with N vertices indexed with 1 through N. The root is vertex 1. There are K kinds of colors indexed with 1 through K. You can paint vertex i with either color c_i or d_i. Note that c_i = d_i may hold, and if so you have to paint vertex i with c_i (=d_i).
Let the colorfulness of tree T be the number of different colors in T. Your task is to write a program that calculates maximum colorfulness for all rooted subtrees. Note that coloring for each rooted subtree is done independently, so previous coloring does not affect to other coloring.
Input
N K
u_1 v_1
:
u_{N-1} v_{N-1}
c_1 d_1
:
c_N d_N
The first line contains two integers N and K in this order.
The following N-1 lines provide information about the edges of G. The i-th line of them contains two integers u_i and v_i, meaning these two vertices are connected with an edge.
The following N lines provide information about color constraints. The i-th line of them contains two integers c_i and d_i explained above.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq K \leq 2\times 10^5
* 1 \leq u_i , v_i \leq N
* 1 \leq c_i , d_i \leq K
* The input graph is a tree.
* All inputs are integers.
Output
Output N lines.
The i-th line of them contains the maximum colorfulness of the rooted subtree of G whose root is i.
Sample Input 1
2 10
1 2
1 9
8 7
Output for Sample Input 1
2
1
Sample Input 2
3 2
1 2
1 3
1 2
1 1
1 2
Output for Sample Input 2
2
1
1
Note that two color options of a vertex can be the same.
Sample Input 3
5 100000
4 3
3 5
1 3
2 1
3 2
1 3
2 1
4 2
1 4
Output for Sample Input 3
4
1
3
1
1
Example
Input
2 10
1 2
1 9
8 7
Output
2
1
|
{
"inputs": [
"A?\n?\n3\n",
"A\nB\n10\n",
"AAAAAAAAAAAAAAAAAAAAA\n?\n300000\n",
"?\n?\n300000\n",
"ABB\nAB\n129133\n",
"A\n?\n10\n",
"A\nA\n300000\n",
"??\n??\n1\n",
"AAAAA\nAAAAA\n13\n",
"?????\n?????\n5\n",
"A\nB\n300000\n",
"AB????\nAB\n300000\n",
"??B?\n?A?\n5\n",
"ABB\nAB\n17767\n",
"A\n?\n5\n",
"A\nA\n129338\n",
"B\nB\n300000\n",
"??B?\n?B?\n5\n",
"B\nA\n300000\n",
"??\n??\n2\n",
"BAAAA\nAAAAA\n13\n",
"??B?\n?A?\n3\n",
"A?\n?\n2\n",
"A\nB\n11\n",
"BBB\nAB\n17767\n",
"A\nA\n50011\n",
"B\nB\n284315\n",
"??B?\n?A?\n4\n",
"A\nB\n50011\n",
"BBA\nAA\n14403\n",
"BBB\nBA\n17860\n",
"BBB\nBA\n32655\n",
"BBB\nBA\n40596\n",
"BBB\nBA\n71722\n",
"A\nA\n91043\n",
"AAAAA\nAAAAA\n2\n",
"?????\n?????\n9\n",
"A\nB\n7\n",
"A\nA\n127479\n",
"??B?\n?B?\n2\n",
"AB????\nBB\n232077\n",
"??B?\n?A?\n2\n",
"A\nA\n73515\n",
"B\nB\n95746\n",
"BBB\nBA\n10899\n",
"A\nB\n36831\n",
"AB@???\nAB\n300000\n",
"ABB\nBA\n17767\n",
"AB@@??\nAB\n300000\n",
"??B?\n??B\n5\n",
"BBA\nAB\n17767\n",
"BBA\nBA\n17767\n",
"AAAAAAAAAAAAAAAAAAABA\n?\n300000\n",
"ABA\nAB\n129133\n",
"AB????\nAB\n232077\n",
"BBA\nAB\n14403\n",
"BBA\nBA\n10899\n",
"AAAAAAAAAAAAAAAAAAABB\n?\n300000\n",
"AAAAB\nAAAAA\n13\n",
"????BA\nAB\n232077\n",
"BBB\nBA\n17767\n",
"BBA\nAB\n10899\n",
"AAAAAAAAAAAAAAAAAAABB\n@\n300000\n",
"BBA\nAB\n11749\n",
"BAB\nAB\n11749\n",
"BAB\nAB\n10435\n",
"ABB\nAB\n10435\n",
"ABB\nBA\n10435\n",
"ABB\nBA\n9755\n",
"BBA\nBA\n9755\n",
"BAA\nBA\n9755\n",
"BAA\nBA\n1604\n",
"AAAAAAAAAAABAAAAAAAAA\n?\n300000\n",
"BBA\nAB\n129133\n",
"AB????\nBA\n300000\n",
"AB@???\nBA\n300000\n",
"BBA\nAB\n35150\n",
"AB@@?>\nAB\n300000\n",
"?B??\n??B\n5\n",
"BBA\nBA\n29015\n",
"AAAAAAAAAAAAAAAAAAABA\n@\n300000\n",
"ABA\nBA\n129133\n",
"BABAA\nAAAAA\n13\n",
"ABB\nAA\n14403\n",
"AAAAAAAAAAAAAAAAAAABB\n>\n300000\n",
"??B?\n?A?\n1\n"
],
"outputs": [
"2\n",
"2046\n",
"690646514\n",
"273052679\n",
"0\n",
"4188162\n",
"276200851\n",
"40\n",
"268369924\n",
"194192\n",
"360325492\n",
"0\n",
"78\n",
"0\n",
"3906\n",
"651187684\n",
"276200851\n",
"64\n",
"360325492\n",
"224\n",
"16382\n",
"32\n",
"2\n",
"4094\n",
"345650929\n",
"69201863\n",
"716784524\n",
"78\n",
"405686776\n",
"683312777\n",
"477257680\n",
"695973257\n",
"885189464\n",
"345642627\n",
"318152748\n",
"36\n",
"34487472\n",
"254\n",
"1840485\n",
"20\n",
"451637407\n",
"22\n",
"71746714\n",
"863864606\n",
"674534832\n",
"860757795\n",
"0\n",
"0\n",
"0\n",
"64\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"16382\n",
"0\n",
"345650929\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"64\n",
"0\n",
"0\n",
"0\n",
"16382\n",
"683312777\n",
"0\n",
"0\n"
]
}
|
Igor the analyst is at work. He learned about a feature in his text editor called "Replace All". Igor is too bored at work and thus he came up with the following problem:
Given two strings x and y which consist of the English letters 'A' and 'B' only, a pair of strings (s, t) is called good if:
* s and t consist of the characters '0' and '1' only.
* 1 ≤ |s|, |t| ≤ n, where |z| denotes the length of string z, and n is a fixed positive integer.
* If we replace all occurrences of 'A' in x and y with the string s, and replace all occurrences of 'B' in x and y with the string t, then the two obtained from x and y strings are equal.
For example, if x = AAB, y = BB and n = 4, then (01, 0101) is one of good pairs of strings, because both obtained after replacing strings are "01010101".
The flexibility of a pair of strings x and y is the number of pairs of good strings (s, t). The pairs are ordered, for example the pairs (0, 1) and (1, 0) are different.
You're given two strings c and d. They consist of characters 'A', 'B' and '?' only. Find the sum of flexibilities of all possible pairs of strings (c', d') such that c' and d' can be obtained from c and d respectively by replacing the question marks with either 'A' or 'B', modulo 109 + 7.
Input
The first line contains the string c (1 ≤ |c| ≤ 3·105).
The second line contains the string d (1 ≤ |d| ≤ 3·105).
The last line contains a single integer n (1 ≤ n ≤ 3·105).
Output
Output a single integer: the answer to the problem, modulo 109 + 7.
Examples
Input
A?
?
3
Output
2
Input
A
B
10
Output
2046
Note
For the first sample, there are four possible pairs of (c', d').
If (c', d') = (AA, A), then the flexibility is 0.
If (c', d') = (AB, A), then the flexibility is 0.
If (c', d') = (AA, B), then the flexibility is 2, as the pairs of binary strings (1, 11), (0, 00) are the only good pairs.
If (c', d') = (AB, B), then the flexibility is 0.
Thus, the total flexibility is 2.
For the second sample, there are 21 + 22 + ... + 210 = 2046 possible binary strings of length not greater 10, and the set of pairs of good strings is precisely the set of pairs (s, s), where s is a binary string of length not greater than 10.
|
{
"inputs": [
"5 1\n2 1 3 2\n2 1 2 2\n0 0",
"5 1\n2 1 3 2\n2 1 2 2\n0 1",
"5 1\n2 1 5 2\n2 1 2 2\n0 1",
"5 1\n1 1 5 2\n2 1 2 2\n0 1",
"5 1\n1 1 0 2\n2 1 2 2\n0 1",
"5 1\n2 1 3 2\n2 1 4 2\n0 1",
"5 1\n2 1 1 2\n2 1 2 2\n0 1",
"5 1\n1 1 5 1\n2 1 2 0\n0 1",
"5 1\n1 1 1 2\n4 1 2 2\n0 1",
"5 1\n1 1 10 1\n2 -1 2 0\n0 2",
"5 1\n2 1 5 3\n2 1 2 2\n0 1",
"5 1\n3 1 3 2\n2 1 4 2\n0 1",
"5 1\n2 1 2 2\n3 1 2 2\n0 1",
"5 1\n3 2 3 2\n2 1 2 2\n0 0",
"5 1\n5 1 3 2\n2 1 4 2\n0 1",
"4 1\n1 1 1 2\n6 1 2 2\n0 1",
"8 1\n1 2 5 1\n2 0 2 0\n0 1",
"8 1\n1 2 7 1\n2 0 2 0\n0 1",
"5 1\n8 1 3 2\n2 0 4 2\n0 1",
"4 1\n8 1 3 2\n2 0 4 2\n0 1",
"5 1\n3 2 1 2\n2 0 3 2\n0 1",
"5 1\n3 3 1 2\n2 0 3 2\n0 1",
"5 1\n2 1 5 2\n4 1 2 2\n0 1",
"5 1\n2 1 5 1\n2 0 2 0\n0 1",
"5 1\n1 2 10 1\n2 -1 2 0\n0 2",
"9 1\n1 2 7 1\n2 0 2 0\n0 1",
"5 1\n1 1 17 1\n2 0 2 2\n0 1",
"5 1\n3 5 1 2\n2 1 3 7\n0 1",
"3 1\n2 1 5 2\n4 1 2 2\n0 1",
"5 1\n1 1 5 4\n2 1 2 3\n0 1",
"5 1\n4 1 5 3\n2 1 2 2\n0 2",
"9 1\n1 3 7 1\n2 0 2 0\n0 1",
"5 1\n1 2 17 1\n2 0 2 2\n0 1",
"5 1\n1 1 10 4\n2 1 2 3\n0 1",
"5 1\n6 1 3 2\n4 0 4 2\n0 0",
"5 1\n8 2 3 2\n3 1 2 2\n0 1",
"5 1\n1 1 11 4\n2 1 2 3\n0 1",
"8 1\n2 1 9 1\n2 1 2 0\n0 1",
"5 1\n2 1 7 2\n2 1 2 2\n0 1",
"5 1\n1 1 5 2\n2 1 2 0\n0 1",
"5 1\n1 1 0 2\n4 1 2 2\n0 1",
"5 1\n2 1 1 2\n3 1 2 2\n0 1",
"5 1\n1 1 5 1\n2 0 2 0\n0 1",
"5 1\n1 1 0 2\n4 0 2 2\n0 1",
"5 1\n1 1 5 1\n2 0 2 0\n0 2",
"5 1\n1 1 1 2\n4 0 2 2\n0 1",
"5 1\n1 1 5 1\n2 -1 2 0\n0 2",
"5 1\n1 1 10 1\n2 0 2 0\n0 2",
"5 1\n1 1 10 1\n3 0 2 0\n0 2",
"5 1\n1 1 10 1\n3 0 2 0\n0 1",
"5 1\n2 2 3 2\n2 1 2 2\n0 0",
"5 1\n2 1 3 2\n2 1 2 0\n0 1",
"5 1\n1 1 5 2\n2 1 2 1\n0 1",
"5 1\n1 1 0 2\n4 1 2 2\n0 2",
"5 1\n1 1 1 2\n6 1 2 2\n0 1",
"5 1\n1 2 5 1\n2 0 2 0\n0 1",
"5 1\n1 1 0 2\n4 0 1 2\n0 1",
"5 1\n1 1 0 1\n2 0 2 0\n0 2",
"5 1\n1 1 1 2\n7 0 2 2\n0 1",
"5 1\n1 1 10 1\n3 0 2 1\n0 1",
"5 1\n1 1 5 2\n2 1 2 1\n0 0",
"5 1\n0 1 0 2\n4 1 2 2\n0 2",
"5 1\n1 1 0 2\n4 0 1 2\n0 2",
"5 1\n1 1 10 1\n2 0 2 1\n0 1",
"5 1\n3 2 3 2\n2 0 2 2\n0 0",
"5 1\n5 1 3 2\n2 0 4 2\n0 1",
"5 1\n1 2 5 2\n2 1 2 1\n0 0",
"5 1\n0 1 0 2\n4 1 2 3\n0 2",
"5 1\n1 1 0 2\n4 0 1 2\n0 4",
"5 1\n1 1 10 1\n2 0 2 2\n0 1",
"5 1\n3 2 3 2\n2 0 3 2\n0 0",
"5 1\n1 2 5 2\n2 2 2 1\n0 0",
"5 1\n0 1 0 2\n2 1 2 3\n0 2",
"5 1\n1 1 0 1\n4 0 1 2\n0 4",
"5 1\n1 1 10 1\n2 0 1 2\n0 1",
"5 1\n3 2 3 2\n2 0 3 2\n0 1",
"5 1\n0 2 0 2\n2 1 2 3\n0 2",
"5 1\n1 1 0 1\n4 0 2 2\n0 4",
"5 1\n1 1 10 1\n2 1 1 2\n0 1",
"5 1\n0 3 0 2\n2 1 2 3\n0 2",
"5 1\n0 1 0 1\n4 0 2 2\n0 4",
"5 1\n0 3 0 3\n2 1 2 3\n0 2",
"8 1\n0 1 0 1\n4 0 2 2\n0 4",
"5 1\n3 3 1 2\n2 0 3 4\n0 1",
"5 1\n0 4 0 3\n2 1 2 3\n0 2",
"8 1\n0 1 0 1\n4 0 2 2\n0 1",
"5 1\n3 3 1 2\n2 0 3 7\n0 1",
"8 1\n0 2 0 1\n4 0 2 2\n0 1",
"5 1\n3 3 1 2\n2 1 3 7\n0 1",
"5 1\n2 1 3 1\n2 1 2 2\n0 0",
"5 1\n2 1 3 2\n3 1 2 2\n0 1",
"5 1\n1 1 5 2\n2 1 2 3\n0 1",
"5 1\n1 1 0 2\n4 1 2 4\n0 1",
"5 1\n2 1 1 2\n3 1 2 2\n0 2",
"5 1\n1 1 5 1\n2 2 2 0\n0 1",
"5 1\n1 1 1 2\n4 1 3 2\n0 1",
"5 1\n1 1 0 2\n1 0 2 2\n0 1",
"5 1\n1 1 2 1\n2 0 2 0\n0 2",
"5 1\n1 1 1 2\n6 0 2 2\n0 1",
"5 1\n1 1 10 1\n4 0 2 0\n0 2",
"10 1\n1 1 10 1\n3 0 2 0\n0 1"
],
"outputs": [
"4.18",
"4.175570504585\n",
"6.175570504585\n",
"5.175570504585\n",
"1.000000000000\n",
"3.351141009170\n",
"2.175570504585\n",
"4.000000000000\n",
"1.175570504585\n",
"9.000000000000\n",
"7.351141009170\n",
"3.526711513755\n",
"2.351141009170\n",
"0.000000000000\n",
"5.526711513755\n",
"1.414213562373\n",
"4.765366864730\n",
"6.765366864730\n",
"8.526711513755\n",
"9.242640687119\n",
"2.000000000000\n",
"3.175570504585\n",
"5.351141009170\n",
"3.000000000000\n",
"10.175570504585\n",
"6.684040286651\n",
"16.000000000000\n",
"4.351141009170\n",
"6.464101615138\n",
"6.351141009170\n",
"9.351141009170\n",
"7.368080573303\n",
"17.175570504585\n",
"11.351141009170\n",
"6.526711513755\n",
"5.000000000000\n",
"12.351141009170\n",
"7.000000000000\n",
"8.175570504585\n",
"5.175570504585\n",
"1.000000000000\n",
"2.175570504585\n",
"4.000000000000\n",
"1.000000000000\n",
"4.000000000000\n",
"1.175570504585\n",
"4.000000000000\n",
"9.000000000000\n",
"9.000000000000\n",
"9.000000000000\n",
"1.000000000000\n",
"3.351141009170\n",
"5.175570504585\n",
"1.000000000000\n",
"1.175570504585\n",
"5.175570504585\n",
"1.000000000000\n",
"1.000000000000\n",
"1.175570504585\n",
"9.000000000000\n",
"5.175570504585\n",
"0.000000000000\n",
"1.000000000000\n",
"9.000000000000\n",
"0.000000000000\n",
"5.526711513755\n",
"4.000000000000\n",
"0.000000000000\n",
"1.000000000000\n",
"9.000000000000\n",
"0.000000000000\n",
"4.000000000000\n",
"0.000000000000\n",
"1.000000000000\n",
"9.000000000000\n",
"0.000000000000\n",
"0.000000000000\n",
"1.000000000000\n",
"9.000000000000\n",
"0.000000000000\n",
"0.000000000000\n",
"0.000000000000\n",
"0.000000000000\n",
"3.175570504585\n",
"0.000000000000\n",
"0.000000000000\n",
"3.175570504585\n",
"0.000000000000\n",
"3.175570504585\n",
"1.000000000000\n",
"3.351141009170\n",
"5.175570504585\n",
"1.000000000000\n",
"2.175570504585\n",
"4.000000000000\n",
"1.175570504585\n",
"1.000000000000\n",
"1.000000000000\n",
"1.175570504585\n",
"9.000000000000\n",
"9.000000000000\n"
]
}
|
In a forest, there lived a spider named Tim. Tim was so smart that he created a huge, well-structured web. Surprisingly, his web forms a set of equilateral and concentric N-sided polygons whose edge lengths form an arithmetic sequence.
<image>
Figure 1: An example web of Tim
Corresponding vertices of the N-sided polygons lie on a straight line, each apart from neighboring ver- tices by distance 1. Neighboring vertices are connected by a thread (shown in the figure as solid lines), on which Tim can walk (you may regard Tim as a point). Radial axes are numbered from 1 to N in a rotational order, so you can denote by (r, i) the vertex on axis i and apart from the center of the web by distance r. You may consider the web as infinitely large, i.e. consisting of infinite number of N-sided polygons, since the web is so gigantic.
Tim’s web is thus marvelous, but currently has one problem: due to rainstorms, some of the threads are damaged and Tim can’t walk on those parts.
Now, a bug has been caught on the web. Thanks to the web having so organized a structure, Tim accu- rately figures out where the bug is, and heads out for that position. You, as a biologist, are interested in whether Tim is smart enough to move through the shortest possible route. To judge that, however, you need to know the length of the shortest route yourself, and thereby decided to write a program which calculates that length.
Input
The input consists of multiple test cases. Each test case begins with a line containing two integers N (3 ≤ N ≤ 100) and X (0 ≤ X ≤ 100), where N is as described above and X denotes the number of damaged threads. Next line contains four integers rS, iS, rT, and iT, meaning that Tim is starting at (rS, iS) and the bug is at (rT, iT). This line is followed by X lines, each containing four integers rA, iA, rB, and iB, meaning that a thread connecting (rA, iA) and (rB, iB) is damaged. Here (rA, iA) and (rB, iB) will be always neighboring to each other. Also, for all vertices (r, i) given above, you may assume 1 ≤ r ≤ 107 and 1 ≤ i ≤ N.
There will be at most 200 test cases. You may also assume that Tim is always able to reach where the bug is.
The input is terminated by a line containing two zeros.
Output
For each test case, print the length of the shortest route in a line. You may print any number of digits after the decimal point, but the error must not be greater than 0.01.
Example
Input
5 1
2 1 3 2
2 1 2 2
0 0
Output
4.18
|
{
"inputs": [
"2 2 2 1\n0 0 0",
"2 2 2 0\n0 0 0",
"2 1 2 0\n-1 -1 0",
"2 0 2 0\n-1 0 0",
"4 2 2 0\n0 0 1",
"3 1 2 0\n-1 0 -1",
"1 2 1 0\n-2 -1 0",
"2 2 3 0\n-1 -1 -1",
"1 1 4 0\n0 1 -1",
"3 2 0 0\n-1 -1 -1",
"1 0 1 0\n0 1 -1",
"1 -1 1 0\n0 1 -1",
"1 0 0 0\n0 0 -1",
"1 1 1 0\n0 0 -1",
"1 2 0 0\n0 0 -1",
"1 2 4 0\n-1 -1 0",
"-1 2 0 0\n-2 0 -1",
"2 1 2 1\n0 0 0",
"1 2 8 0\n-1 -1 0",
"1 -2 1 0\n-1 0 -1",
"2 3 3 0\n0 0 -1",
"2 2 8 0\n-1 -1 -1",
"4 1 4 0\n0 2 0",
"8 1 4 0\n0 2 -1",
"8 1 6 0\n0 2 0",
"8 2 6 0\n0 2 0",
"13 2 6 0\n0 2 0",
"13 2 12 0\n0 2 0",
"13 2 22 0\n-1 2 0",
"26 2 22 0\n-1 2 0",
"36 2 22 0\n-1 2 0",
"36 2 43 0\n-1 2 0",
"5 2 43 0\n-1 2 0",
"0 4 -1 0\n1 -2 -1",
"5 2 47 0\n-1 4 0",
"5 4 47 0\n-1 4 0",
"5 8 47 0\n-1 4 0",
"5 8 88 0\n-1 4 0",
"3 8 88 0\n-2 8 -1",
"3 9 88 0\n-2 8 -1",
"3 9 82 0\n-2 8 -1",
"3 4 1 0\n-1 -1 -1",
"4 3 3 0\n-1 0 1",
"7 1 2 0\n-1 0 1",
"6 2 2 0\n0 0 2",
"4 4 2 0\n0 -1 -2",
"15 1 4 0\n0 2 -1",
"36 2 44 0\n-1 2 0",
"10 2 43 0\n-1 2 0",
"5 2 37 0\n-1 4 0",
"3 8 47 0\n-1 4 0",
"5 8 35 0\n-1 4 0",
"9 8 88 0\n-2 8 -1",
"0 9 82 0\n-2 8 -1",
"1 9 82 0\n-2 8 -1",
"5 4 1 0\n-1 -1 -1",
"4 2 1 1\n0 0 0",
"6 2 6 0\n-1 0 1",
"1 5 2 0\n-2 1 0",
"0 3 13 0\n-1 1 2",
"2 2 2 0\n-1 0 0",
"2 2 2 0\n-1 -1 0",
"2 1 2 0\n-1 0 0",
"2 2 2 0\n0 0 1",
"1 2 2 0\n-1 -1 0",
"2 1 2 0\n-1 -1 1",
"2 1 2 0\n-1 0 -1",
"2 0 2 0\n0 0 0",
"1 2 2 0\n-2 -1 0",
"1 2 2 0\n0 0 1",
"3 1 2 0\n-1 1 -1",
"1 2 1 0\n-1 -1 0",
"1 1 2 0\n-1 1 -1",
"2 2 2 0\n-1 -1 -1",
"1 1 2 0\n0 1 -1",
"2 2 0 0\n-1 -1 -1",
"1 0 4 0\n0 1 -1",
"3 2 1 0\n-1 -1 -1",
"1 -1 1 0\n0 0 -1",
"1 -1 0 0\n0 0 -1",
"1 1 0 0\n0 0 -1",
"0 2 0 0\n0 0 -1",
"0 2 0 0\n-1 0 -1",
"0 2 0 0\n-2 0 -1",
"0 2 2 0\n0 0 0",
"2 1 2 0\n0 0 0",
"2 2 2 0\n-1 1 0",
"2 1 2 0\n-1 -1 -1",
"3 1 2 0\n-1 0 0",
"2 0 2 0\n-2 0 0",
"2 2 2 0\n-1 0 1",
"2 0 2 0\n-1 -1 1",
"2 1 2 0\n-2 0 -1",
"2 0 2 0\n0 0 1",
"4 2 2 0\n-1 0 1",
"1 2 2 0\n-2 -2 0",
"3 2 2 0\n-1 0 -1",
"1 2 2 0\n0 0 0",
"1 2 1 0\n-2 -1 -1",
"1 0 1 0\n-1 -1 0",
"1 1 2 0\n-1 2 -1"
],
"outputs": [
"24",
"24\n",
"16\n",
"8\n",
"40\n",
"22\n",
"10\n",
"32\n",
"18\n",
"12\n",
"2\n",
"-2\n",
"0\n",
"6\n",
"4\n",
"28\n",
"-4\n",
"14\n",
"52\n",
"-6\n",
"42\n",
"72\n",
"48\n",
"88\n",
"124\n",
"152\n",
"232\n",
"412\n",
"712\n",
"1336\n",
"1816\n",
"3412\n",
"622\n",
"-8\n",
"678\n",
"886\n",
"1302\n",
"2368\n",
"1984\n",
"2166\n",
"2022\n",
"38\n",
"66\n",
"46\n",
"56\n",
"64\n",
"158\n",
"3488\n",
"1072\n",
"538\n",
"1082\n",
"990\n",
"3136\n",
"1476\n",
"1658\n",
"58\n",
"26\n",
"120\n",
"34\n",
"78\n",
"24\n",
"24\n",
"16\n",
"24\n",
"16\n",
"16\n",
"16\n",
"8\n",
"16\n",
"16\n",
"22\n",
"10\n",
"10\n",
"24\n",
"10\n",
"8\n",
"8\n",
"22\n",
"-2\n",
"-2\n",
"2\n",
"0\n",
"0\n",
"0\n",
"8\n",
"16\n",
"24\n",
"16\n",
"22\n",
"8\n",
"24\n",
"8\n",
"16\n",
"8\n",
"40\n",
"16\n",
"32\n",
"16\n",
"10\n",
"2\n",
"10\n"
]
}
|
Example
Input
2 2 2 1
0 0 0
Output
24
|
{
"inputs": [
"3 2\n6 2 6\n",
"6 9\n9 9 9 9 9 9\n",
"1 500000\n500000\n",
"18 4\n2 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\n",
"1 1\n500000\n",
"9 2\n1 2 1 2 1 2 1 3 3\n",
"2 1\n1 2\n",
"18 1\n2 2 2 2 1 1 1 1 2 1 2 2 1 2 2 2 2 2\n",
"18 5\n4 4 4 6 6 4 1 1 1 1 3 3 4 5 6 4 1 3\n",
"18 1\n3 3 1 3 1 1 3 4 2 2 2 1 2 1 4 1 4 3\n",
"18 2\n5 3 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 1\n",
"18 3\n7 3 5 7 5 4 4 1 2 6 5 5 6 6 6 3 1 1\n",
"13 4\n1 4 3 4 3 3 4 1 1 3 4 3 4\n",
"18 1\n5 4 7 9 2 5 1 2 5 8 8 3 8 4 4 6 3 7\n",
"29 3\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 3 1 4 2 2 3 4 2 4 2\n",
"39 1\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 2 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 2 4\n",
"18 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"18 1\n8 2 3 1 8 3 3 2 7 5 8 2 7 1 4 3 1 3\n",
"11 4\n1 4 3 4 3 3 4 1 1 3 4\n",
"18 2\n3 3 2 2 3 2 1 2 2 1 3 1 1 3 3 3 3 2\n",
"1 316327\n500000\n",
"18 5\n2 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\n",
"9 2\n1 2 1 2 1 2 1 3 0\n",
"18 1\n3 3 1 3 1 1 3 4 2 2 3 1 2 1 4 1 4 3\n",
"18 2\n5 3 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 2\n",
"18 1\n5 4 7 9 2 5 1 2 5 8 8 3 2 4 4 6 3 7\n",
"29 3\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 6 1 4 2 2 3 4 2 4 2\n",
"39 1\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 3 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 2 4\n",
"18 2\n3 3 2 2 3 2 1 2 2 1 3 1 1 3 3 3 5 2\n",
"3 2\n6 2 0\n",
"9 2\n2 2 1 2 1 2 1 3 0\n",
"39 1\n4 2 1 1 3 5 1 5 1 1 3 3 4 3 1 1 4 5 1 5 3 3 3 1 5 1 2 1 1 4 1 1 5 2 2 1 1 1 4\n",
"18 2\n3 3 2 2 3 2 1 2 2 1 3 0 1 3 3 3 5 1\n",
"2 0\n1 2\n",
"18 5\n4 4 4 6 6 4 1 1 1 1 3 3 4 5 6 1 1 3\n",
"13 4\n1 4 3 4 3 3 4 1 1 1 4 3 4\n",
"18 1\n8 2 3 1 7 3 3 2 7 5 8 2 7 1 4 3 1 3\n",
"11 4\n1 4 3 4 3 3 4 2 1 3 4\n",
"6 9\n9 9 1 9 9 9\n",
"18 5\n1 4 9 5 8 3 8 9 5 5 8 1 1 6 6 5 9 8\n",
"18 5\n4 4 4 6 6 4 1 1 1 1 3 4 4 5 6 1 1 3\n",
"18 1\n3 3 1 3 1 1 3 4 2 2 3 1 3 1 4 1 4 3\n",
"18 2\n5 0 4 2 3 4 3 4 1 5 4 1 3 3 2 3 4 2\n",
"13 4\n1 4 3 4 2 3 4 1 1 1 4 3 4\n",
"18 1\n5 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\n",
"29 3\n1 4 3 4 3 3 4 1 1 3 4 1 3 3 4 1 3 1 2 6 1 4 2 2 3 4 2 4 3\n",
"18 1\n8 2 3 1 7 3 3 2 7 5 8 2 7 2 4 3 1 3\n",
"11 8\n1 4 3 4 3 3 4 2 1 3 4\n",
"18 2\n3 3 2 2 3 2 1 2 2 1 3 0 1 3 3 3 5 2\n",
"6 9\n9 9 1 18 9 9\n",
"18 5\n1 4 9 2 8 3 8 9 5 5 8 1 1 6 6 5 9 8\n",
"9 2\n2 2 1 2 2 2 1 3 0\n",
"18 0\n3 3 1 3 1 1 3 4 2 2 3 1 3 1 4 1 4 3\n",
"18 2\n5 0 4 2 6 4 3 4 1 5 4 1 3 3 2 3 4 2\n",
"13 7\n1 4 3 4 2 3 4 1 1 1 4 3 4\n",
"18 1\n3 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\n",
"18 1\n8 2 3 1 7 2 3 2 7 5 8 2 7 2 4 3 1 3\n",
"11 8\n1 4 3 4 3 3 4 4 1 3 4\n",
"6 9\n9 9 1 18 3 9\n",
"18 5\n1 4 9 2 8 3 8 9 5 5 8 1 1 6 6 5 9 6\n",
"9 2\n2 3 1 2 2 2 1 3 0\n",
"18 2\n5 0 2 2 6 4 3 4 1 5 4 1 3 3 2 3 4 2\n",
"13 7\n1 4 3 4 2 3 4 1 1 1 5 3 4\n",
"18 1\n2 4 7 9 2 5 1 2 5 8 8 2 2 4 4 6 3 7\n",
"18 1\n8 2 3 1 7 2 3 2 7 5 8 4 7 2 4 3 1 3\n",
"11 8\n1 4 3 4 3 3 2 4 1 3 4\n",
"18 2\n3 3 2 2 3 2 1 2 2 2 3 0 1 3 3 3 5 1\n",
"6 9\n9 9 1 18 3 13\n",
"18 5\n1 4 9 2 8 3 8 9 8 5 8 1 1 6 6 5 9 6\n",
"18 2\n5 0 2 2 6 4 3 4 1 5 4 1 3 3 2 3 6 2\n",
"13 7\n1 4 3 5 2 3 4 1 1 1 5 3 4\n",
"18 1\n2 4 7 9 2 5 1 2 5 8 0 2 2 4 4 6 3 7\n",
"11 8\n1 0 3 4 3 3 2 4 1 3 4\n",
"18 2\n3 3 3 2 3 2 1 2 2 2 3 0 1 3 3 3 5 1\n",
"6 9\n9 9 1 18 3 7\n",
"18 5\n1 4 9 2 8 3 8 9 8 5 8 1 1 9 6 5 9 6\n",
"18 2\n5 0 2 2 6 4 3 4 1 5 4 1 3 5 2 3 6 2\n",
"13 3\n1 4 3 5 2 3 4 1 1 1 5 3 4\n",
"18 1\n2 0 7 9 2 5 1 2 5 8 0 2 2 4 4 6 3 7\n",
"11 8\n1 0 3 4 3 3 2 4 1 0 4\n",
"18 2\n3 3 3 2 3 2 0 2 2 2 3 0 1 3 3 3 5 1\n",
"6 9\n9 9 1 1 3 7\n",
"18 5\n1 4 9 2 8 3 8 9 8 5 8 1 1 9 6 4 9 6\n",
"18 2\n5 0 2 2 6 4 3 4 1 5 4 1 3 8 2 3 6 2\n",
"13 3\n1 4 3 5 2 3 4 1 1 1 5 3 3\n",
"11 14\n1 0 3 4 3 3 2 4 1 0 4\n",
"18 2\n3 3 3 2 3 2 0 2 2 2 6 0 1 3 3 3 5 1\n",
"18 5\n1 4 9 2 7 3 8 9 8 5 8 1 1 9 6 4 9 6\n",
"18 2\n5 0 2 2 6 4 3 4 1 5 4 1 3 8 2 2 6 2\n",
"13 5\n1 4 3 5 2 3 4 1 1 1 5 3 4\n",
"18 5\n1 4 9 2 7 3 8 9 8 5 8 1 1 9 6 6 9 6\n",
"18 2\n5 0 1 2 6 4 3 4 1 5 4 1 3 8 2 2 6 2\n"
],
"outputs": [
"2\n",
"6\n",
"1\n",
"5\n",
"1\n",
"5\n",
"2\n",
"12\n",
"6\n",
"9\n",
"6\n",
"6\n",
"7\n",
"4\n",
"12\n",
"19\n",
"18\n",
"5\n",
"6\n",
"11\n",
"1\n",
"6\n",
"4\n",
"8\n",
"7\n",
"3\n",
"12\n",
"19\n",
"10\n",
"2\n",
"5\n",
"20\n",
"9\n",
"1\n",
"6\n",
"8\n",
"6\n",
"6\n",
"6\n",
"6\n",
"7\n",
"8\n",
"7\n",
"8\n",
"4\n",
"12\n",
"5\n",
"4\n",
"10\n",
"5\n",
"5\n",
"6\n",
"7\n",
"6\n",
"5\n",
"4\n",
"6\n",
"5\n",
"4\n",
"5\n",
"5\n",
"7\n",
"4\n",
"5\n",
"5\n",
"4\n",
"10\n",
"3\n",
"5\n",
"7\n",
"4\n",
"5\n",
"4\n",
"9\n",
"3\n",
"5\n",
"7\n",
"6\n",
"5\n",
"3\n",
"9\n",
"4\n",
"4\n",
"7\n",
"7\n",
"3\n",
"8\n",
"4\n",
"8\n",
"5\n",
"4\n",
"7\n"
]
}
|
You are given array a of length n. You can choose one segment [l, r] (1 ≤ l ≤ r ≤ n) and integer value k (positive, negative or even zero) and change a_l, a_{l + 1}, ..., a_r by k each (i.e. a_i := a_i + k for each l ≤ i ≤ r).
What is the maximum possible number of elements with value c that can be obtained after one such operation?
Input
The first line contains two integers n and c (1 ≤ n ≤ 5 ⋅ 10^5, 1 ≤ c ≤ 5 ⋅ 10^5) — the length of array and the value c to obtain.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 5 ⋅ 10^5) — array a.
Output
Print one integer — the maximum possible number of elements with value c which can be obtained after performing operation described above.
Examples
Input
6 9
9 9 9 9 9 9
Output
6
Input
3 2
6 2 6
Output
2
Note
In the first example we can choose any segment and k = 0. The array will stay same.
In the second example we can choose segment [1, 3] and k = -4. The array will become [2, -2, 2].
|
{
"inputs": [
"3 2\n2 6\n4 3\n1 5",
"3 4\n1 4 7 10\n2 5 8 11\n3 6 9 12",
"3 2\n2 5\n4 3\n1 5",
"3 2\n2 6\n4 3\n2 5",
"3 2\n1 6\n4 3\n2 5",
"3 2\n1 6\n4 4\n2 5",
"3 4\n1 4 7 10\n2 6 8 11\n3 6 9 12",
"3 2\n2 5\n3 3\n1 5",
"3 2\n2 6\n4 3\n2 6",
"3 2\n1 6\n4 3\n2 6",
"3 2\n1 6\n4 3\n1 5",
"3 4\n1 4 8 10\n2 5 8 11\n3 6 9 12",
"3 4\n1 4 7 10\n2 6 8 9\n3 6 9 12",
"3 4\n1 4 7 10\n1 6 8 11\n3 6 9 12",
"3 4\n1 4 5 10\n2 5 8 11\n3 6 9 12",
"3 4\n2 4 7 10\n2 5 8 11\n3 6 9 12",
"3 4\n2 4 7 10\n1 6 8 11\n3 6 9 12",
"3 4\n2 4 7 10\n1 5 8 11\n3 6 9 12",
"3 4\n2 4 7 10\n1 6 8 11\n3 5 9 12",
"3 4\n2 4 7 10\n2 6 8 11\n3 5 9 12",
"3 2\n1 6\n4 4\n1 5",
"3 4\n1 4 7 10\n1 6 8 9\n3 6 9 12",
"3 4\n1 4 7 10\n2 5 8 11\n3 5 9 12",
"3 2\n2 6\n3 3\n2 5",
"3 4\n1 4 7 10\n1 6 8 10\n3 6 9 12",
"3 2\n2 6\n3 3\n1 5",
"3 2\n1 6\n4 3\n1 6",
"3 4\n2 4 5 10\n2 5 8 11\n3 6 9 12",
"3 4\n1 4 7 10\n1 6 8 9\n2 6 9 12",
"3 2\n2 6\n4 1\n4 5",
"3 4\n2 4 7 10\n1 5 8 11\n3 6 12 12",
"3 4\n1 4 8 10\n1 6 8 10\n3 6 9 12",
"3 2\n2 6\n3 1\n4 5",
"3 2\n2 5\n3 3\n2 5",
"3 4\n2 4 7 10\n2 5 8 11\n1 6 9 12",
"3 4\n2 4 7 10\n2 6 8 11\n3 7 9 12",
"3 4\n2 4 7 10\n1 6 8 9\n3 6 9 12",
"3 4\n1 4 7 10\n2 5 8 11\n1 6 9 12",
"3 2\n1 5\n4 3\n1 5",
"3 4\n1 4 7 10\n3 6 8 11\n3 6 9 12",
"3 4\n1 4 5 10\n1 5 8 11\n3 6 9 12",
"3 4\n4 4 7 10\n2 5 8 11\n3 6 9 12",
"3 4\n1 4 7 10\n1 5 8 11\n3 6 12 12",
"3 4\n2 4 8 10\n1 6 8 10\n3 6 9 12",
"3 4\n2 4 8 10\n2 6 8 11\n3 7 9 12",
"3 4\n4 4 8 10\n2 5 8 11\n3 6 9 12",
"3 2\n1 5\n4 3\n2 6",
"3 4\n1 4 8 10\n2 5 8 11\n1 6 9 12",
"3 4\n2 4 7 10\n2 6 8 9\n3 6 9 12",
"3 4\n2 4 7 10\n1 8 8 11\n3 6 9 12",
"3 4\n1 4 7 10\n2 5 8 12\n3 5 9 12",
"3 4\n4 1 7 10\n2 5 8 11\n3 6 9 12",
"3 4\n4 1 7 10\n2 7 8 11\n3 6 9 12",
"3 2\n2 5\n3 3\n1 6",
"3 2\n1 6\n4 4\n2 6",
"3 4\n1 4 7 10\n2 6 8 9\n3 6 9 9",
"3 4\n2 4 5 10\n2 6 8 11\n3 6 9 12",
"3 4\n2 4 7 10\n2 6 8 11\n1 7 9 12",
"3 2\n2 5\n4 4\n1 5",
"3 4\n2 4 7 10\n3 6 8 11\n3 6 9 12",
"3 4\n2 4 8 10\n1 6 5 10\n3 6 9 12",
"3 4\n2 4 8 10\n2 6 8 11\n3 7 9 11",
"3 4\n4 4 5 10\n2 5 8 11\n3 6 9 12",
"3 4\n1 4 7 10\n1 6 8 9\n3 6 9 9",
"3 4\n2 4 7 10\n2 6 8 12\n1 7 9 12",
"3 2\n2 5\n4 4\n1 6",
"3 4\n2 4 7 11\n3 6 8 11\n3 6 9 12",
"3 4\n2 4 7 10\n2 6 8 11\n3 6 9 12",
"3 2\n2 6\n3 3\n2 6",
"3 4\n2 1 5 10\n2 5 8 11\n3 6 9 12",
"3 4\n2 4 7 10\n1 8 8 11\n3 6 12 12",
"3 2\n1 5\n3 3\n2 5",
"3 4\n4 4 7 10\n2 5 5 11\n3 6 9 12",
"3 4\n2 4 5 10\n1 8 8 11\n3 6 9 12",
"3 4\n1 1 7 10\n2 6 8 9\n3 6 9 9",
"3 4\n2 4 5 9\n2 6 8 11\n3 6 9 12",
"3 4\n2 4 8 10\n3 6 8 11\n3 7 9 11",
"3 2\n1 6\n3 3\n2 6",
"3 4\n3 4 7 10\n1 8 8 11\n3 6 12 12",
"3 4\n2 4 5 9\n2 6 8 11\n2 6 9 12",
"3 2\n2 6\n4 3\n1 6",
"3 4\n1 4 7 10\n2 6 8 9\n3 7 9 12",
"3 4\n1 4 7 10\n1 6 8 11\n1 6 9 12",
"3 4\n2 4 7 10\n1 6 7 11\n3 5 9 12",
"3 4\n1 4 7 10\n1 6 8 9\n2 5 9 12",
"3 2\n1 5\n3 3\n2 6",
"3 4\n1 4 7 10\n2 7 8 12\n3 5 9 12",
"3 4\n1 4 7 10\n2 6 8 9\n3 6 12 9",
"3 4\n2 4 7 10\n2 6 8 11\n3 7 9 11",
"3 4\n4 4 5 10\n2 5 8 11\n3 6 10 12",
"3 4\n2 4 7 10\n1 6 8 9\n3 6 9 9",
"3 4\n1 4 7 10\n1 6 5 11\n1 6 9 12",
"3 4\n1 4 7 10\n2 6 5 11\n1 6 9 12",
"3 2\n2 5\n4 3\n2 5",
"3 2\n1 5\n3 3\n1 5",
"3 4\n2 4 5 10\n1 6 8 11\n3 6 9 12",
"3 4\n4 4 7 10\n1 5 8 11\n3 6 9 12",
"3 2\n1 6\n3 4\n1 5",
"3 4\n2 4 8 11\n1 6 8 10\n3 6 9 12",
"3 4\n1 4 8 10\n2 5 8 11\n1 6 9 9",
"3 4\n2 4 7 11\n2 6 8 11\n1 7 9 12",
"3 2\n4 5\n4 1\n1 5"
],
"outputs": [
"2 6\n4 3\n5 1\n2 1\n4 3\n5 6",
"1 4 7 10\n5 8 11 2\n9 12 3 6\n1 4 3 2\n5 8 7 6\n9 12 11 10",
"5 2 \n3 4 \n1 5 \n1 2 \n3 4 \n5 5 \n",
"6 2 \n3 4 \n2 5 \n2 2 \n3 4 \n6 5 \n",
"6 1 \n3 4 \n2 5 \n2 1 \n3 4 \n6 5 \n",
"6 1 \n4 4 \n2 5 \n2 1 \n4 4 \n6 5 \n",
"10 4 7 1 \n8 11 2 6 \n3 6 12 9 \n3 4 2 1 \n8 6 7 6 \n10 11 12 9 \n",
"5 2 \n3 3 \n1 5 \n1 2 \n3 3 \n5 5 \n",
"6 2 \n3 4 \n2 6 \n2 2 \n3 4 \n6 6 \n",
"6 1 \n3 4 \n2 6 \n2 1 \n3 4 \n6 6 \n",
"6 1 \n3 4 \n1 5 \n1 1 \n3 4 \n6 5 \n",
"10 4 8 1 \n8 11 2 5 \n3 6 12 9 \n3 4 2 1 \n8 6 8 5 \n10 11 12 9 \n",
"10 4 7 1 \n8 9 2 6 \n3 6 12 9 \n3 4 2 1 \n8 6 7 6 \n10 9 12 9 \n",
"10 4 7 1 \n8 11 1 6 \n3 6 12 9 \n3 4 1 1 \n8 6 7 6 \n10 11 12 9 \n",
"10 4 5 1 \n8 11 2 5 \n3 6 12 9 \n3 4 2 1 \n8 6 5 5 \n10 11 12 9 \n",
"10 4 7 2 \n8 11 2 5 \n3 6 12 9 \n3 4 2 2 \n8 6 7 5 \n10 11 12 9 \n",
"10 4 7 2 \n8 11 1 6 \n3 6 12 9 \n3 4 1 2 \n8 6 7 6 \n10 11 12 9 \n",
"10 4 7 2 \n8 11 1 5 \n3 6 12 9 \n3 4 1 2 \n8 6 7 5 \n10 11 12 9 \n",
"10 4 7 2 \n8 11 1 6 \n3 5 12 9 \n3 4 1 2 \n8 5 7 6 \n10 11 12 9 \n",
"10 4 7 2 \n8 11 2 6 \n3 5 12 9 \n3 4 2 2 \n8 5 7 6 \n10 11 12 9 \n",
"6 1 \n4 4 \n1 5 \n1 1 \n4 4 \n6 5 \n",
"10 4 7 1 \n8 9 1 6 \n3 6 12 9 \n3 4 1 1 \n8 6 7 6 \n10 9 12 9 \n",
"10 4 7 1 \n8 11 2 5 \n3 5 12 9 \n3 4 2 1 \n8 5 7 5 \n10 11 12 9 \n",
"6 2 \n3 3 \n2 5 \n2 2 \n3 3 \n6 5 \n",
"10 4 7 1 \n8 10 1 6 \n3 6 12 9 \n3 4 1 1 \n8 6 7 6 \n10 10 12 9 \n",
"6 2 \n3 3 \n1 5 \n1 2 \n3 3 \n6 5 \n",
"6 1 \n3 4 \n1 6 \n1 1 \n3 4 \n6 6 \n",
"10 4 5 2 \n8 11 2 5 \n3 6 12 9 \n3 4 2 2 \n8 6 5 5 \n10 11 12 9 \n",
"10 4 7 1 \n8 9 1 6 \n2 6 12 9 \n2 4 1 1 \n8 6 7 6 \n10 9 12 9 \n",
"6 2 \n1 4 \n4 5 \n1 2 \n4 4 \n6 5 \n",
"10 4 7 2 \n8 11 1 5 \n3 6 12 12 \n3 4 1 2 \n8 6 7 5 \n10 11 12 12 \n",
"10 4 8 1 \n8 10 1 6 \n3 6 12 9 \n3 4 1 1 \n8 6 8 6 \n10 10 12 9 \n",
"6 2 \n1 3 \n4 5 \n1 2 \n4 3 \n6 5 \n",
"5 2 \n3 3 \n2 5 \n2 2 \n3 3 \n5 5 \n",
"10 4 7 2 \n8 11 2 5 \n1 6 12 9 \n1 4 2 2 \n8 6 7 5 \n10 11 12 9 \n",
"10 4 7 2 \n8 11 2 6 \n3 7 12 9 \n3 4 2 2 \n8 7 7 6 \n10 11 12 9 \n",
"10 4 7 2 \n8 9 1 6 \n3 6 12 9 \n3 4 1 2 \n8 6 7 6 \n10 9 12 9 \n",
"10 4 7 1 \n8 11 2 5 \n1 6 12 9 \n1 4 2 1 \n8 6 7 5 \n10 11 12 9 \n",
"5 1 \n3 4 \n1 5 \n1 1 \n3 4 \n5 5 \n",
"10 4 7 1 \n8 11 3 6 \n3 6 12 9 \n3 4 3 1 \n8 6 7 6 \n10 11 12 9 \n",
"10 4 5 1 \n8 11 1 5 \n3 6 12 9 \n3 4 1 1 \n8 6 5 5 \n10 11 12 9 \n",
"10 4 7 4 \n8 11 2 5 \n3 6 12 9 \n3 4 2 4 \n8 6 7 5 \n10 11 12 9 \n",
"10 4 7 1 \n8 11 1 5 \n3 6 12 12 \n3 4 1 1 \n8 6 7 5 \n10 11 12 12 \n",
"10 4 8 2 \n8 10 1 6 \n3 6 12 9 \n3 4 1 2 \n8 6 8 6 \n10 10 12 9 \n",
"10 4 8 2 \n8 11 2 6 \n3 7 12 9 \n3 4 2 2 \n8 7 8 6 \n10 11 12 9 \n",
"10 4 8 4 \n8 11 2 5 \n3 6 12 9 \n3 4 2 4 \n8 6 8 5 \n10 11 12 9 \n",
"5 1 \n3 4 \n2 6 \n2 1 \n3 4 \n5 6 \n",
"10 4 8 1 \n8 11 2 5 \n1 6 12 9 \n1 4 2 1 \n8 6 8 5 \n10 11 12 9 \n",
"10 4 7 2 \n8 9 2 6 \n3 6 12 9 \n3 4 2 2 \n8 6 7 6 \n10 9 12 9 \n",
"10 4 7 2 \n8 11 1 8 \n3 6 12 9 \n3 4 1 2 \n8 6 7 8 \n10 11 12 9 \n",
"10 4 7 1 \n8 12 2 5 \n3 5 12 9 \n3 4 2 1 \n8 5 7 5 \n10 12 12 9 \n",
"10 1 7 4 \n8 11 2 5 \n3 6 12 9 \n3 1 2 4 \n8 6 7 5 \n10 11 12 9 \n",
"10 1 7 4 \n8 11 2 7 \n3 6 12 9 \n3 1 2 4 \n8 6 7 7 \n10 11 12 9 \n",
"5 2 \n3 3 \n1 6 \n1 2 \n3 3 \n5 6 \n",
"6 1 \n4 4 \n2 6 \n2 1 \n4 4 \n6 6 \n",
"10 4 7 1 \n8 9 2 6 \n3 6 9 9 \n3 4 2 1 \n8 6 7 6 \n10 9 9 9 \n",
"10 4 5 2 \n8 11 2 6 \n3 6 12 9 \n3 4 2 2 \n8 6 5 6 \n10 11 12 9 \n",
"10 4 7 2 \n8 11 2 6 \n1 7 12 9 \n1 4 2 2 \n8 7 7 6 \n10 11 12 9 \n",
"5 2 \n4 4 \n1 5 \n1 2 \n4 4 \n5 5 \n",
"10 4 7 2 \n8 11 3 6 \n3 6 12 9 \n3 4 3 2 \n8 6 7 6 \n10 11 12 9 \n",
"10 4 8 2 \n5 10 1 6 \n3 6 12 9 \n3 4 1 2 \n5 6 8 6 \n10 10 12 9 \n",
"10 4 8 2 \n8 11 2 6 \n3 7 11 9 \n3 4 2 2 \n8 7 8 6 \n10 11 11 9 \n",
"10 4 5 4 \n8 11 2 5 \n3 6 12 9 \n3 4 2 4 \n8 6 5 5 \n10 11 12 9 \n",
"10 4 7 1 \n8 9 1 6 \n3 6 9 9 \n3 4 1 1 \n8 6 7 6 \n10 9 9 9 \n",
"10 4 7 2 \n8 12 2 6 \n1 7 12 9 \n1 4 2 2 \n8 7 7 6 \n10 12 12 9 \n",
"5 2 \n4 4 \n1 6 \n1 2 \n4 4 \n5 6 \n",
"11 4 7 2 \n8 11 3 6 \n3 6 12 9 \n3 4 3 2 \n8 6 7 6 \n11 11 12 9 \n",
"10 4 7 2 \n8 11 2 6 \n3 6 12 9 \n3 4 2 2 \n8 6 7 6 \n10 11 12 9 \n",
"6 2 \n3 3 \n2 6 \n2 2 \n3 3 \n6 6 \n",
"10 1 5 2 \n8 11 2 5 \n3 6 12 9 \n3 1 2 2 \n8 6 5 5 \n10 11 12 9 \n",
"10 4 7 2 \n8 11 1 8 \n3 6 12 12 \n3 4 1 2 \n8 6 7 8 \n10 11 12 12 \n",
"5 1 \n3 3 \n2 5 \n2 1 \n3 3 \n5 5 \n",
"10 4 7 4 \n5 11 2 5 \n3 6 12 9 \n3 4 2 4 \n5 6 7 5 \n10 11 12 9 \n",
"10 4 5 2 \n8 11 1 8 \n3 6 12 9 \n3 4 1 2 \n8 6 5 8 \n10 11 12 9 \n",
"10 1 7 1 \n8 9 2 6 \n3 6 9 9 \n3 1 2 1 \n8 6 7 6 \n10 9 9 9 \n",
"9 4 5 2 \n8 11 2 6 \n3 6 12 9 \n3 4 2 2 \n8 6 5 6 \n9 11 12 9 \n",
"10 4 8 2 \n8 11 3 6 \n3 7 11 9 \n3 4 3 2 \n8 7 8 6 \n10 11 11 9 \n",
"6 1 \n3 3 \n2 6 \n2 1 \n3 3 \n6 6 \n",
"10 4 7 3 \n8 11 1 8 \n3 6 12 12 \n3 4 1 3 \n8 6 7 8 \n10 11 12 12 \n",
"9 4 5 2 \n8 11 2 6 \n2 6 12 9 \n2 4 2 2 \n8 6 5 6 \n9 11 12 9 \n",
"6 2 \n3 4 \n1 6 \n1 2 \n3 4 \n6 6 \n",
"10 4 7 1 \n8 9 2 6 \n3 7 12 9 \n3 4 2 1 \n8 7 7 6 \n10 9 12 9 \n",
"10 4 7 1 \n8 11 1 6 \n1 6 12 9 \n1 4 1 1 \n8 6 7 6 \n10 11 12 9 \n",
"10 4 7 2 \n7 11 1 6 \n3 5 12 9 \n3 4 1 2 \n7 5 7 6 \n10 11 12 9 \n",
"10 4 7 1 \n8 9 1 6 \n2 5 12 9 \n2 4 1 1 \n8 5 7 6 \n10 9 12 9 \n",
"5 1 \n3 3 \n2 6 \n2 1 \n3 3 \n5 6 \n",
"10 4 7 1 \n8 12 2 7 \n3 5 12 9 \n3 4 2 1 \n8 5 7 7 \n10 12 12 9 \n",
"10 4 7 1 \n8 9 2 6 \n3 6 9 12 \n3 4 2 1 \n8 6 7 6 \n10 9 9 12 \n",
"10 4 7 2 \n8 11 2 6 \n3 7 11 9 \n3 4 2 2 \n8 7 7 6 \n10 11 11 9 \n",
"10 4 5 4 \n8 11 2 5 \n3 6 12 10 \n3 4 2 4 \n8 6 5 5 \n10 11 12 10 \n",
"10 4 7 2 \n8 9 1 6 \n3 6 9 9 \n3 4 1 2 \n8 6 7 6 \n10 9 9 9 \n",
"10 4 7 1 \n5 11 1 6 \n1 6 12 9 \n1 4 1 1 \n5 6 7 6 \n10 11 12 9 \n",
"10 4 7 1 \n5 11 2 6 \n1 6 12 9 \n1 4 2 1 \n5 6 7 6 \n10 11 12 9 \n",
"5 2 \n3 4 \n2 5 \n2 2 \n3 4 \n5 5 \n",
"5 1 \n3 3 \n1 5 \n1 1 \n3 3 \n5 5 \n",
"10 4 5 2 \n8 11 1 6 \n3 6 12 9 \n3 4 1 2 \n8 6 5 6 \n10 11 12 9 \n",
"10 4 7 4 \n8 11 1 5 \n3 6 12 9 \n3 4 1 4 \n8 6 7 5 \n10 11 12 9 \n",
"6 1 \n4 3 \n1 5 \n1 1 \n4 3 \n6 5 \n",
"11 4 8 2 \n8 10 1 6 \n3 6 12 9 \n3 4 1 2 \n8 6 8 6 \n11 10 12 9 \n",
"10 4 8 1 \n8 11 2 5 \n1 6 9 9 \n1 4 2 1 \n8 6 8 5 \n10 11 9 9 \n",
"11 4 7 2 \n8 11 2 6 \n1 7 12 9 \n1 4 2 2 \n8 7 7 6 \n11 11 12 9 \n",
"5 4 \n4 1 \n1 5 \n1 1 \n4 4 \n5 5 \n"
]
}
|
We have a grid with N rows and M columns of squares. Each integer from 1 to NM is written in this grid once. The number written in the square at the i-th row from the top and the j-th column from the left is A_{ij}.
You need to rearrange these numbers as follows:
1. First, for each of the N rows, rearrange the numbers written in it as you like.
2. Second, for each of the M columns, rearrange the numbers written in it as you like.
3. Finally, for each of the N rows, rearrange the numbers written in it as you like.
After rearranging the numbers, you want the number written in the square at the i-th row from the top and the j-th column from the left to be M\times (i-1)+j. Construct one such way to rearrange the numbers. The constraints guarantee that it is always possible to achieve the objective.
Constraints
* 1 \leq N,M \leq 100
* 1 \leq A_{ij} \leq NM
* A_{ij} are distinct.
Input
Input is given from Standard Input in the following format:
N M
A_{11} A_{12} ... A_{1M}
:
A_{N1} A_{N2} ... A_{NM}
Output
Print one way to rearrange the numbers in the following format:
B_{11} B_{12} ... B_{1M}
:
B_{N1} B_{N2} ... B_{NM}
C_{11} C_{12} ... C_{1M}
:
C_{N1} C_{N2} ... C_{NM}
Here B_{ij} is the number written in the square at the i-th row from the top and the j-th column from the left after Step 1, and C_{ij} is the number written in that square after Step 2.
Examples
Input
3 2
2 6
4 3
1 5
Output
2 6
4 3
5 1
2 1
4 3
5 6
Input
3 4
1 4 7 10
2 5 8 11
3 6 9 12
Output
1 4 7 10
5 8 11 2
9 12 3 6
1 4 3 2
5 8 7 6
9 12 11 10
|
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],
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|
You are given a box full of mirrors. Box consists of grid of size n × m. Each cell of the grid contains a mirror put in the shape of '\' or ' / ' (45 degree to the horizontal or vertical line). But mirrors in some cells have been destroyed. You want to put new mirrors into these grids so that the following two conditions are satisfied:
1. If you put a light ray horizontally/vertically into the middle of any unit segment that is side of some border cell, the light will go out from the neighboring unit segment to the segment you put the ray in.
2. each unit segment of the grid of the mirror box can be penetrated by at least one light ray horizontally/vertically put into the box according to the rules of the previous paragraph
<image>
After you tried putting some mirrors, you find out that there are many ways of doing so. How many possible ways are there? The answer might be large, so please find the result modulo prime number MOD.
Input
The first line contains three integers n, m, MOD (1 ≤ n, m ≤ 100, 3 ≤ MOD ≤ 109 + 7, MOD is prime), m, n indicates the dimensions of a box and MOD is the number to module the answer.
The following n lines each contains a string of length m. Each string contains only ' / ', '\', '*', where '*' denotes that the mirror in that grid has been destroyed.
It is guaranteed that the number of '*' is no more than 200.
Output
Output the answer modulo MOD.
Examples
Input
2 2 1000000007
*/
/*
Output
1
Input
2 2 1000000007
**
\\
Output
1
Input
2 2 3
**
**
Output
2
Note
The only way for sample 1 is shown on the left picture from the statement.
The only way for sample 2 is shown on the right picture from the statement.
For the third sample, there are 5 possibilities that are listed below:
1.
<image>
<image>
2.
<image>
<image>
3.
<image>
<image>
4.
<image>
<image>
5.
<image>
<image>
The answer is then module by 3 so the output should be 2.
|
{
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],
"outputs": [
"010101",
"01010",
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"0101010\n",
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"010101\n",
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]
}
|
Sonya decided to organize an exhibition of flowers. Since the girl likes only roses and lilies, she decided that only these two kinds of flowers should be in this exhibition.
There are n flowers in a row in the exhibition. Sonya can put either a rose or a lily in the i-th position. Thus each of n positions should contain exactly one flower: a rose or a lily.
She knows that exactly m people will visit this exhibition. The i-th visitor will visit all flowers from l_i to r_i inclusive. The girl knows that each segment has its own beauty that is equal to the product of the number of roses and the number of lilies.
Sonya wants her exhibition to be liked by a lot of people. That is why she wants to put the flowers in such way that the sum of beauties of all segments would be maximum possible.
Input
The first line contains two integers n and m (1≤ n, m≤ 10^3) — the number of flowers and visitors respectively.
Each of the next m lines contains two integers l_i and r_i (1≤ l_i≤ r_i≤ n), meaning that i-th visitor will visit all flowers from l_i to r_i inclusive.
Output
Print the string of n characters. The i-th symbol should be «0» if you want to put a rose in the i-th position, otherwise «1» if you want to put a lily.
If there are multiple answers, print any.
Examples
Input
5 3
1 3
2 4
2 5
Output
01100
Input
6 3
5 6
1 4
4 6
Output
110010
Note
In the first example, Sonya can put roses in the first, fourth, and fifth positions, and lilies in the second and third positions;
* in the segment [1…3], there are one rose and two lilies, so the beauty is equal to 1⋅ 2=2;
* in the segment [2…4], there are one rose and two lilies, so the beauty is equal to 1⋅ 2=2;
* in the segment [2…5], there are two roses and two lilies, so the beauty is equal to 2⋅ 2=4.
The total beauty is equal to 2+2+4=8.
In the second example, Sonya can put roses in the third, fourth, and sixth positions, and lilies in the first, second, and fifth positions;
* in the segment [5…6], there are one rose and one lily, so the beauty is equal to 1⋅ 1=1;
* in the segment [1…4], there are two roses and two lilies, so the beauty is equal to 2⋅ 2=4;
* in the segment [4…6], there are two roses and one lily, so the beauty is equal to 2⋅ 1=2.
The total beauty is equal to 1+4+2=7.
|
{
"inputs": [
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"7\n4\n-1\n-1\n30\n26\n21\n1"
],
"outputs": [
"1 10\n1 11\n2 8\n2 15\n3 5\n3 9\n4 5\n4 10\n5 15\n6 12\n6 14\n7 13\n9 12\n11 13",
"-1",
"1 2\n1 3\n1 5\n3 4\n5 6\n6 7",
"-1\n",
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"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n"
]
}
|
You are given a sequence D_1, D_2, ..., D_N of length N. The values of D_i are all distinct. Does a tree with N vertices that satisfies the following conditions exist?
* The vertices are numbered 1,2,..., N.
* The edges are numbered 1,2,..., N-1, and Edge i connects Vertex u_i and v_i.
* For each vertex i, the sum of the distances from i to the other vertices is D_i, assuming that the length of each edge is 1.
If such a tree exists, construct one such tree.
Constraints
* 2 \leq N \leq 100000
* 1 \leq D_i \leq 10^{12}
* D_i are all distinct.
Input
Input is given from Standard Input in the following format:
N
D_1
D_2
:
D_N
Output
If a tree with n vertices that satisfies the conditions does not exist, print `-1`.
If a tree with n vertices that satisfies the conditions exist, print n-1 lines. The i-th line should contain u_i and v_i with a space in between. If there are multiple trees that satisfy the conditions, any such tree will be accepted.
Examples
Input
7
10
15
13
18
11
14
19
Output
1 2
1 3
1 5
3 4
5 6
6 7
Input
2
1
2
Output
-1
Input
15
57
62
47
45
42
74
90
75
54
50
66
63
77
87
51
Output
1 10
1 11
2 8
2 15
3 5
3 9
4 5
4 10
5 15
6 12
6 14
7 13
9 12
11 13
|
{
"inputs": [
"4 5 3 1 5\n",
"5 1 2 1 2\n",
"3 3 1 1 1\n",
"2 313 856 964 421\n",
"61 464 623 89 548\n",
"37 261 207 1 1000\n",
"4 202 512 995 375\n",
"3 3 1 6 9\n",
"213 480 811 134 745\n",
"1 10 2 6 10\n",
"6 5 7 10 4\n",
"2 7 6 2 3\n",
"29 344 406 900 1\n",
"1 2 8 8 5\n",
"1 1 1 1 1\n",
"424 41 41 909 909\n",
"641 31 29 161 802\n",
"12 462 8 311 327\n",
"15 14 32 65 28\n",
"1 2 8 9 8\n",
"9 5 7 8 7\n",
"637 324 69 612 998\n",
"884 913 263 641 265\n",
"2 9 8 8 9\n",
"13 849 819 723 918\n",
"894 197 325 232 902\n",
"485 117 368 567 609\n",
"69 1 2 1 2\n",
"436 306 266 493 580\n",
"8 8 1 1 1\n",
"2 3 9 8 2\n",
"1000 1000 1000 1000 1000\n",
"3 313 856 964 421\n",
"3 3 1 11 9\n",
"2 2 9 8 1\n",
"61 538 623 89 548\n",
"7 202 512 995 375\n",
"213 480 811 69 745\n",
"1 10 2 4 10\n",
"6 10 7 10 4\n",
"2 7 9 2 3\n",
"39 344 406 900 1\n",
"424 41 41 740 909\n",
"641 28 29 161 802\n",
"12 462 8 130 327\n",
"8 14 32 65 28\n",
"2 5 7 8 7\n",
"637 324 69 612 540\n",
"884 913 263 641 150\n",
"2 9 8 8 10\n",
"13 849 819 475 918\n",
"894 197 197 232 902\n",
"485 228 368 567 609\n",
"131 1 2 1 2\n",
"436 306 266 59 580\n",
"8 9 1 1 1\n",
"2 3 14 8 2\n",
"4 9 3 1 5\n",
"3 3 1 2 1\n",
"73 538 623 89 548\n",
"7 237 512 995 375\n",
"6 3 1 11 9\n",
"213 480 811 33 745\n",
"1 10 2 1 10\n",
"6 10 7 5 4\n",
"2 9 9 2 3\n",
"39 333 406 900 1\n",
"641 28 35 161 802\n",
"12 166 8 130 327\n",
"10 14 32 65 28\n",
"637 324 69 612 177\n",
"884 913 263 266 150\n",
"2 9 8 8 7\n",
"13 849 744 475 918\n",
"894 141 197 232 902\n",
"131 1 2 1 4\n",
"436 306 337 59 580\n",
"8 9 1 1 2\n",
"2 2 9 8 2\n",
"4 8 3 1 5\n",
"3 3 1 3 1\n",
"73 538 623 89 474\n",
"7 237 22 995 375\n",
"6 3 1 1 9\n",
"213 562 811 33 745\n",
"1 10 2 1 18\n",
"6 7 7 5 4\n",
"2 13 9 2 3\n",
"39 640 406 900 1\n",
"641 28 35 240 802\n",
"12 166 8 130 523\n",
"10 14 47 65 28\n",
"637 442 69 612 177\n",
"884 913 263 96 150\n",
"13 849 744 475 316\n",
"859 306 337 59 580\n",
"8 9 2 1 2\n",
"4 15 3 1 5\n",
"3 3 1 3 2\n",
"73 538 675 89 474\n",
"7 237 22 995 530\n",
"3 3 1 1 9\n",
"213 763 811 33 745\n",
"6 7 7 5 2\n",
"2 13 9 1 3\n",
"39 640 406 900 2\n",
"641 38 35 240 802\n",
"23 166 8 130 523\n",
"10 4 47 65 28\n",
"637 349 69 612 177\n",
"884 913 263 96 222\n",
"859 306 337 59 344\n",
"8 9 2 2 2\n",
"2 2 9 11 1\n",
"4 15 5 1 5\n",
"73 538 675 89 583\n",
"7 237 22 995 732\n",
"3 3 1 2 9\n",
"200 763 811 33 745\n",
"4 7 7 5 2\n",
"2 13 16 1 3\n",
"641 38 35 240 265\n",
"31 166 8 130 523\n",
"10 4 47 9 28\n",
"637 240 69 612 177\n",
"884 913 263 171 222\n",
"859 163 337 59 344\n",
"16 9 2 2 2\n",
"7 15 5 1 5\n"
],
"outputs": [
"Friendship\n",
"First\n",
"Second\n",
"Friendship\n",
"First\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"First\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Friendship\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Friendship\n",
"Friendship\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Friendship\n",
"Friendship\n",
"First\n",
"Second\n",
"Friendship\n",
"First\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"First\n",
"First\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n",
"First\n",
"Second\n",
"Second\n"
]
}
|
Two boys decided to compete in text typing on the site "Key races". During the competition, they have to type a text consisting of s characters. The first participant types one character in v1 milliseconds and has ping t1 milliseconds. The second participant types one character in v2 milliseconds and has ping t2 milliseconds.
If connection ping (delay) is t milliseconds, the competition passes for a participant as follows:
1. Exactly after t milliseconds after the start of the competition the participant receives the text to be entered.
2. Right after that he starts to type it.
3. Exactly t milliseconds after he ends typing all the text, the site receives information about it.
The winner is the participant whose information on the success comes earlier. If the information comes from both participants at the same time, it is considered that there is a draw.
Given the length of the text and the information about participants, determine the result of the game.
Input
The first line contains five integers s, v1, v2, t1, t2 (1 ≤ s, v1, v2, t1, t2 ≤ 1000) — the number of characters in the text, the time of typing one character for the first participant, the time of typing one character for the the second participant, the ping of the first participant and the ping of the second participant.
Output
If the first participant wins, print "First". If the second participant wins, print "Second". In case of a draw print "Friendship".
Examples
Input
5 1 2 1 2
Output
First
Input
3 3 1 1 1
Output
Second
Input
4 5 3 1 5
Output
Friendship
Note
In the first example, information on the success of the first participant comes in 7 milliseconds, of the second participant — in 14 milliseconds. So, the first wins.
In the second example, information on the success of the first participant comes in 11 milliseconds, of the second participant — in 5 milliseconds. So, the second wins.
In the third example, information on the success of the first participant comes in 22 milliseconds, of the second participant — in 22 milliseconds. So, it is be a draw.
|
{
"inputs": [
"2\n31\n4 1\n160\n9 2\n\nSAMPLE",
"2\n31\n4 1\n98\n9 2\n\nSAMPLE",
"2\n31\n7 1\n98\n17 2\n\nSAMOLE",
"2\n6\n7 1\n98\n17 2\n\nSAMOLE",
"2\n6\n4 2\n98\n24 3\n\nSAMOLE",
"2\n6\n4 2\n152\n24 3\n\nSAMOLE",
"2\n12\n4 1\n152\n24 3\n\nSAMOLE",
"2\n12\n4 1\n72\n24 3\n\nELOMAS",
"2\n12\n4 1\n11\n24 3\n\nEKOMAS",
"2\n12\n4 1\n11\n19 3\n\nEKOMAS",
"2\n12\n7 1\n20\n19 3\n\nEKOMAS",
"2\n12\n7 1\n20\n19 6\n\nEKPLAS",
"2\n26\n9 0\n20\n26 0\n\nEKPLAS",
"2\n26\n9 0\n33\n10 0\n\nEKPLAS",
"2\n39\n9 0\n33\n10 0\n\nEKPLAS",
"2\n39\n9 0\n33\n2 0\n\nEKPLAS",
"2\n39\n9 0\n53\n2 0\n\nEKPLAS",
"2\n28\n9 0\n53\n2 0\n\nEKPALS",
"2\n28\n9 0\n53\n3 0\n\nEKPBLR",
"2\n28\n9 0\n86\n3 0\n\nEKPBLR",
"2\n10\n3 0\n86\n3 0\n\nEPRBLK",
"2\n3\n3 0\n86\n3 0\n\nEPRBLK",
"2\n0\n3 0\n86\n3 0\n\nEPRBLK",
"2\n0\n3 0\n86\n3 1\n\nEPRBLK",
"2\n0\n3 0\n22\n3 2\n\nEPRBLK",
"2\n0\n3 0\n3\n1 2\n\nEPRBLK",
"2\n0\n2 -1\n5\n1 4\n\nEPRBLJ",
"2\n1\n2 -1\n5\n1 4\n\nEPRBLJ",
"2\n2\n4 0\n5\n1 4\n\nEPRBLJ",
"2\n2\n4 0\n4\n1 4\n\nEPRBLJ",
"2\n1\n12 0\n4\n0 0\n\nEPRBLJ",
"2\n0\n16 0\n4\n0 0\n\nJLBRPE",
"2\n0\n16 0\n0\n-1 0\n\nJLBRPE",
"2\n1\n22 0\n0\n-2 1\n\nEPRBLJ",
"2\n2\n22 0\n0\n-2 1\n\nEPRBLJ",
"2\n31\n4 1\n20\n9 2\n\nSAMPLE",
"2\n49\n4 1\n98\n9 2\n\nSAMPLE",
"2\n31\n4 1\n98\n0 2\n\nSAMOLE",
"2\n6\n7 1\n70\n17 2\n\nSAMOLE",
"2\n6\n4 2\n28\n17 2\n\nSAMOLE",
"2\n1\n4 2\n98\n24 3\n\nSAMOLE",
"2\n10\n4 2\n152\n24 3\n\nSAMOLE",
"2\n20\n4 1\n152\n24 3\n\nSAMOLE",
"2\n12\n4 1\n152\n24 5\n\nELOMAS",
"2\n12\n5 1\n11\n24 3\n\nEKOMAS",
"2\n16\n7 0\n20\n19 0\n\nEKPLAS",
"2\n16\n14 1\n20\n19 0\n\nEKPLAS",
"2\n26\n9 0\n23\n26 0\n\nEKPLAS",
"2\n43\n9 0\n33\n10 0\n\nEKPLAS",
"2\n39\n16 0\n53\n2 0\n\nEKPLAS",
"2\n28\n0 0\n53\n2 0\n\nEKPALS",
"2\n28\n9 1\n53\n3 0\n\nEKPBLR",
"2\n28\n9 0\n158\n3 0\n\nEKPBLR",
"2\n28\n11 0\n19\n3 0\n\nEKRBLP",
"2\n47\n3 0\n86\n3 0\n\nEKRBLP",
"2\n0\n3 0\n22\n5 2\n\nEPRBLK",
"2\n1\n3 0\n3\n1 2\n\nEPRBLK",
"2\n2\n4 0\n7\n1 0\n\nEPRBLJ",
"2\n2\n12 0\n6\n0 0\n\nEPRBLJ",
"2\n0\n16 0\n8\n-1 0\n\nJLBRPE",
"2\n4\n22 -2\n0\n-2 1\n\nEPRBLJ",
"2\n31\n4 1\n191\n0 2\n\nSAMOLE",
"2\n31\n3 1\n37\n17 2\n\nSAMOLE",
"2\n6\n7 2\n98\n20 2\n\nSAMOLE",
"2\n20\n4 1\n176\n24 3\n\nSAMOLE",
"2\n12\n2 0\n11\n19 3\n\nEKOMAS",
"2\n4\n7 0\n20\n19 0\n\nEKPLAS",
"2\n26\n9 0\n6\n10 0\n\nEKPKAS",
"2\n39\n9 0\n33\n13 0\n\nEKPLAS",
"2\n39\n10 0\n33\n2 0\n\nSALPKE",
"2\n13\n9 0\n53\n4 0\n\nEKPALS",
"2\n28\n5 0\n158\n3 0\n\nEKPBLR",
"2\n79\n3 0\n86\n3 0\n\nEKRBLP",
"2\n3\n3 0\n86\n2 1\n\nEPRBLK",
"2\n1\n4 0\n6\n1 4\n\nEQRBLJ",
"2\n0\n31 0\n2\n0 0\n\nJLBRPE",
"2\n43\n4 2\n98\n9 2\n\nSAMPLE",
"2\n31\n4 1\n100\n0 2\n\nSAMOLE",
"2\n31\n3 1\n37\n14 2\n\nSAMOLE",
"2\n7\n7 2\n98\n24 2\n\nSEMOLA",
"2\n5\n4 1\n152\n24 3\n\nSAMOLE",
"2\n20\n4 0\n176\n24 3\n\nSAMOLE",
"2\n12\n4 0\n69\n24 3\n\nELOMAS",
"2\n12\n3 1\n72\n24 3\n\nEKO@MS",
"2\n12\n2 0\n11\n32 3\n\nEKOMAS",
"2\n12\n6 1\n20\n20 3\n\nEKPMAS",
"2\n30\n12 2\n20\n19 0\n\nEKPLAS",
"2\n5\n9 0\n6\n10 0\n\nEKPKAS",
"2\n43\n9 0\n33\n17 0\n\nEPKLAS",
"2\n39\n10 0\n33\n0 0\n\nSALPKE",
"2\n39\n0 0\n53\n2 0\n\nEKPLBS",
"2\n15\n5 0\n158\n3 0\n\nEKPBLR",
"2\n1\n3 -1\n2\n0 4\n\nEPRBLJ",
"2\n1\n2 0\n10\n2 4\n\nJLBRPE",
"2\n0\n22 -1\n1\n-2 -1\n\nJLBRPE",
"2\n1\n1 -3\n1\n1 0\n\nDPRBLJ",
"2\n23\n4 1\n100\n0 2\n\nSAMOLE",
"2\n6\n2 1\n8\n17 2\n\nSAMOLE",
"2\n7\n7 2\n61\n24 2\n\nSEMOLA",
"2\n10\n4 1\n167\n24 3\n\nSAMOLE",
"2\n20\n4 0\n83\n24 3\n\nSAMOLE"
],
"outputs": [
"11\n000\n",
"11\n90\n",
"00\n90\n",
"6\n90\n",
"6\n01\n",
"6\n112\n",
"01\n112\n",
"01\n01\n",
"01\n11\n",
"01\n00\n",
"00\n00\n",
"00\n20\n",
"20\n20\n",
"20\n33\n",
"30\n33\n",
"30\n31\n",
"30\n51\n",
"20\n51\n",
"20\n50\n",
"20\n80\n",
"10\n80\n",
"3\n80\n",
"0\n80\n",
"0\n00\n",
"0\n20\n",
"0\n3\n",
"0\n5\n",
"1\n5\n",
"2\n5\n",
"2\n4\n",
"1\n4\n",
"0\n4\n",
"0\n0\n",
"1\n0\n",
"2\n0\n",
"11\n20\n",
"01\n90\n",
"11\n98\n",
"6\n70\n",
"6\n20\n",
"1\n01\n",
"10\n112\n",
"00\n112\n",
"01\n011\n",
"12\n11\n",
"10\n20\n",
"01\n20\n",
"20\n21\n",
"40\n33\n",
"31\n51\n",
"28\n51\n",
"00\n50\n",
"20\n108\n",
"20\n10\n",
"40\n80\n",
"0\n22\n",
"1\n3\n",
"2\n7\n",
"2\n6\n",
"0\n8\n",
"4\n0\n",
"11\n119\n",
"00\n30\n",
"6\n98\n",
"00\n116\n",
"10\n00\n",
"4\n20\n",
"20\n6\n",
"30\n30\n",
"39\n31\n",
"10\n51\n",
"23\n108\n",
"70\n80\n",
"3\n00\n",
"1\n6\n",
"0\n2\n",
"41\n90\n",
"11\n001\n",
"00\n31\n",
"7\n90\n",
"5\n112\n",
"20\n116\n",
"10\n01\n",
"00\n01\n",
"10\n11\n",
"01\n02\n",
"30\n20\n",
"5\n6\n",
"40\n30\n",
"39\n33\n",
"39\n51\n",
"10\n108\n",
"1\n2\n",
"1\n10\n",
"0\n1\n",
"1\n1\n",
"01\n001\n",
"6\n8\n",
"7\n61\n",
"01\n107\n",
"20\n01\n"
]
}
|
Gudi enters the castle, and moves along the main path. Suddenly, a block in the ground opens and she falls into it! Gudi slides down and lands in a dark room. A mysterious voice announces:
Intruders are not allowed inside the castle. To proceed, you must
solve my puzzle. Here is a string S indexed from 1 to N,
consisting of digits from 0-9. If you summon the spell "Sera", the
string will be rotated clockwise by H positions. If you summon the
spell "Xhaka", the number A will be added to all the even-indexed
digits of the string. For example, if H = 1 A = 3 "Sera" and
"Xhaka" on the string "781" will result in strings ""178" and "711"
respectively i.e. digits post 9 are cycled back to 0. The objective is
to obtain the lexicographically smallest string possible as a result
of applying any of the two spells any number of times in any order. Find the string
and I shall set you free
Input
The first line contains an integer T. T testcases follow.
First line of each test contains the string S.
The next line contains two space-separated integers A and H.
Output
Print the answer to each testcase in a new line.
Constraints
1 ≤ T ≤ 10
1 ≤ N, H ≤ 6
1 ≤ A ≤ 10
SAMPLE INPUT
2
31
4 1
160
9 2
SAMPLE OUTPUT
11
000
Explanation
For the first testcase, we can summon the spells as:
31 --(Sera)- -> 13 --(Xhaka)- -> 17 --(Xhaka)- -> 11, and it is the smallest possible answer.
|
{
"inputs": [
"5 4 10 1 6\n1 1 5\n1 5 5\n1 3 2\n1 5 2\n2 1\n2 2\n",
"5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3\n",
"1 1 2 1 1\n2 1\n",
"1 1 2 0 1\n2 1\n",
"5 4 10 1 6\n1 1 5\n1 5 5\n1 3 2\n1 5 1\n2 1\n2 2\n",
"5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 0\n1 3 2\n2 1\n2 3\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3\n",
"5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 2\n",
"5 4 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 2\n",
"5 4 10 1 6\n1 1 4\n1 5 5\n1 3 2\n1 5 2\n2 1\n2 2\n",
"5 3 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 0\n1 3 2\n2 1\n2 3\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 4 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 1 1\n2 2\n1 4 2\n1 5 2\n2 1\n2 3\n",
"5 4 10 1 6\n1 1 5\n1 5 3\n1 3 2\n1 5 2\n2 1\n2 2\n",
"5 4 1 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 2\n",
"5 4 10 1 6\n1 2 4\n1 5 5\n1 3 2\n1 5 2\n2 1\n2 2\n",
"5 3 2 1 8\n1 1 0\n1 5 3\n1 2 1\n2 2\n1 4 0\n1 3 2\n2 1\n2 3\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 5 1\n2 2\n1 4 2\n1 3 2\n2 1\n2 3\n",
"5 4 20 1 6\n1 1 4\n1 2 5\n1 3 2\n1 5 1\n2 1\n2 2\n",
"5 2 2 2 8\n1 1 1\n1 5 3\n1 1 1\n2 2\n1 4 2\n1 5 2\n2 1\n2 3\n",
"1 1 3 0 1\n2 1\n",
"2 1 3 0 1\n2 1\n",
"1 1 2 2 1\n2 1\n",
"5 4 10 1 6\n1 1 4\n1 5 5\n1 3 2\n1 5 1\n2 1\n2 2\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 2 1\n2 2\n1 4 2\n1 5 2\n2 1\n2 3\n",
"2 1 3 0 1\n2 2\n",
"1 1 2 4 1\n2 1\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 2 1\n2 2\n1 4 4\n1 5 2\n2 1\n2 3\n",
"1 1 2 3 1\n2 1\n",
"1 2 3 0 1\n2 1\n",
"1 1 1 2 1\n2 1\n",
"5 4 20 1 6\n1 1 4\n1 5 5\n1 3 2\n1 5 1\n2 1\n2 2\n",
"2 1 6 0 1\n2 2\n",
"1 1 1 4 1\n2 1\n",
"1 0 1 2 1\n2 1\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 1 1\n2 2\n1 4 2\n1 5 3\n2 1\n2 3\n",
"2 1 11 0 1\n2 2\n",
"2 1 1 4 1\n2 1\n",
"1 0 1 2 1\n2 2\n",
"5 2 2 1 8\n1 2 1\n1 5 3\n1 1 1\n2 2\n1 4 2\n1 5 3\n2 1\n2 3\n",
"2 1 0 4 1\n2 1\n",
"1 0 1 4 1\n2 2\n",
"2 1 0 5 1\n2 1\n",
"2 1 0 2 1\n2 1\n",
"1 1 2 1 1\n2 2\n",
"1 1 2 0 1\n2 2\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 2 2\n2 2\n1 4 2\n1 3 2\n2 1\n2 3\n",
"5 2 2 1 8\n1 1 2\n1 5 3\n1 2 1\n2 2\n1 4 0\n1 3 2\n2 1\n2 2\n",
"2 1 3 0 1\n2 3\n",
"2 1 2 4 1\n2 1\n",
"5 2 2 1 8\n1 1 1\n1 5 3\n1 2 1\n2 2\n1 4 4\n1 5 1\n2 1\n2 3\n",
"1 1 2 3 1\n2 2\n",
"1 1 1 0 1\n2 1\n",
"2 0 11 0 1\n2 2\n",
"1 0 2 4 1\n2 2\n"
],
"outputs": [
"7\n1\n",
"3\n6\n4\n",
"0\n",
"0\n",
"6\n1\n",
"3\n4\n4\n",
"3\n6\n4\n",
"3\n6\n5\n",
"1\n2\n1\n",
"7\n1\n",
"3\n2\n2\n",
"4\n6\n3\n",
"3\n4\n3\n",
"5\n1\n",
"1\n1\n1\n",
"7\n0\n",
"2\n2\n1\n",
"3\n6\n3\n",
"1\n1\n",
"4\n4\n4\n",
"0\n",
"0\n",
"0\n",
"6\n1\n",
"3\n4\n4\n",
"0\n",
"0\n",
"3\n4\n4\n",
"0\n",
"0\n",
"0\n",
"6\n1\n",
"0\n",
"0\n",
"0\n",
"3\n4\n3\n",
"0\n",
"0\n",
"0\n",
"3\n4\n4\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"3\n6\n4\n",
"3\n4\n3\n",
"0\n",
"0\n",
"3\n4\n4\n",
"0\n",
"0\n",
"0\n",
"0\n"
]
}
|
A factory produces thimbles in bulk. Typically, it can produce up to a thimbles a day. However, some of the machinery is defective, so it can currently only produce b thimbles each day. The factory intends to choose a k-day period to do maintenance and construction; it cannot produce any thimbles during this time, but will be restored to its full production of a thimbles per day after the k days are complete.
Initially, no orders are pending. The factory receives updates of the form di, ai, indicating that ai new orders have been placed for the di-th day. Each order requires a single thimble to be produced on precisely the specified day. The factory may opt to fill as many or as few of the orders in a single batch as it likes.
As orders come in, the factory owner would like to know the maximum number of orders he will be able to fill if he starts repairs on a given day pi. Help the owner answer his questions.
Input
The first line contains five integers n, k, a, b, and q (1 ≤ k ≤ n ≤ 200 000, 1 ≤ b < a ≤ 10 000, 1 ≤ q ≤ 200 000) — the number of days, the length of the repair time, the production rates of the factory, and the number of updates, respectively.
The next q lines contain the descriptions of the queries. Each query is of one of the following two forms:
* 1 di ai (1 ≤ di ≤ n, 1 ≤ ai ≤ 10 000), representing an update of ai orders on day di, or
* 2 pi (1 ≤ pi ≤ n - k + 1), representing a question: at the moment, how many orders could be filled if the factory decided to commence repairs on day pi?
It's guaranteed that the input will contain at least one query of the second type.
Output
For each query of the second type, print a line containing a single integer — the maximum number of orders that the factory can fill over all n days.
Examples
Input
5 2 2 1 8
1 1 2
1 5 3
1 2 1
2 2
1 4 2
1 3 2
2 1
2 3
Output
3
6
4
Input
5 4 10 1 6
1 1 5
1 5 5
1 3 2
1 5 2
2 1
2 2
Output
7
1
Note
Consider the first sample.
We produce up to 1 thimble a day currently and will produce up to 2 thimbles a day after repairs. Repairs take 2 days.
For the first question, we are able to fill 1 order on day 1, no orders on days 2 and 3 since we are repairing, no orders on day 4 since no thimbles have been ordered for that day, and 2 orders for day 5 since we are limited to our production capacity, for a total of 3 orders filled.
For the third question, we are able to fill 1 order on day 1, 1 order on day 2, and 2 orders on day 5, for a total of 4 orders.
|
{
"inputs": [
"7 2\nabacaba\naa\n",
"15 6\nqwertyhgfdsazxc\nqa\n",
"7 3\nasddsaf\nsd\n",
"4 2\nbbaa\nab\n",
"200 100\ncxqtpwtozcnavklpcksprgecocdraaryxzztqkcfzsrhdrzabtwdukzmsgpnvvgigbtyaxubrngiomfatojjvnvhogqqlujsrglodzwmpyjijtzdzcczlxvhmkkefuereazzwfqbndaccpvlupgixdezadhvwdfzxqzmnkcgwktubylaiezruthgdzqqdrsrorvganxf\nwt\n",
"200 20\nbcbabacbaaaccbbaaabcabccaacaccccbbcbcacaacbaaababcbcaccbbbbcabccaaabbbbaabbbacbbbcacaaccbbbcbbcbbabbcbbcaaacccaccacbccbaccaccaababbccbcccaacbabccbbacbccbccaabaaacaabaaacabcacccbcccaacaccabcaabcbbaacaa\naa\n",
"2 1\naa\nsb\n",
"200 100\nktlrcnrfmafobkjlianalpfkbfqmfjfbknqsocotoscohffjmbjsbbridajqsiegdgishnshsapmriacllkkkdklgghdqekqbdlcolroalqofkekrdtparekephodbbpehmpttdtqoejmiecdfblnlhsalahtekmrhtdkabshcarcidnqbpqoregtfdhqdjdpprtkabi\nll\n",
"200 20\nepajbenfcpoajfftqhjnsafpcsjdenebneehortdglpprkjeampeomldcierqdhlsfnhdlbodaneglrhhoggrdgfnbnlpdgphbienmdarrlaqggticlipopftangkddprrpitdepmhftbeihpknkhjstqbpsemdoomrrghkrqnpnsbtjafmdnqdiiblkskgadtstfnpa\nao\n",
"200 150\nkegdqehqjvqcbcrzovuueubttwyimeddqhazvdfvsmjvbozipwtpgfukiflhtpvdonfnaclrlxkqwnkmeoydwclgjfqanltdcijpiqpbbcmglionapitprpovmmxbkdoqylehyzasfiwlnyujffmcljztmakzwwoarfzgvuofujfxocltljbknjyvxzdrwgrgydpsuwv\nht\n",
"200 1\nstjfrqjrbjdooiolrmhtfieofdafjpqpltiarfkgfnqggqbmljnrlsohplehtjsghsdeofkpgjrnmkohlirgeqsctbdjbqojdnjtmlhjmostdlplfqgsloahpjipkinpelstrstpplqtddeajbigmaatcmtolbkemacaetpbdiclfodsgmmkaoneqfeothhamjsdphhh\nce\n",
"200 150\nshjhthdtsclitsndedjdjfifsrmenhamjcfalglldleihmmjqjfcksbedssiaacgqgspoojlgcretioiaakgngkintpjgjngodjqrifbmptemedchnngkplrmbteetnjasfaiqmomgktlkljgrccqtilgprrqctrefmchsnokanksoceinfanhrdrrkhhofhnchhcjef\nej\n",
"200 20\nhbadbbhfcafhcecgfcecbbaagbegbahcdacgcfbefafhbhcehffhfbfahfgcghhhefhcadgeghdagbadhgabfgchgbgebgdffbhebhgccgefhgadchghhfbhdeeahagghgegbebfbabedefdgdbbcbagfdebbdddfddacfefabbhceahhfhebecbbfegbahfgaghdhca\nde\n",
"11 4\nbdfbdbccdad\nab\n",
"200 1\ncccbaacabcbbabbccbcaaabbbacacccbacaaababcabbaabacabaacbaacbaaccbcaabccabbaabcacabcaaaaaabaccbcacbbacabbaaccacabbcbcaaacaaccaccbabaaccbbccbaabbabbbaaaaacbacbcbaacbccabccbaacbacaaabbcbaaaacbccbbababacac\nac\n",
"200 150\neabadadbeaeddccaabddacabacbaeecdbcdaadceaaaaacbabeaadbbcdbdabaeedbcaacdcecababaceeecddcbcabdcddedecccbcdcdeddacebbaacebbeccceeccabcedbdcdcdecadcebcaeeddbbdcebabdccbaddcbdacebaccececdadabdebcbcbbaedace\ncc\n",
"200 20\nebjicbdicahigdfhbgcjgbhchcfcbdjadhhgjeejagfgdbhabiedejcfdffafgfbfbaggdcjjhhdbhhjadgefgdffhcjchjgiagcfehhedgedbjjibcbhcddibejiifdhgfjchbdeefhbdeaifhceiibaggdcegfdafhfdhggjafacagddgeajichjbgidjcgbaiabfg\nbi\n",
"200 0\naaaaabbbbaccbacabaacaaaccccaabbabaacbabcbabbcbcbbaaaacccaabaabbbcbccccbbccaaacbabbabbbaaaccabaaacababacccbcaccccbbacbaccaccccaabaabaabbabcaaacbcbaaabacaaccbacaabacbcababccccaabaaaabcbcbbaabcabcaccccbb\nca\n",
"200 200\naaaaaaaaaaaaaaaaaaaaaaaaaacaaaaaaaaaaaaaaaabaaaaaaaaaaaacaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabcbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbbb\nba\n",
"2 2\nas\nsa\n",
"200 1\nheeaccgddefffgbegdfdefefabdgcabegecbbffagfcegdbaedgdeafahahebbegeebfgbfdefbddegbgbaebcfgedhdfgcfdbafggffbaebddehabhdedffbfebbcdccgcbbffdbbabddabdahgbadgeehdachhceefcfacdccfhbbaehegaebccebfgahfedahfdgf\nch\n",
"200 190\nghcebcdabheeeaeabfghdbegecabebhbahdhfchabchchbdcbcaebaebdbgebebhdadgegdahhdaaabehhgghchadfbggbgecahagdfceeffchfddecfgcdbbdhhecfhdfefdbeagcgaedahdebfffhecfcbbcdceghbfcggeaegcdhdchhebffhgchbgacddabcfbcg\nha\n",
"200 20\nbbbbaaaccacdddeebdbddaadeedcbbdcaedccebcbbabccecacaaacdcaeaaaadaadbaabbeceecacdadebdddadeeadeedccdaaaeeabdbaabeccbedcaaccbbdbabbcdbdbcadeceadaacaaaabaadedecaaaabceeecadbaaacceedaebaedbcbcaabcdabcbdbca\ncd\n",
"200 0\naeceedcbdeedaaaededcdeceeabdcaddaccaaccdbdeeeddaededcbbceeeeebbcbcbcbeddadcaeaabbecbdceabcbbdeaeecedeeecaccbacebaaecadbaccbadcbdbebcaeebecdddbaaaaeacbbacbbbedabeaaccbddacedccdaaaeaeebbbabebcebccbbdbba\nac\n",
"2 1\nas\nsa\n",
"2 0\nas\nas\n",
"200 0\nesiqcqkirmeamjmggfdgrkdjirlesspqqdprrapiaasmserepidgbisilehqmgiddgfssqfmmdsiisdlkhpeqnieghbfpantckqngrehsjcqreplogtljajppamnhlbpbmrmmrirmboacjjpnrdonkachnfcndbmmjfkateltmemofalfplhgrsecpkgmajnpstgpheb\ngb\n",
"200 100\nbcacabeccaceeedbbaacedacadeebbecedebbedeaccdbabeedbccbebabcaccdeeccbdddbabdeadaedadbbddbaedbbadbcbbbdbdaceeaddeaebbbaabedabceebcccbbdcbcdbbedbdccaeacdccdcdaeaccbaebabbecaeeccbdbbaeeccbacaaebadccdcdbbb\ndc\n",
"200 190\nddeaecceeacbccbdbdaaecbeccddbdcdaaeababdccbdeedcaddaeaacbcdebccdaabbdeecdabadaadebaacbebcecdcecbccbaedbeaacddbccdcecbedcdaaccceeebeeceedaadceeedcebeecbcbddeaacddadddeecbacbaddabdeabbcccedbbbabdadcadeb\ndc\n",
"200 1\nbbddbbcddeaaeacbdaabccdcacbddaaeaeddadcaedccdbadecabdeabecdbdddcacebaaeddecbedccdacedecabbadcacaaebbaaaeadccebbabddddbecebadaadeceaccdaceabadcebeaadacbadacbbbcdcacbdaaeadabaecdbcbbdbbbdabdeceeeacaadae\ned\n",
"200 150\nbbbacaabaabaccbbcbbaacbcabacbcaaabcccabaacabaacbcbcccacbccccbaabbccccacccccbcaccbcbcaaaccbbbbbbabbcbcbcacababcccaccbcaabbbacaaacbcacaacbabbcbaacacabcccbbcccbbacbaabbccbaaabccccbbababaccacaccaaacbbcbab\naa\n",
"200 1\nhfgeibjadejebicjdbaebagbjhfegebddcdjdffchiehcghabddgbigjfahaachhdebeihbdcdbcgecifghdejhcehbfhihiebgigfdebjebaiidfffdbcfedbiiaffddijabegdhighgaaeefebabaagjaajdcebicddfdjdegdhfefaagbhiiigbeajaachajejfae\nbi\n",
"200 100\nbbbcccabbccabcccacabacbacaaabccbccbbcaabcbbbaaccbcbcaabbbbcbaaaabaccccbbabbaccacbaacababcbbbbcacaaabaccccbcbbaabcaaabbccbccbbcccabbcbbcccbbccccbcccbcbaabbbcbabcccbbbbcabacaccbcabccbacbbacbcabbacccaccc\nab\n",
"200 150\njbihceccaifigibbjechghaceaffchfjbhajifehfgcadcahgfecahagefjbjdjfdcdehiaicicdgfcadiafbjhigfcidbhfcchfacaibjeijagdiceaadggjcahdfghifebcabccdahbgheacifeiidaagceechdfadhebdaehcjdebccjbjdahhfacihijgdgihhfb\nfd\n",
"200 1\nnryukcmomvckaoezqcowohrtnyyriiphwavhkluujzbjizrxqiqgmgpvqcdgjejxwvcpbbxspcgtixwvnstzyeqcekkkzsypvihejncvvirqzlktjoxocutwrqjorxwfzucxoowxyzooiabssvluagzehhsemtutsnrbbdbphmcqbybpxtgjerpeitdjhnwmvfynvsyu\nxg\n",
"200 190\neaicbbaajbbcdfaefbebidiaecbhfeaeedgaaedfcdaeaehfcejfjghifdaijddcebecfdfffjabjfaecgbebbbdaffghfjfabcdjhgjihhdieffhgjjfjcchbhegbigefbbageeididibihhgihhecbaadecbaaigfjejddgecdgehihefacgdjgdjgcbhfgbbhcdbj\nha\n",
"200 0\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naa\n",
"200 200\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\nba\n",
"200 190\ncbccbbccaabacbbcbccbaccbcaababaacbbaaabccacababaacabbccacabacbcccbcabacabbacbbbcacbbcbbbbcccbbacbbbabcbccbcbbcbcabbabaacaacbacbccbccccaccccbacbacbabcbbaabcbacbbbcaccaaaccabcbbcbaaaacacacccbcacacbcabbc\nbb\n",
"200 150\nhbbfcgafgcfcgcaadbcgefbgafbdfdachggccbacgcddghbeeadafgbfggddefeaagchddbfebddaghaghbcfgebaadeaageefbgghgachabfcbadadhgbbegegehcgfhdghaedcffffbaghfdhfdhdgfcdfaaadbdgebffcegdfggeaheghafddfaeebeagfcbdhddh\ndg\n",
"200 200\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\naa\n",
"200 100\nhageafgacbdbffeahgchedebcdgdgbahcfhbgfghdfgdaefahhbcgabcbhggbbfbfdcffhcaddebdbhhgdheefabgfcdgbhaddgbbhdbedhhgegfebdeeehdhggcgbacfhebaebdddfdeacfhbdgfhdbefdeaefccbdhfefdaaeegahabbgbedagcaaccdhccaabdafh\nhd\n",
"200 200\nnljzwiuvzizliajmqfyxyawpnlmyvmmbiqqoovvjyqlbenvdfhvueifaxpdyiiapysheelmlcebpedcqkvdkeklgiviheqnfipxdgdjppjuqdrmchtgefflwibhatoxecnbqzqftnudewkncezvbpzxeiyfpqrkfeghguiucodhtemmcpgxfyvqkhrzjkvlerchpxklt\ndv\n",
"200 100\njfajfiiicgiehiihdbgghhiihijcejjabibhjcjdgdagbidecgifaagcehbjjbcgjcgijhjeegadcfjbfaahbfhbaddadgdfbjiahfcbhfbicffbhdiaafjjchjgbhdeehdgddahibehdhaeibhfbchadfjchgddgfhfjgihhgejdheajjjfbdibjadchgeeiggifice\ncf\n",
"200 190\ngpjlioirtffmgrmpaclokbglatpgqerrekmnppsttsmdootsaikijsseegrfhkqlspqddjeajngcostnjrjpbiedpsjjanpqmcdepclblllbbjcerhagfcfprlraggghgpmlqcpggqqqpecmomldjqmbgfciotqbtgggfddofahlfgpbnflbgktfgqrldgonnkmqhpic\ngs\n",
"200 0\nadagbgbcbdbbfdcdgfgagefceahdaafdcabfefcgbgecfgbggcfgbfbdabedfehdffhhcfeheacfgacdbbcgacagceaaeaefhfbadcbbfeffeacbhcebhdafgcedcfbdahadcbcdaadbeachbafebecbfhecdcfgabfdbgdcaghhhfahgeeahchbbcdfdfcffffgcdbh\nag\n",
"200 0\ndchhfdcbiiibjhaecegaecfhdaedfhaffgaecaaecifdeefahcceahhacbijdjfdjbahjigjjidhdfebeggehgheaeibbegiajfbajjeffiiebidegjdjhedebdffgddbajefbfgeieidifjibjibbaebigibfddaidajfbajiiefgbjjefgdccicdabefcehjahhffg\nff\n",
"200 0\naonhtwfbjnceqdqitfcbizkxvmyizzuvbwkqtqwisxdlqfqcufmqqnfwknyvuttjcpkwmwqewstelpfdqacsfdheqlouhefsuvqvxxarjgpfqgsvxnqwyozlbzqxvdjkehbkmvtljioxfyiyabeklqjinclkoybfohjltjtrsokxqzyaurziicldapzqauqjzsxajjba\njk\n",
"200 190\nsxiwlhhumpluwfgjbuatlyfqnohqrneofdmmdyyrhiduckgtbubdyqrfnbyoitxergxnyzrnyuzcwzxbyyccxmdphkzqzjfmyvxhwedcmgcvhfhlzvzkmszgntyoenhrpyjkbmwiigalspfnfmvyrdtfgobcfxayvovdgzneqmfcvzfselroobmikqsklutxiezjbebv\nto\n",
"200 20\ncdraadywlpsubhlnmdekghqsdtpxrshaurfiimzznqaslmqwvwkfabgtzolgoixoqkclfhikifrwxkdjtbegwnwrjiqsghayeymyakykomohtcrnmkquqoemvvkbqwcvciheafldcajarhxcigmndjhroeukpqpbawguvvtnohpyktxsiasqpnathvevcmkqcgwhojti\nrp\n",
"200 100\nfxnagvrorsrdqqzdghturzeialybutkwgcknmzqxzfdwvhdazedxigpulvpccadnbqfwzzaereufekkmhvxlzcczdztjijypmwzdolgrsjulqqgohvnvjjotafmoignrbuxaytbgigvvnpgsmzkudwtbazrdhrszfckqtzzxyraardcocegrpskcplkvanczotwptqxc\nwt\n",
"2 1\naa\nbs\n",
"200 100\nibaktrppdjdqhdftgeroqpbqndicrachsbakdthrmkethalashlnlbfdceimjeoqtdttpmhepbbdohpekeraptdrkekfoqlaorlocldbqkeqdhgglkdkkkllcairmpashsnhsigdgeisqjadirbbsjbmjffhocsotocosqnkbfjfmqfbkfplanailjkbofamfrncrltk\nll\n",
"200 1\nstjrrqjrbjdooiolrmhtfieofdafjpqpltiaffkgfnqggqbmljnrlsohplehtjsghsdeofkpgjrnmkohlirgeqsctbdjbqojdnjtmlhjmostdlplfqgsloahpjipkinpelstrstpplqtddeajbigmaatcmtolbkemacaetpbdiclfodsgmmkaoneqfeothhamjsdphhh\nce\n",
"200 150\nshjhthdtsclitsndedjdjfifsrmenhamjcfalglldleihmmjqjfcksbedssiaacgqgspoojlgcretioiaakgngkintpjgjngodjqrifbmptemedchnngkplrmbteetnjasfaiqmomgktlkljgrccqtilgprrqctrefmchsnokanksoceinfanhrdrrkhhofhnchhcjef\ndj\n",
"200 1\ncccbaacabcbbabbccbcaaabbbacacccbacaaababcabbaabacabaacbaacbaaccbcaabccabbaabcacabcaaaaaabaccbcacbbacabbaaccacabbcbcaaacaaccaccbabaaccbbccbaabbabbbaaaaacbacbcbaacbccabbcbaacbacaaabbcbaaaacbccbcababacac\nac\n",
"200 20\ngfbaiabgcjdigbjhcijaegddgacafajgghdfhfadfgecdggabiiechfiaedbhfeedbhcjfghdfiijebiddchbcbijjbdegdehhefcgaigjhcjchffdgfegdajhhbdhhjjcdggabfbfgfaffdfcjedeibahbdgfgajeejghhdajdbcfchchbgjcgbhfdgihacidbcijbe\nbi\n",
"200 0\naaaaabbbbaccbacabaacaaaccccaabbabaacbabcbabbcbcbbaaaacccaabaabbbcbccccbbccaaacbabbabbbaaaccabaabcababacccbcaccccbbacbaccaccccaabaabaabbabcaaacbcbaaabacaaccbacaabacbcababccccaabaaaabcbcbbaabcabcaccccbb\nca\n",
"2 2\nas\nas\n",
"200 1\nheeaccgddefffgbegdfdefefabdgcabegecbbffagfcegdbaedgdeafahahebbegeebfgbfdefbddegbgbaebcfgedhdfgcfdbafggffbaebddehabhdedffbfebbcdccgcbbffdbbabddabdahgbadheehdachhceefcfacdccfhbbaehegaebccebfgahfedahfdgf\nch\n",
"200 190\nghcebcdabheeeaeabfghdbegecabebhbahdhfchabchchbdcbcaebaebdbgebebhdadgegdahhdaaabehhgghchadfbggbgecahagdfceeffchfddecfgcdbbdhhecfhdfefdbeagcgaedahddbfffhecfcbbcdceghbfcggeaegcdhdchhebffhgchbgacddabcfbcg\nha\n",
"200 33\nbbbbaaaccacdddeebdbddaadeedcbbdcaedccebcbbabccecacaaacdcaeaaaadaadbaabbeceecacdadebdddadeeadeedccdaaaeeabdbaabeccbedcaaccbbdbabbcdbdbcadeceadaacaaaabaadedecaaaabceeecadbaaacceedaebaedbcbcaabcdabcbdbca\ncd\n",
"200 1\nbbddbbcddeaaeacbdaabccdcacbddaaeaeddadcaedccdbadecabdeabecdbdddcacebaaeddecbedccdacedecabbadcacaaebbaaaeadccebbabddddbecebadaadeceaccdaceabadcebeaadacbadacbbbcdcacbdaaeadabaecdbcbbdbbbdabdeceeeacaadae\nec\n",
"200 73\nbbbacaabaabaccbbcbbaacbcabacbcaaabcccabaacabaacbcbcccacbccccbaabbccccacccccbcaccbcbcaaaccbbbbbbabbcbcbcacababcccaccbcaabbbacaaacbcacaacbabbcbaacacabcccbbcccbbacbaabbccbaaabccccbbababaccacaccaaacbbcbab\naa\n",
"200 1\nhfgeibjadejebicjdbaebagbjhfegebddcdjdffchiehcghabddgbigjfahaachhdebeihbdcdbcgecifghdejhcehbfhihiebgigfdebjebaiidfffdbcfedbiiaffddijabegdhighgaaeefebabaagjaajdcebicddfdjdegdhfefaagbhiiigceajaachajejfae\nbi\n",
"200 000\nbbbcccabbccabcccacabacbacaaabccbccbbcaabcbbbaaccbcbcaabbbbcbaaaabaccccbbabbaccacbaacababcbbbbcacaaabaccccbcbbaabcaaabbccbccbbcccabbcbbcccbbccccbcccbcbaabbbcbabcccbbbbcabacaccbcabccbacbbacbcabbacccaccc\nab\n",
"200 45\njbihceccaifigibbjechghaceaffchfjbhajifehfgcadcahgfecahagefjbjdjfdcdehiaicicdgfcadiafbjhigfcidbhfcchfacaibjeijagdiceaadggjcahdfghifebcabccdahbgheacifeiidaagceechdfadhebdaehcjdebccjbjdahhfacihijgdgihhfb\nfd\n",
"200 1\nnryukcmomvckaoezqcowohrtnyyriiphwavhkluujzbjizrxqiqgmgpvqcdgjejxwvcpbbxspcgtixwvnstzyeqcekkkzsypvihejncvvirqzlktjoxocutwrqjorxwfzucxoowxyzooiabssvluagzehhsemtutsnrbbdbphmcqbybpxtgjerpeitdjhnwmvfynvsyu\nxh\n",
"200 60\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\nba\n",
"200 190\ncbccbbccaabacbbcbccbaccbcaababaacbbaaabccacababaacabbccacabacbcccbcabacabbacbbbcacbbcbbbbcccbbacbbbabcbccbcbbcbcabbabaacaacb`cbccbccccaccccbacbacbabcbbaabcbacbbbcaccaaaccabcbbcbaaaacacacccbcacacbcabbc\nbb\n",
"200 150\nhddhdbcfgaebeeafddfahgehaeggfdgecffbegdbdaaafdcfgdhdfhdfhgabffffcdeahgdhfgchegegebbghdadabcfbahcaghggbfeegaaedaabegfcbhgahgaddbefbddhcgaaefeddggfbgfadaeebhgddcgcabccgghcadfdbfagbfegcbdaacgcfcgfagcfbbh\ndg\n",
"200 125\nnljzwiuvzizliajmqfyxyawpnlmyvmmbiqqoovvjyqlbenvdfhvueifaxpdyiiapysheelmlcebpedcqkvdkeklgiviheqnfipxdgdjppjuqdrmchtgefflwibhatoxecnbqzqftnudewkncezvbpzxeiyfpqrkfeghguiucodhtemmcpgxfyvqkhrzjkvlerchpxklt\ndv\n",
"200 1\nadagbgbcbdbbfdcdgfgagefceahdaafdcabfefcgbgecfgbggcfgbfbdabedfehdffhhcfeheacfgacdbbcgacagceaaeaefhfbadcbbfeffeacbhcebhdafgcedcfbdahadcbcdaadbeachbafebecbfhecdcfgabfdbgdcaghhhfahgeeahchbbcdfdfcffffgcdbh\nag\n",
"200 0\ndchhfdcbiiibjhaecegaecfhdaedfhaffgaecaafcifdeefahcceahhacbijdjfdjbahjigjjidhdfebeggehgheaeibbegiajfbajjeffiiebidegjdjhedebdffgddbajefbfgeieidifjibjibbaebigibfddaidajfbajiiefgbjjefgdccicdabefcehjahhffg\nff\n",
"200 190\nsxiwlhhumpluwfgjbuatlyfqnohqrneofdmmdyyrhiduckgtbubdyqrfnbyoitxergxnyzrnyuzcwzxbyyccxmdphkzqzjfmyvxhwedcmgcvhfhlzvzkmszgntyoenhrpyjkbmwiigalspfnfmvyrdtfgobcfxayvovdgzneqmfcvzfselroobmikqsklutxiezjbebv\ntp\n",
"200 38\ncdraadywlpsubhlnmdekghqsdtpxrshaurfiimzznqaslmqwvwkfabgtzolgoixoqkclfhikifrwxkdjtbegwnwrjiqsghayeymyakykomohtcrnmkquqoemvvkbqwcvciheafldcajarhxcigmndjhroeukpqpbawguvvtnohpyktxsiasqpnathvevcmkqcgwhojti\nrp\n",
"7 3\nabacaba\naa\n",
"7 3\nasedsaf\nsd\n",
"200 100\nfxnagvrorsrdqqzdghturzeialybutkwgcknmzqxzfdwvhdazedxigpulvpccadnbqfwzzaereufekkmhvxlzcczdztjijypmwzdolgrsjulqqgohvnvjjotafmoignrbuxaytbgigvvnpgsmzkudwtbazrdhrszfckqtzzxyraardcocegrpskcplkvanczotwptqxc\nws\n",
"200 100\nibaktrppdjdqhdftgeroqpbqndicrachsbakdthrmkethalashlnlbfdceimjeoqtdttpmhepbbdohpekeraptdrkekfoqlaorlocldbqkeqdhgglkdkkkllcairmpashsnhsigdgeisqjadirbbsjbmjffhocsotocosqnkbfjfmqfbkfplanailjkbofamfrncrltk\nlm\n",
"200 1\nstjrrqjrbjdooiolrmhtfieofdafjpqpltiaffkgfnqggqbmljnrlsohplehtjsghsdeofkpgjrnmkohlirgeqsctbdjbqojdnjtmlhjmostdlplfqgsloahpjipkinpelstrstpplqtddeajbigmaatcmtolbkemacaetpbdiclfodsgmmkaoneqfeothhamjsdphhh\nec\n",
"200 150\nshjhthdtsclitsndedjdjfifsrmenhamjcfalglldleihmmjqjfcksbedssiaacgqgspoojlgcretioiaakgngkintpjgjngodjqrifbmptemddchnngkplrmbteetnjasfaiqmomgktlkljgrccqtilgprrqctrefmchsnokanksoceinfanhrdrrkhhofhnchhcjef\ndj\n",
"200 0\naaaaabbbbaccbacabaacaaaccccaabbabaacbabcbabbcbcbbaaaacccaabaabbbcbccccbbccaaacbabbabbbaaaccabaabcababacccbbaccccbbacbaccaccccaabaabaabbabcaaacbcbaaabacaaccbacaacacbcababccccaabaaaabcbcbbaabcabcaccccbb\nca\n",
"200 1\nheeaccgddefffgbegdfdefefacdgcabegecbbffagfcegdbaedgdeafahahebbegeebfgbfdefbddegbgbaebcfgedhdfgcfdbafggffbaebddehabhdedffbfebbcdccgcbbffdbbabddabdahgbadheehdachhceefcfacdccfhbbaehegaebccebfgahfedahfdgf\nch\n",
"200 0\nesiqcqkirmeamjmggfdgrkdjirlesspqqdprrapiaasmserepidgbisilehqmgiddgfssqfmmdsiisdlkhpeqnieghbfpantckqngrehsjcqreplogtljajppamnhlbpbmrmmrirmboacjjpnrdonkachnfcndbmmjfkateltmemofalfplhgrsecpkgmajnpstgpheb\nbh\n",
"200 1\nbbddbbcddeaaeacbdaabccdcacbddaaeaeddadcaedccdbadecabdeabecdbdddcacebaaeddecbedccdacedecabbadcacaaebbaaaeadccebbabddddbecebadaadeceaccdaceabadcebeaadacbadacbbbcdcacbdaaeadabaecdbcbbdbbbdabdeceeeacaadae\neb\n",
"200 73\nbbbacaabaabaccbbcbbaacbcabacbcaaabcccabaacabaacbcbcccacbccccbaabbccccacccccbcaccbcbcaaaccbbbbbbabbcbcbcacababcccaccbcaabbbacaaacbcacaacbabbcbaacacabcccbbcccbbacbaabbccbaaabccccbbababaccacaccaaacbbcbab\nab\n",
"200 2\nhfgeibjadejebicjdbaebagbjhfegebddcdjdffchiehcghabddgbigjfahaachhdebeihbdcdbcgecifghdejhcehbfhihiebgigfdebjebaiidfffdbcfedbiiaffddijabegdhighgaaeefebabaagjaajdcebicddfdjdegdhfefaagbhiiigceajaachajejfae\nbi\n",
"200 000\nbbbcccabbccabcccacabacbacaaabccbccbbcaabcbbbaaccbcbcaabbbbcbaaaabaccccbbabbaccacbaacababcbbbbcacaaabaccccbcbbaabcaaabbccbccbbcccabbcbbcccbbccccbcccbcbaabbbcbabcbcbbbbcabacaccbcabccbacbbacbcabbacccaccc\nab\n",
"200 45\njbihceccaifigibbjechghaceaffchfjbhajifehfgcadcahgfecahagefjbjdjfdcdehiaicicdgfcadiafbjhigfcidbhfcchfacaibjeijagdiceaadggjcahdfghifebcabccdahbgheacifeiidaagceechdfadhebdaehcjdebccjbjdahhfacihijgdgihhfb\ndf\n",
"200 1\nuysvnyfvmwnhjdtieprejgtxpbybqcmhpbdbbrnstutmeshhezgaulvssbaioozyxwooxcuzfwxrojqrwtucoxojtklzqrivvcnjehivpyszkkkecqeyztsnvwxitgcpsxbbpcvwxjejgdcqvpgmgqiqxrzijbzjuulkhvawhpiiryyntrhowocqzeoakcvmomckuyrn\nxh\n",
"200 14\naaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb\nba\n",
"200 98\nhddhdbcfgaebeeafddfahgehaeggfdgecffbegdbdaaafdcfgdhdfhdfhgabffffcdeahgdhfgchegegebbghdadabcfbahcaghggbfeegaaedaabegfcbhgahgaddbefbddhcgaaefeddggfbgfadaeebhgddcgcabccgghcadfdbfagbfegcbdaacgcfcgfagcfbbh\ndg\n",
"11 0\nbdfbdbccdad\nab\n",
"2 1\nar\nsa\n",
"2 0\nar\nas\n",
"200 0\nesiqcqkirmeamjmggfdgrkdjirlesspqqdprrapiaasmserepidgbisilehqmgiddgfssqfmmdsiisdlkhpeqnieghbfpantckqngrehsjcqreplogtljajppamnhlbpbmrmmrirmboacjjpnrdonkachnfcndbmmjfkateltmemofalfplhgrsecpkgmajnpstgpheb\nbg\n",
"200 190\nddeaecceeacbccbdbdaaecbeccddbdcdaaeababdccbdeedcaddaeaacbcdebccdaabbdeecdabadaadebaacbebcecdcecbccbaedbeaacddbccdcecbedcdaaccceeebeeceedaadceeedcebeecbcbddeaacddadddeecbacbaddabdeabbcccedbbbabdadcadeb\ncd\n",
"15 8\nqwertyhgfdsazxc\nqa\n",
"4 1\nbbaa\nab\n",
"2 1\nab\nbs\n",
"200 33\nbbbbaaaccacdddeebdbddaadeedcbbdcaedccebcbbabccecacaaacdcaeaaaadaadbaabbeceecacdadebdddadeeadeedccdaaaeeabdbaabeccbedcaaccbbdbabbcdbdbcadeceadaacaaaabaadedecaaaabceeecadbaaacceedaebaedbcbcaabcdabcbdbca\nce\n",
"2 1\nar\nas\n",
"2 0\nar\n`s\n",
"200 190\ncbccbbccaabacbbcbccbaccbcaababaacbbaaabccacababaacabbccacabacbcccbcabacabbacbbbcacbbcbbbbcccbbacbbbabcbccacbbcbcabbabaacaacb`cbccbccccaccccbacbacbabcbbaabcbacbbbcaccaaaccabcbbcbaaaacacacccbcacacbcabbc\nbb\n"
],
"outputs": [
"15\n",
"16\n",
"10\n",
"3\n",
"3125\n",
"3741\n",
"0\n",
"6216\n",
"318\n",
"6380\n",
"25\n",
"7065\n",
"674\n",
"10\n",
"2464\n",
"19503\n",
"600\n",
"2206\n",
"10000\n",
"1\n",
"167\n",
"10000\n",
"1435\n",
"713\n",
"0\n",
"1\n",
"59\n",
"6428\n",
"10000\n",
"608\n",
"19900\n",
"282\n",
"8984\n",
"8355\n",
"32\n",
"10000\n",
"19900\n",
"10000\n",
"19900\n",
"9177\n",
"19900\n",
"5415\n",
"10000\n",
"4106\n",
"9927\n",
"232\n",
"276\n",
"32\n",
"9938\n",
"274\n",
"3179\n",
"0\n",
"6216\n",
"25\n",
"6956\n",
"2474\n",
"555\n",
"2181\n",
"1\n",
"178\n",
"10000\n",
"2023\n",
"564\n",
"8911\n",
"281\n",
"1943\n",
"1575\n",
"46\n",
"5100\n",
"19900\n",
"9585\n",
"4966\n",
"260\n",
"300\n",
"9734\n",
"652\n",
"21\n",
"8\n",
"2979\n",
"3368\n",
"35\n",
"7035\n",
"2158\n",
"193\n",
"24\n",
"605\n",
"6754\n",
"303\n",
"1984\n",
"1440\n",
"44\n",
"1351\n",
"5635\n",
"0\n",
"0\n",
"0\n",
"25\n",
"10000\n",
"25\n",
"1\n",
"0\n",
"1943\n",
"1\n",
"0\n",
"19900\n"
]
}
|
You are given two strings s and t consisting of lowercase Latin letters. The length of t is 2 (i.e. this string consists only of two characters).
In one move, you can choose any character of s and replace it with any lowercase Latin letter. More formally, you choose some i and replace s_i (the character at the position i) with some character from 'a' to 'z'.
You want to do no more than k replacements in such a way that maximizes the number of occurrences of t in s as a subsequence.
Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.
Input
The first line of the input contains two integers n and k (2 ≤ n ≤ 200; 0 ≤ k ≤ n) — the length of s and the maximum number of moves you can make. The second line of the input contains the string s consisting of n lowercase Latin letters. The third line of the input contains the string t consisting of two lowercase Latin letters.
Output
Print one integer — the maximum possible number of occurrences of t in s as a subsequence if you replace no more than k characters in s optimally.
Examples
Input
4 2
bbaa
ab
Output
3
Input
7 3
asddsaf
sd
Output
10
Input
15 6
qwertyhgfdsazxc
qa
Output
16
Input
7 2
abacaba
aa
Output
15
Note
In the first example, you can obtain the string "abab" replacing s_1 with 'a' and s_4 with 'b'. Then the answer is 3.
In the second example, you can obtain the string "ssddsdd" and get the answer 10.
In the fourth example, you can obtain the string "aaacaaa" and get the answer 15.
|
{
"inputs": [
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n7 6 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n7 6 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n14 6 5 4 3 2 1\n",
"2\n3 1\n7 6 3 5 4 2 1\n3 2\n14 6 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 1\n23 6 5 4 3 2 1\n",
"2\n3 1\n7 6 3 5 4 2 1\n3 1\n23 6 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n14 9 5 6 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n17 6 8 4 5 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n14 6 8 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n13 6 8 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n23 6 5 4 3 2 1\n",
"2\n3 2\n14 6 3 5 4 2 1\n3 2\n23 6 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n21 6 8 4 3 2 1\n",
"2\n3 2\n11 6 3 5 4 2 1\n3 2\n7 6 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n14 12 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n17 6 8 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n14 9 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n10 9 5 4 3 2 1\n",
"2\n3 2\n14 6 3 5 4 2 1\n3 2\n23 9 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n17 5 8 4 3 2 1\n",
"2\n3 2\n14 6 3 5 4 2 1\n3 2\n23 13 5 4 3 2 1\n",
"2\n3 2\n14 10 3 5 4 2 1\n3 2\n23 13 5 4 3 2 1\n",
"2\n3 2\n11 6 3 5 4 2 1\n3 2\n21 6 8 4 3 2 1\n",
"2\n3 2\n15 6 3 5 4 2 1\n3 2\n23 9 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n18 9 5 6 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 1\n14 6 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n9 5 8 4 3 2 1\n",
"2\n3 2\n14 6 3 5 4 2 1\n3 2\n23 13 6 4 3 2 1\n",
"2\n3 2\n11 6 3 5 4 2 1\n3 2\n21 6 5 4 3 2 1\n",
"2\n3 2\n14 6 3 5 4 2 1\n3 2\n21 13 6 4 3 2 1\n",
"2\n3 2\n14 10 3 5 4 2 1\n3 2\n23 12 5 4 3 2 1\n",
"2\n3 2\n14 10 3 5 4 2 1\n3 2\n23 12 9 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n13 5 8 4 3 2 1\n",
"2\n3 2\n14 6 3 5 4 2 1\n3 2\n44 13 5 4 3 2 1\n",
"2\n3 2\n11 6 3 5 4 2 1\n3 2\n21 7 8 4 3 2 1\n",
"2\n3 2\n15 6 3 5 4 2 1\n3 2\n23 7 5 4 3 2 1\n",
"2\n3 2\n7 6 3 5 4 2 1\n3 2\n18 9 10 6 3 2 1\n",
"2\n3 1\n14 10 3 5 4 2 1\n3 2\n23 12 9 4 3 2 1\n",
"2\n3 2\n14 6 3 5 4 2 1\n3 1\n44 13 5 4 3 2 1\n"
],
"outputs": [
"10\n1 1 3 3 \n8\n1 1 1 3 \n",
"10\n1 1 3 3 \n8\n1 1 1 3 \n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"1\n1 1 1 1 1 1\n8\n1 1 1 3\n",
"10\n1 1 3 3\n1\n1 1 1 1 1 1\n",
"1\n1 1 1 1 1 1\n1\n1 1 1 1 1 1\n",
"10\n1 1 3 3\n9\n1 1 1 3\n",
"10\n1 1 3 3\n10\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n9\n1 1 1 3\n",
"10\n1 1 3 3\n1\n1 1 1 1 1 1\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n8\n1 1 1 3\n",
"10\n1 1 3 3\n10\n1 1 1 3\n",
"1\n1 1 1 1 1 1\n8\n1 1 1 3\n",
"10\n1 1 3 3\n1\n1 1 1 1 1 1\n"
]
}
|
Drazil likes heap very much. So he created a problem with heap:
There is a max heap with a height h implemented on the array. The details of this heap are the following:
This heap contains exactly 2^h - 1 distinct positive non-zero integers. All integers are distinct. These numbers are stored in the array a indexed from 1 to 2^h-1. For any 1 < i < 2^h, a[i] < a[\left ⌊{i/2}\right ⌋].
Now we want to reduce the height of this heap such that the height becomes g with exactly 2^g-1 numbers in heap. To reduce the height, we should perform the following action 2^h-2^g times:
Choose an index i, which contains an element and call the following function f in index i:
<image>
Note that we suppose that if a[i]=0, then index i don't contain an element.
After all operations, the remaining 2^g-1 element must be located in indices from 1 to 2^g-1. Now Drazil wonders what's the minimum possible sum of the remaining 2^g-1 elements. Please find this sum and find a sequence of the function calls to achieve this value.
Input
The first line of the input contains an integer t (1 ≤ t ≤ 70 000): the number of test cases.
Each test case contain two lines. The first line contains two integers h and g (1 ≤ g < h ≤ 20). The second line contains n = 2^h-1 distinct positive integers a[1], a[2], …, a[n] (1 ≤ a[i] < 2^{20}). For all i from 2 to 2^h - 1, a[i] < a[\left ⌊{i/2}\right ⌋].
The total sum of n is less than 2^{20}.
Output
For each test case, print two lines.
The first line should contain one integer denoting the minimum sum after reducing the height of heap to g. The second line should contain 2^h - 2^g integers v_1, v_2, …, v_{2^h-2^g}. In i-th operation f(v_i) should be called.
Example
Input
2
3 2
7 6 3 5 4 2 1
3 2
7 6 5 4 3 2 1
Output
10
3 2 3 1
8
2 1 3 1
|
{
"inputs": [
"5",
"1",
"4",
"2",
"3",
"8",
"11",
"10",
"7",
"6",
"12",
"14",
"9",
"19",
"16",
"15",
"13",
"23",
"32",
"58",
"99",
"34",
"54",
"35",
"40",
"67",
"41",
"62",
"49",
"24",
"17",
"18",
"21",
"25",
"20",
"30",
"56",
"29",
"66",
"27",
"22",
"105",
"43",
"38",
"28",
"89",
"26",
"46",
"39",
"79",
"45",
"51",
"102",
"31",
"69",
"60",
"108",
"53",
"48",
"74",
"44",
"47",
"70",
"120",
"36",
"42",
"109",
"52",
"81",
"59",
"77",
"68",
"50",
"143",
"122",
"106",
"87",
"103",
"112",
"134",
"75",
"61",
"188",
"73",
"170",
"149",
"125",
"86",
"214",
"37",
"118",
"95",
"76",
"291",
"123",
"72",
"133",
"190",
"96",
"101",
"57"
],
"outputs": [
"130000",
"105000\n",
"123000\n",
"111000\n",
"117000\n",
"152000\n",
"177000\n",
"168000\n",
"144000\n",
"137000\n",
"186000\n",
"206000\n",
"160000\n",
"265000\n",
"228000\n",
"217000\n",
"196000\n",
"324000\n",
"507000\n",
"1823000\n",
"13530000\n",
"560000\n",
"1499000\n",
"588000\n",
"753000\n",
"2833000\n",
"791000\n",
"2218000\n",
"1173000\n",
"341000\n",
"240000\n",
"252000\n",
"293000\n",
"359000\n",
"279000\n",
"459000\n",
"1653000\n",
"437000\n",
"2698000\n",
"396000\n",
"308000\n",
"18135000\n",
"873000\n",
"682000\n",
"416000\n",
"8303000\n",
"377000\n",
"1012000\n",
"717000\n",
"5094000\n",
"963000\n",
"1294000\n",
"15664000\n",
"482000\n",
"3124000\n",
"2011000\n",
"20995000\n",
"1427000\n",
"1117000\n",
"3990000\n",
"917000\n",
"1063000\n",
"3281000\n",
"37712000\n",
"618000\n",
"831000\n",
"22045000\n",
"1359000\n",
"5617000\n",
"1915000\n",
"4620000\n",
"2975000\n",
"1232000\n",
"115848000\n",
"41578000\n",
"19042000\n",
"7530000\n",
"16448000\n",
"25522000\n",
"74673000\n",
"4190000\n",
"2112000\n",
"1040975000\n",
"3800000\n",
"432541000\n",
"155251000\n",
"48132000\n",
"7171000\n",
"3701387000\n",
"649000\n",
"34205000\n",
"11129000\n",
"4400000\n",
"158467928000\n",
"43657000\n",
"3619000\n",
"71117000\n",
"1147676000\n",
"11686000\n",
"14918000\n",
"1736000\n"
]
}
|
Your friend who lives in undisclosed country is involved in debt. He is borrowing 100,000-yen from a loan shark. The loan shark adds 5% interest of the debt and rounds it to the nearest 1,000 above week by week.
Write a program which computes the amount of the debt in n weeks.
Input
An integer n (0 ≤ n ≤ 100) is given in a line.
Output
Print the amout of the debt in a line.
Example
Input
5
Output
130000
|
{
"inputs": [
"3\na\naa\naa\na\n",
"5\nba\na\nabab\na\naba\nbaba\nab\naba\n",
"2\na\nc\n",
"5\na\na\nab\nba\naba\naba\nbaba\nabab\n",
"4\nab\na\nb\nbab\nab\naba\n",
"5\na\naa\naaa\naaaa\nb\nba\nbaa\nbaaa\n",
"4\na\nba\naba\nb\nba\nbab\n",
"4\na\nb\nab\nab\nbab\naba\n",
"5\nbaba\nabab\na\nab\naba\na\nba\naba\n",
"4\nzn\nz\nn\nnzn\nzn\nznz\n",
"4\nb\nab\nbab\na\nab\naba\n",
"4\nb\nbb\nbba\nbbb\nba\na\n",
"8\na\nha\naha\nhaha\nahaha\nhahaha\nahahaha\nh\nha\nhah\nhaha\nhahah\nhahaha\nhahahah\n",
"3\na\na\nba\nab\n",
"4\nza\na\nz\naza\nza\nzaz\n",
"4\na\nab\nbab\nb\nab\naba\n",
"5\nabab\nbaba\nb\nb\nbab\nbab\nba\nab\n",
"3\na\nza\naz\na\n",
"4\nc\ncb\nb\nbcb\ncb\ncbc\n",
"4\na\nc\nac\nab\naba\nbac\n",
"3\na\nb\naa\nab\n",
"5\nc\ncd\ncdc\ncdcc\nb\ncb\nccb\ndccb\n",
"3\na\naa\nba\nb\n",
"5\nbaaa\nbaa\nba\nb\naaaa\naaa\naa\na\n",
"4\nb\nbb\nbbb\na\nba\nbba\n",
"4\naba\na\nba\nb\nba\nbab\n",
"4\nbab\nab\na\nab\naba\nb\n",
"2\nz\nz\n",
"3\nb\nb\nab\nba\n",
"5\nba\na\na\naba\nbaba\nab\naba\nabab\n",
"5\nb\nb\nba\nab\nbab\nbab\nabab\nbaba\n",
"5\nh\nhwh\nwhwh\nhw\nh\nwh\nhwh\nhwhw\n",
"3\nba\nab\na\na\n",
"5\nba\na\nbaba\nabab\na\naba\nab\naba\n",
"5\nxy\nyx\nx\nx\nxyx\nxyx\nyxyx\nxyxy\n",
"3\nah\nha\nh\nh\n",
"5\nba\na\nbaba\na\naba\nabab\nab\naba\n",
"18\nd\nh\ndj\nxh\ndjs\njxh\ndjsh\nzjxh\ndjshf\nkzjxh\ndjshfk\nhkzjxh\ndjshfkj\nkhkzjxh\ndjshfkje\nskhkzjxh\ndjshfkjeh\ndskhkzjxh\ndjshfkjehd\nhdskhkzjxh\ndjshfkjehds\nehdskhkzjxh\ndjshfkjehdsk\njehdskhkzjxh\ndjshfkjehdskh\nkjehdskhkzjxh\ndjshfkjehdskhk\nfkjehdskhkzjxh\ndjshfkjehdskhkz\nhfkjehdskhkzjxh\ndjshfkjehdskhkzj\nshfkjehdskhkzjxh\ndjshfkjehdskhkzjx\njshfkjehdskhkzjxh\n",
"4\nbab\naba\nab\nab\na\nb\n",
"3\na\nb\naa\nba\n",
"2\nz\n{\n",
"3\na\naa\nab\nb\n",
"2\n`\nc\n",
"2\n_\nc\n",
"2\n_\nb\n",
"2\n^\nc\n",
"2\n^\nb\n",
"2\n]\nb\n",
"2\n^\na\n",
"2\n_\na\n",
"2\n_\n`\n",
"2\n`\na\n",
"2\n`\n`\n",
"2\n]\na\n",
"2\n^\nd\n",
"2\n_\nd\n",
"2\n`\nd\n",
"2\n`\ne\n",
"2\na\ne\n",
"2\nb\ne\n",
"2\nc\ne\n",
"2\nb\nf\n",
"2\nc\nf\n",
"2\nd\nf\n",
"2\nd\ne\n",
"2\nd\nd\n",
"2\nc\nd\n",
"2\nc\nc\n",
"2\ny\nz\n",
"2\na\nb\n",
"2\n\\\na\n",
"2\n_\n_\n",
"2\n`\nb\n",
"2\n]\nd\n",
"2\n]\nc\n",
"2\n^\n`\n",
"2\n^\n_\n",
"2\n\\\nc\n",
"2\n]\n`\n",
"2\na\na\n",
"2\n\\\nd\n",
"2\na\nd\n",
"2\n_\ne\n",
"2\nb\nd\n",
"2\na\nf\n",
"2\n`\nf\n",
"2\ne\ne\n",
"2\n\\\n`\n",
"2\nb\ng\n",
"2\ne\nf\n",
"2\nb\nc\n",
"2\na\ng\n",
"2\ny\n{\n",
"2\n^\ne\n",
"2\n[\na\n",
"2\n]\ne\n",
"2\n\\\ne\n",
"2\n^\n^\n",
"2\n\\\nb\n",
"2\n[\nd\n",
"2\n\\\n_\n",
"2\nb\nb\n",
"2\nb\nh\n",
"2\n_\nf\n",
"2\n\\\nf\n",
"2\n[\ne\n",
"2\n`\ng\n",
"2\n]\n_\n",
"2\ne\ng\n",
"2\n[\n`\n",
"2\nc\nh\n",
"2\nf\nf\n",
"2\na\nh\n",
"2\ny\n|\n",
"2\n^\nf\n",
"2\n]\nf\n",
"2\n[\nf\n",
"2\n[\nc\n",
"2\nZ\nf\n",
"2\n\\\n^\n",
"2\nc\ng\n",
"2\n]\ng\n",
"2\n\\\ng\n"
],
"outputs": [
"PPSS",
"SPPSPSPS",
"PS",
"PSPSPSSP",
"PPSSSP",
"SSSSPPPP",
"SPSPSP",
"PSPSSP",
"SPPPPSSS",
"PPSSSP",
"SPSPSP",
"PPSPSS",
"SPSPSPSPSPSPSP",
"PSSP",
"PSPSSP",
"PPSSSP",
"SPPSPSPS",
"PSPS",
"PPSSSP",
"PSSPPS",
"PSPS",
"PPPPSSSS",
"SSPP",
"PPPPSSSS",
"PPPSSS",
"SSPPSP",
"SPPSPS",
"PS",
"PSSP",
"SPSPSPSP",
"PSPSPSSP",
"PPSPSSSP",
"SPPS",
"SPSPSPPS",
"PSPSPSSP",
"SPPS",
"SPSSPPPS",
"PSPSPSPSPSPSPSPSPSPSPSPSPSPSPSPSPS",
"SPPSPS",
"SPSP",
"PS",
"PPSS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS",
"PS"
]
}
|
Ivan wants to play a game with you. He picked some string s of length n consisting only of lowercase Latin letters.
You don't know this string. Ivan has informed you about all its improper prefixes and suffixes (i.e. prefixes and suffixes of lengths from 1 to n-1), but he didn't tell you which strings are prefixes and which are suffixes.
Ivan wants you to guess which of the given 2n-2 strings are prefixes of the given string and which are suffixes. It may be impossible to guess the string Ivan picked (since multiple strings may give the same set of suffixes and prefixes), but Ivan will accept your answer if there is at least one string that is consistent with it. Let the game begin!
Input
The first line of the input contains one integer number n (2 ≤ n ≤ 100) — the length of the guessed string s.
The next 2n-2 lines are contain prefixes and suffixes, one per line. Each of them is the string of length from 1 to n-1 consisting only of lowercase Latin letters. They can be given in arbitrary order.
It is guaranteed that there are exactly 2 strings of each length from 1 to n-1. It is also guaranteed that these strings are prefixes and suffixes of some existing string of length n.
Output
Print one string of length 2n-2 — the string consisting only of characters 'P' and 'S'. The number of characters 'P' should be equal to the number of characters 'S'. The i-th character of this string should be 'P' if the i-th of the input strings is the prefix and 'S' otherwise.
If there are several possible answers, you can print any.
Examples
Input
5
ba
a
abab
a
aba
baba
ab
aba
Output
SPPSPSPS
Input
3
a
aa
aa
a
Output
PPSS
Input
2
a
c
Output
PS
Note
The only string which Ivan can guess in the first example is "ababa".
The only string which Ivan can guess in the second example is "aaa". Answers "SPSP", "SSPP" and "PSPS" are also acceptable.
In the third example Ivan can guess the string "ac" or the string "ca". The answer "SP" is also acceptable.
|
{
"inputs": [
"98765432109876543210\n58",
"30\n4",
"1000000009\n1",
"98765432109876543210\n66",
"30\n1",
"1000000009\n2",
"98765432109876543210\n18",
"1000000009\n4",
"98765432109876543210\n11",
"1000000009\n5",
"98765432109876543210\n12",
"1000000009\n9",
"98765432109876543210\n10",
"1000000009\n7",
"98765432109876543210\n15",
"1000000009\n12",
"98765432109876543210\n4",
"1000000009\n15",
"98765432109876543210\n8",
"1000000009\n29",
"98765432109876543210\n7",
"1000000009\n56",
"98765432109876543210\n5",
"1000000009\n66",
"98765432109876543210\n3",
"98765432109876543210\n1",
"98765432109876543210\n39",
"30\n2",
"98765432109876543210\n19",
"1000000009\n3",
"98765432109876543210\n13",
"98765432109876543210\n6",
"98765432109876543210\n26",
"1000000009\n6",
"98765432109876543210\n9",
"1000000009\n10",
"98765432109876543210\n27",
"1000000009\n18",
"98765432109876543210\n16",
"98765432109876543210\n14",
"1000000009\n51",
"1000000009\n75",
"98765432109876543210\n2",
"98765432109876543210\n29",
"98765432109876543210\n24",
"1000000009\n8",
"1000000009\n19",
"98765432109876543210\n54",
"1000000009\n34",
"98765432109876543210\n47",
"1000000009\n23",
"1000000009\n26",
"98765432109876543210\n25",
"98765432109876543210\n17",
"1000000009\n14",
"98765432109876543210\n20",
"1000000009\n63",
"98765432109876543210\n31",
"1000000009\n41",
"98765432109876543210\n33",
"98765432109876543210\n28",
"1000000009\n13",
"1000000009\n72",
"98765432109876543210\n45",
"1000000009\n57",
"98765432109876543210\n57",
"98765432109876543210\n65",
"98765432109876543210\n63",
"1000000009\n62",
"98765432109876543210\n22",
"98765432109876543210\n59",
"98765432109876543210\n97",
"98765432109876543210\n41",
"98765432109876543210\n23",
"98765432109876543210\n21",
"98765432109876543210\n35",
"98765432109876543210\n69",
"98765432109876543210\n44",
"30\n8",
"1000000009\n11",
"98765432109876543210\n46",
"1000000009\n20",
"98765432109876543210\n34",
"1000000009\n17",
"98765432109876543210\n32",
"1000000009\n22",
"98765432109876543210\n30",
"1000000009\n16",
"1000000009\n42",
"1000000009\n61",
"98765432109876543210\n50",
"98765432109876543210\n42",
"98765432109876543210\n55",
"1000000009\n25",
"1000000009\n24",
"98765432109876543210\n48",
"98765432109876543210\n36",
"98765432109876543210\n51",
"98765432109876543210\n53",
"1000000009\n28",
"98765432109876543210\n68",
"1000000009\n30",
"1000000009\n44"
],
"outputs": [
"635270834",
"6",
"2",
"678072802\n",
"30\n",
"500000004\n",
"852803440\n",
"250000009\n",
"501683936\n",
"200000001\n",
"209841644\n",
"111111112\n",
"851852334\n",
"142857050\n",
"674053666\n",
"83333291\n",
"629630477\n",
"66651211\n",
"314818988\n",
"25565760\n",
"503655900\n",
"9517662\n",
"703704661\n",
"478731\n",
"839507766\n",
"518523284\n",
"772518915\n",
"14\n",
"718682927\n",
"333333336\n",
"441374130\n",
"419788043\n",
"901127825\n",
"166666667\n",
"279835922\n",
"100000000\n",
"642931187\n",
"55555555\n",
"412818589\n",
"736741034\n",
"22505751\n",
"3003\n",
"259261642\n",
"386989694\n",
"504107386\n",
"124999946\n",
"53411337\n",
"823773924\n",
"35037630\n",
"324382258\n",
"43783125\n",
"31147743\n",
"668067881\n",
"205984306\n",
"71437638\n",
"313585115\n",
"1446445\n",
"224694643\n",
"45433800\n",
"768608849\n",
"474811186\n",
"76924167\n",
"24310\n",
"475898053\n",
"7658190\n",
"862438114\n",
"469617749\n",
"992761288\n",
"2001285\n",
"358809540\n",
"429129094\n",
"411923813\n",
"778314984\n",
"687850651\n",
"709084011\n",
"319483398\n",
"491455370\n",
"9815769\n",
"3\n",
"90909090\n",
"244252932\n",
"51760359\n",
"580681766\n",
"58567041\n",
"480570386\n",
"47326521\n",
"306285029\n",
"62353113\n",
"44865975\n",
"2714319\n",
"817703504\n",
"717456176\n",
"606842315\n",
"35135304\n",
"39544000\n",
"130378139\n",
"618199337\n",
"134551917\n",
"215427926\n",
"26180847\n",
"979267466\n",
"26117982\n",
"42126975\n"
]
}
|
Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:
* The sum of the digits in base ten is a multiple of D.
Constraints
* All values in input are integers.
* 1 \leq K < 10^{10000}
* 1 \leq D \leq 100
Input
Input is given from Standard Input in the following format:
K
D
Output
Print the number of integers satisfying the condition, modulo 10^9 + 7.
Examples
Input
30
4
Output
6
Input
1000000009
1
Output
2
Input
98765432109876543210
58
Output
635270834
|
{
"inputs": [
"3\n8 3\n0 1\n4 8",
"1\n1 1",
"2\n1 2\n3 2",
"2\n1 3\n3 1",
"1\n0 0",
"2\n1 5\n5 1",
"3\n8 3\n-1 1\n5 8",
"2\n0 2\n3 1",
"2\n0 1\n3 2",
"2\n1 4\n5 2",
"3\n8 3\n-1 0\n4 8",
"1\n2 2",
"1\n-1 -1",
"2\n1 0\n1 2",
"2\n2 3\n2 1",
"1\n3 3",
"1\n-2 -2",
"2\n1 0\n2 3",
"2\n-1 2\n4 1",
"2\n2 3\n3 2",
"1\n-3 -3",
"2\n2 1\n2 3",
"2\n0 2\n4 2",
"2\n0 0\n2 2",
"2\n0 4\n5 1",
"2\n2 5\n5 2",
"2\n1 3\n4 2",
"2\n1 1\n1 1",
"2\n-2 2\n4 0",
"2\n2 2\n3 3",
"2\n1 2\n2 1",
"2\n2 0\n1 3",
"2\n1 1\n0 0",
"2\n-2 1\n4 1",
"2\n0 1\n1 0",
"3\n11 3\n-1 1\n2 8",
"2\n0 3\n4 1",
"2\n0 2\n2 0",
"2\n2 2\n2 2",
"1\n-6 -6",
"2\n2 2\n1 1",
"1\n-4 -4",
"2\n-1 0\n2 1",
"2\n-4 1\n6 1",
"2\n1 1\n2 2",
"2\n0 0\n1 1",
"2\n2 1\n1 2",
"2\n0 1\n2 1",
"2\n2 4\n3 1",
"2\n2 2\n4 4",
"2\n0 0\n4 4",
"2\n3 0\n0 3",
"2\n1 2\n0 -1",
"2\n1 0\n0 1",
"2\n1 -1\n1 3",
"2\n1 4\n3 0",
"2\n1 0\n3 4",
"2\n0 0\n3 3",
"2\n0 -1\n1 2",
"2\n1 3\n2 0",
"2\n2 0\n0 2",
"2\n1 -1\n0 2",
"2\n0 0\n0 0",
"2\n-1 1\n1 -1",
"2\n1 1\n3 3",
"2\n-1 -1\n1 1",
"2\n4 4\n2 2",
"1\n4 4",
"2\n2 0\n2 4",
"2\n0 1\n0 -1",
"2\n-1 2\n2 -1",
"2\n2 2\n0 0",
"2\n1 2\n1 0",
"2\n-1 -1\n0 0",
"2\n0 3\n3 0",
"2\n0 3\n2 -1",
"2\n2 -1\n-1 2",
"2\n0 2\n1 -1",
"2\n-1 1\n2 0",
"2\n2 1\n-1 0",
"2\n-1 2\n3 0",
"2\n1 5\n6 2",
"2\n1 0\n4 5",
"2\n1 2\n4 3",
"2\n2 4\n2 0",
"1\n0 0",
"1\n-1 -1",
"1\n2 2",
"2\n0 2\n4 2",
"1\n-2 -2",
"1\n-3 -3",
"2\n0 3\n4 1",
"2\n1 2\n1 0",
"2\n1 4\n4 1",
"1\n4 4",
"2\n0 1\n3 2",
"1\n3 3",
"1\n-4 -4",
"2\n1 2\n2 1",
"2\n0 0\n3 3",
"2\n1 4\n3 0",
"2\n1 1\n3 3",
"2\n1 3\n3 1"
],
"outputs": [
"9",
"0",
"2",
"3\n",
"0\n",
"5\n",
"9\n",
"2\n",
"1\n",
"4\n",
"8\n",
"0\n",
"0\n",
"2\n",
"3\n",
"0\n",
"0\n",
"3\n",
"2\n",
"3\n",
"0\n",
"3\n",
"2\n",
"0\n",
"4\n",
"5\n",
"3\n",
"0\n",
"2\n",
"0\n",
"2\n",
"3\n",
"0\n",
"1\n",
"1\n",
"9\n",
"3\n",
"2\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"2\n",
"1\n",
"4\n",
"0\n",
"0\n",
"3\n",
"2\n",
"1\n",
"3\n",
"4\n",
"4\n",
"0\n",
"2\n",
"3\n",
"2\n",
"2\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"4\n",
"1\n",
"2\n",
"0\n",
"2\n",
"0\n",
"3\n",
"3\n",
"2\n",
"2\n",
"1\n",
"0\n",
"2\n",
"5\n",
"5\n",
"2\n",
"4\n",
"0\n",
"0\n",
"0\n",
"2\n",
"0\n",
"0\n",
"3\n",
"2\n",
"4\n",
"0\n",
"1\n",
"0\n",
"0\n",
"2\n",
"0\n",
"4\n",
"0\n",
"3\n"
]
}
|
You are given sequences A and B consisting of non-negative integers. The lengths of both A and B are N, and the sums of the elements in A and B are equal. The i-th element in A is A_i, and the i-th element in B is B_i.
Tozan and Gezan repeats the following sequence of operations:
* If A and B are equal sequences, terminate the process.
* Otherwise, first Tozan chooses a positive element in A and decrease it by 1.
* Then, Gezan chooses a positive element in B and decrease it by 1.
* Then, give one candy to Takahashi, their pet.
Tozan wants the number of candies given to Takahashi until the process is terminated to be as large as possible, while Gezan wants it to be as small as possible. Find the number of candies given to Takahashi when both of them perform the operations optimally.
Constraints
* 1 \leq N \leq 2 × 10^5
* 0 \leq A_i,B_i \leq 10^9(1\leq i\leq N)
* The sums of the elements in A and B are equal.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 B_1
:
A_N B_N
Output
Print the number of candies given to Takahashi when both Tozan and Gezan perform the operations optimally.
Examples
Input
2
1 2
3 2
Output
2
Input
3
8 3
0 1
4 8
Output
9
Input
1
1 1
Output
0
|
{
"inputs": [
"3\njohn johanna\nira ira\nkayla jayla",
"3\njohn johanna\nira ria\nkayla jayla",
"3\njohn johanna\nria ria\nkayla jayla",
"3\njogn johanna\nria qia\nkayma jayla",
"3\nipoh o`gomka\nbjr bjr\njmya` aayjk",
"3\njohn johanna\nria ria\nkayma jayla",
"3\njohn johanna\nria qia\nkayma jayla",
"3\nngoj johanna\nria qia\nkayma jayla",
"3\nngoj johanna\nria qi`\nkayma jayla",
"3\nngoj joganna\nria qi`\nkayma jayla",
"3\nngoj joganna\nria qi`\nkaxma jayla",
"3\nngpj joganna\nria qi`\nkaxma jayla",
"3\njpgn joganna\nria qi`\nkaxma jayla",
"3\njpgn joganna\nair qi`\nkaxma jayla",
"3\njpgn joganna\nari qi`\nkaxma jayla",
"3\njpgn jog`nna\nari qi`\nkaxma jayla",
"3\njpgn jog`nna\nari qi`\namxak jayla",
"3\njgpn jog`nna\nari qi`\namxak jayla",
"3\njgpn jog`nna\nari qi`\namxak alyaj",
"3\nnpgj jog`nna\nari qi`\namxak jayla",
"3\npngj jog`nna\nari qi`\namxak jayla",
"3\npngj jog`nna\nari qi`\nkmxaa jayla",
"3\npngj ann`goj\nari qi`\nkmxaa jayla",
"3\npngj ann`goj\nari qj`\nkmxaa jayla",
"3\njgnp ann`goj\nari qj`\nkmxaa jayla",
"3\njgnp ann`goj\nari qi`\nkmxaa jayla",
"3\njgnp ann`gok\nari qi`\nkmxaa jayla",
"3\njgnp ann`gok\nari qi`\nkmxaa layja",
"3\njgnp ann`gok\nari qi`\naaxmk layja",
"3\njgnp ann`gok\nari qj`\naaxmk layja",
"3\npngj ann`gok\nari qj`\naaxmk layja",
"3\npnhj ann`gok\nari qj`\naaxmk layja",
"3\npnhj ann`gok\nari qj`\naaxmk ajyal",
"3\npnhj ann`gok\naqi qj`\naaxmk ajyal",
"3\njhnp ann`gok\nari qj`\naaxmk layja",
"3\njhnp ann`gok\nair qj`\naaxmk layja",
"3\njhnp ann`gok\nria qj`\naaxmk layja",
"3\njhnp ann`gok\nrja qj`\naaxmk layja",
"3\njhnp ann`gok\najr qj`\naaxmk layja",
"3\njhnp ann`gok\najr rj`\naaxmk layja",
"3\njhnp ann`gok\najr rj`\naaxmk kayja",
"3\njhnp ann`gok\najr rj`\nkmxaa kayja",
"3\njhnp ann`gok\najr `jr\nkmxaa kayja",
"3\njhnp ann`gok\najr `jr\naaxmk kayja",
"3\njgnp ann`gok\najr `jr\naaxmk kayja",
"3\njhnp annog`k\najr `jr\naaxmk kayja",
"3\njhnp annog`k\nrja `jr\naaxmk kayja",
"3\njhnp aknog`n\nrja `jr\naaxmk kayja",
"3\njhnp aknog`n\nrja `jr\n`axmk kayja",
"3\njhnp akmog`n\nrja `jr\n`axmk kayja",
"3\npnhj akmog`n\nrja `jr\n`axmk kayja",
"3\npnhj akmog`n\nrja `jr\nkmxa` kayja",
"3\npnhj akmog`n\nrja ajr\nkmxa` kayja",
"3\npnhj akmog`n\nrjb ajr\nkmxa` kayja",
"3\npnhj akmog`n\nrjb ajr\njmxa` kayja",
"3\nnphj akmog`n\nrjb ajr\njmxa` kayja",
"3\nnphj akmog`n\nbjr ajr\njmxa` kayja",
"3\nnpjh akmog`n\nbjr ajr\njmxa` kayja",
"3\nnpjh akmog`n\nbjr ajr\njmya` kayja",
"3\nnpjh n`gomka\nbjr ajr\njmya` kayja",
"3\njpnh n`gomka\nbjr ajr\njmya` kayja",
"3\njpoh n`gomka\nbjr ajr\njmya` kayja",
"3\njpoh n`gomka\nbjr ajr\n`aymj kayja",
"3\njpoh n`gomka\nbjr ajr\njmya` aayjk",
"3\njpoh n`gomka\nbjr rja\njmya` aayjk",
"3\nhopj n`gomka\nbjr rja\njmya` aayjk",
"3\njpoh n`gomka\nbjr rjb\njmya` aayjk",
"3\njpoh o`gomka\nbjr rjb\njmya` aayjk",
"3\nipoh o`gomka\nbjr rjb\njmya` aayjk",
"3\nipoh o`gomka\nbjr rjb\njmya` kjyaa",
"3\nipoh oagomka\nbjr bjr\njmya` aayjk",
"3\nipoh obgomka\nbjr bjr\njmya` aayjk",
"3\nipoh obgomka\nbjr bjr\njmyb` aayjk",
"3\nipoh obgomka\nbjr bjr\nimyb` aayjk",
"3\nhopi obgomka\nbjr bjr\nimyb` aayjk",
"3\nhopi obgomka\nbjr bjr\nimyb` aayjl",
"3\nnhoj johanna\nira ira\nkayla jayla",
"3\njohn johanna\nria ria\nkaylb jayla",
"3\njnhn johanna\nria qia\nkayma jayla",
"3\njogn johanna\nira qia\nkayma jayla",
"3\nngoj johanna\nria aiq\nkayma jayla",
"3\nngoj johanna\nria qi`\nkayma jaylb",
"3\njogn joganna\nria qi`\nkayma jayla",
"3\nngoj joganna\nria qi`\nkaxma alyaj",
"3\nngoj jogann`\nria qi`\nkaxma jayla",
"3\njpgn jogann`\nria qi`\nkaxma jayla",
"3\njogn joganna\nair qi`\nkaxma jayla",
"3\nnpgj joganna\nari qi`\nkaxma jayla",
"3\njpgn jog`nna\nari qi`\nkaxma jazla",
"3\njpgn jog`nna\nira qi`\namxak jayla",
"3\njgpn jog`mna\nari qi`\namxak jayla",
"3\njgpn jog`nna\nari `iq\namxak alyaj",
"3\njgpn jog`nna\nari qi`\namxak jayma",
"3\npngj jog`nna\nari qi`\namxak alyaj",
"3\npngj jog`nna\nari qi`\njmxaa jayla",
"3\npngj ann`goj\nari qi`\nkmxaa jayl`",
"3\npngj ano`gnj\nari qj`\nkmxaa jayla",
"3\njngp ann`goj\nari qj`\nkmxaa jayla",
"3\njgnp ann`goj\nari qi`\namxak jayla",
"3\njgnp ann`gok\nira qi`\nkmxaa jayla",
"3\njgnp bnn`gok\nari qi`\nkmxaa layja"
],
"outputs": [
"YES\nYES\nNO\n",
"YES\nNO\nNO\n",
"YES\nYES\nNO\n",
"NO\nNO\nNO\n",
"NO\nYES\nNO\n",
"YES\nYES\nNO\n",
"YES\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nYES\nNO\n",
"NO\nYES\nNO\n",
"NO\nYES\nNO\n",
"NO\nYES\nNO\n",
"NO\nYES\nNO\n",
"NO\nYES\nNO\n",
"NO\nYES\nNO\n",
"YES\nYES\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"YES\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"YES\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\n"
]
}
|
In an attempt to control the rise in population, Archer was asked to come up with a plan. This time he is targeting marriages. Archer, being as intelligent as he is, came up with the following plan:
A man with name M is allowed to marry a woman with name W, only if M is a subsequence of W or W is a subsequence of M.
A is said to be a subsequence of B, if A can be obtained by deleting some elements of B without changing the order of the remaining elements.
Your task is to determine whether a couple is allowed to marry or not, according to Archer's rule.
Input
The first line contains an integer T, the number of test cases. T test cases follow. Each test case contains two space separated strings M and W.
Output
For each test case print "YES" if they are allowed to marry, else print "NO". (quotes are meant for clarity, please don't print them)
Constraints
1 ≤ T ≤ 100
1 ≤ |M|, |W| ≤ 25000 (|A| denotes the length of the string A.)
All names consist of lowercase English letters only.
Example
Input:
3
john johanna
ira ira
kayla jayla
Output:
YES
YES
NO
Explanation
Case 1: Consider S = "johanna". So, S[0] = 'j', S[1] = 'o', S[2] = 'h' and so on. If we remove the indices [3, 4, 6] or [3, 5, 6] from S, it becomes "john". Hence "john" is a subsequence of S, so the answer is "YES".
Case 2: Any string is a subsequence of it self, as it is formed after removing "0" characters. Hence the answer is "YES".
Case 3: "jayla" can not be attained from "kayla" as removing any character from "kayla" would make the string length smaller than "jayla", also there is no 'j' in "kayla". Similar reasoning can be applied to see why "kayla" can't be attained from "jayla". Hence the answer is "NO".
|
{
"inputs": [
"7 2\n1 2\n1 3\n1 4\n3 5\n3 6\n3 7\n2 7\n",
"6 4\n1 2\n2 3\n2 4\n4 5\n4 6\n2 4 5 6\n",
"10 3\n10 5\n3 2\n6 8\n1 5\n10 4\n6 1\n9 8\n2 9\n7 3\n3 9 1\n",
"16 8\n16 12\n16 15\n15 9\n15 13\n16 3\n15 2\n15 10\n1 2\n6 16\n5 15\n2 7\n15 4\n14 15\n11 16\n8 5\n5 10 14 6 8 3 1 9\n",
"8 5\n2 5\n1 8\n6 7\n3 4\n6 8\n8 5\n5 3\n1 6 7 3 8\n",
"15 2\n7 12\n13 11\n6 8\n2 15\n10 9\n5 1\n13 5\n5 4\n14 3\n8 9\n8 4\n4 7\n12 14\n5 2\n7 4\n",
"31 29\n10 14\n16 6\n23 22\n25 23\n2 27\n24 17\n20 8\n5 2\n8 24\n16 5\n10 26\n8 7\n5 29\n20 16\n13 9\n13 21\n24 30\n13 1\n10 15\n23 3\n25 10\n2 25\n20 13\n25 11\n8 12\n30 28\n20 18\n5 4\n23 19\n16 31\n13 14 3 30 5 6 26 22 25 1 23 7 31 12 16 28 17 2 8 18 24 4 20 21 15 11 9 29 10\n",
"13 11\n4 11\n2 7\n4 13\n8 12\n8 9\n8 6\n3 8\n4 1\n2 10\n2 5\n3 4\n3 2\n10 4 5 6 1 2 3 9 13 7 12\n",
"21 20\n16 9\n7 11\n4 12\n2 17\n17 7\n5 2\n2 8\n4 10\n8 19\n6 15\n2 6\n12 18\n16 5\n20 16\n6 14\n5 3\n5 21\n20 1\n17 13\n6 4\n6 4 18 11 14 1 19 15 10 8 9 17 16 3 20 13 2 5 12 21\n",
"9 6\n1 6\n3 4\n9 7\n3 2\n8 7\n2 1\n6 7\n3 5\n2 5 1 6 3 9\n",
"26 22\n20 16\n2 7\n7 19\n5 9\n20 23\n22 18\n24 3\n8 22\n16 10\n5 2\n7 15\n22 14\n25 4\n25 11\n24 13\n8 24\n13 1\n20 8\n22 6\n7 26\n16 12\n16 5\n13 21\n25 17\n2 25\n16 4 7 24 10 12 2 23 20 1 26 14 8 9 3 6 21 13 11 18 22 17\n",
"1 1\n1\n",
"36 5\n36 33\n11 12\n14 12\n25 24\n27 26\n23 24\n20 19\n1 2\n3 2\n17 18\n33 34\n23 1\n32 31\n12 15\n25 26\n4 5\n5 8\n5 6\n26 29\n1 9\n35 33\n33 32\n16 1\n3 4\n31 30\n16 17\n19 21\n1 30\n7 5\n9 10\n13 12\n19 18\n10 11\n22 19\n28 26\n29 12 11 17 33\n",
"15 7\n5 4\n12 5\n7 13\n10 11\n3 8\n6 12\n3 15\n1 3\n5 14\n7 9\n1 10\n6 1\n12 7\n10 2\n4 10 8 13 1 7 9\n",
"17 12\n5 2\n4 3\n8 17\n2 4\n2 8\n17 12\n8 10\n6 11\n16 7\n4 14\n15 13\n6 9\n4 6\n15 16\n16 5\n9 1\n4 8 1 9 3 12 15 10 13 6 14 16\n",
"43 13\n7 28\n17 27\n39 8\n21 3\n17 20\n17 2\n9 6\n35 23\n43 22\n7 41\n5 24\n26 11\n21 43\n41 17\n16 5\n25 15\n39 10\n18 7\n37 33\n39 13\n39 16\n10 12\n1 21\n2 25\n14 36\n12 7\n16 34\n24 4\n25 40\n5 29\n37 31\n3 32\n22 14\n16 35\n5 37\n10 38\n25 19\n9 1\n26 42\n43 26\n10 30\n33 9\n28 6 42 38 27 32 8 11 36 7 41 29 19\n",
"20 2\n1 16\n12 5\n15 19\n18 9\n8 4\n10 16\n9 16\n20 15\n14 19\n7 4\n18 12\n17 12\n2 20\n6 14\n3 19\n7 19\n18 15\n19 13\n9 11\n12 18\n",
"4 2\n4 3\n3 1\n1 2\n3 4\n",
"63 20\n35 26\n54 5\n32 56\n56 53\n59 46\n37 31\n46 8\n4 1\n2 47\n59 42\n55 11\n62 6\n30 7\n60 24\n41 36\n34 22\n24 34\n21 2\n12 52\n8 44\n60 21\n24 30\n48 35\n48 25\n32 57\n20 37\n11 54\n11 62\n42 58\n31 43\n12 23\n55 48\n51 55\n41 27\n25 33\n21 18\n42 12\n4 15\n51 60\n62 39\n46 41\n57 9\n30 61\n31 4\n58 13\n34 29\n37 32\n18 16\n57 45\n2 49\n40 51\n43 17\n40 20\n20 59\n8 19\n58 10\n43 63\n54 50\n18 14\n25 38\n56 28\n35 3\n41 36 18 28 54 22 20 6 23 38 33 52 48 44 29 56 63 4 27 50\n",
"31 16\n3 25\n8 1\n1 9\n1 23\n16 15\n10 6\n25 30\n20 29\n2 24\n3 7\n19 22\n2 12\n16 4\n7 26\n31 10\n17 13\n25 21\n7 18\n28 2\n6 27\n19 5\n13 3\n17 31\n10 16\n20 14\n8 19\n6 11\n28 20\n13 28\n31 8\n31 27 25 20 26 8 28 15 18 17 10 23 4 16 30 22\n",
"56 34\n7 31\n47 6\n13 4\n51 29\n13 12\n10 52\n10 41\n1 47\n47 54\n9 1\n4 27\n4 40\n49 19\n21 26\n24 33\n56 49\n41 56\n7 23\n41 48\n16 34\n35 9\n56 51\n5 43\n44 46\n10 25\n49 2\n1 21\n9 32\n33 20\n16 5\n5 35\n55 50\n55 53\n37 44\n43 15\n4 55\n8 10\n8 24\n21 42\n37 8\n39 13\n49 38\n39 16\n50 3\n55 7\n51 45\n21 11\n51 28\n50 18\n50 30\n5 37\n7 17\n35 22\n47 36\n35 14\n3 38 47 22 34 10 54 50 9 52 36 1 21 29 28 6 13 39 4 40 53 51 35 55 45 18 44 20 42 31 11 46 41 12\n",
"7 5\n6 4\n5 6\n6 7\n2 3\n5 2\n2 1\n4 6 1 7 3\n",
"53 30\n41 42\n27 24\n13 11\n10 11\n32 33\n34 33\n37 40\n21 22\n21 20\n46 47\n2 1\n31 30\n29 30\n11 14\n42 43\n50 51\n34 35\n36 35\n24 23\n48 47\n41 1\n28 29\n45 44\n16 15\n5 4\n6 5\n18 19\n9 8\n37 38\n11 12\n39 37\n49 48\n50 49\n43 44\n50 53\n3 4\n50 52\n24 25\n7 6\n46 45\n2 3\n17 18\n31 32\n19 20\n7 8\n15 1\n36 37\n23 22\n9 10\n17 16\n24 26\n28 1\n38 52 41 35 53 43 3 29 36 4 23 20 46 5 40 30 49 25 16 48 17 27 21 9 45 44 15 13 14 2\n",
"5 4\n2 3\n2 1\n3 5\n4 3\n4 2 5 1\n",
"10 5\n4 5\n9 1\n1 2\n7 1\n5 1\n10 1\n7 3\n6 3\n5 8\n5 2 7 10 1\n",
"5 1\n1 2\n2 3\n3 4\n4 5\n4\n",
"12 9\n11 12\n1 10\n1 7\n5 6\n8 7\n9 8\n4 5\n1 4\n2 3\n1 2\n10 11\n4 9 11 3 5 12 8 6 7\n",
"32 28\n30 12\n30 27\n24 32\n6 13\n11 5\n4 30\n8 28\n9 20\n8 20\n7 20\n5 30\n18 5\n20 14\n23 20\n17 20\n8 26\n20 1\n15 2\n20 13\n24 20\n22 24\n25 16\n2 3\n19 5\n16 10\n31 2\n29 5\n20 16\n2 20\n5 21\n5 20\n32 11 6 12 22 30 23 21 14 13 1 20 7 25 9 29 10 27 5 19 24 31 15 26 8 3 28 17\n",
"54 8\n33 9\n39 36\n22 14\n24 13\n8 50\n34 52\n47 2\n35 44\n16 54\n34 25\n1 3\n39 11\n9 17\n43 19\n10 40\n47 38\n5 37\n21 47\n37 12\n16 6\n37 7\n32 26\n39 42\n44 10\n1 18\n37 8\n9 1\n8 24\n10 33\n33 53\n5 4\n21 30\n9 31\n24 28\n24 49\n16 5\n34 35\n21 48\n47 43\n13 34\n39 16\n10 27\n22 32\n43 22\n13 46\n33 23\n44 15\n1 21\n8 41\n43 45\n5 29\n35 20\n13 51\n40 50 33 14 48 25 44 9\n",
"29 6\n16 9\n20 13\n24 3\n24 28\n22 12\n10 11\n10 26\n22 4\n10 27\n5 1\n2 23\n23 5\n16 7\n8 24\n7 19\n19 17\n8 10\n20 16\n20 25\n24 20\n23 15\n22 29\n2 8\n7 22\n2 21\n23 14\n19 18\n19 6\n19 17 18 27 29 4\n",
"10 2\n6 9\n6 2\n1 6\n4 10\n3 7\n9 4\n9 5\n6 7\n2 8\n7 6\n",
"28 6\n25 21\n9 18\n25 1\n16 5\n9 11\n28 19\n5 2\n20 16\n20 13\n2 23\n5 25\n8 24\n14 27\n3 15\n24 28\n8 10\n22 14\n14 17\n13 9\n3 22\n22 26\n16 7\n2 8\n25 3\n3 12\n14 4\n9 6\n28 27 22 24 20 16\n",
"7 5\n1 5\n4 1\n1 3\n7 1\n1 6\n1 2\n2 4 1 3 7\n",
"10 4\n8 7\n7 6\n1 2\n3 2\n3 4\n6 5\n10 7\n7 9\n5 4\n9 5 10 4\n",
"4 2\n2 3\n2 1\n2 4\n3 4\n",
"10 2\n5 1\n1 3\n3 4\n4 2\n5 10\n1 9\n3 8\n4 7\n2 6\n3 4\n",
"2 1\n2 1\n1\n",
"10 4\n2 3\n4 2\n8 9\n6 5\n8 1\n5 1\n8 10\n7 5\n1 2\n4 10 2 5\n",
"19 11\n8 9\n10 13\n16 15\n6 4\n3 2\n17 16\n4 7\n1 14\n10 11\n15 14\n4 3\n10 12\n4 5\n2 1\n16 19\n8 1\n10 9\n18 16\n10 14 18 12 17 11 19 8 1 3 9\n",
"10 9\n3 9\n4 8\n10 1\n2 3\n5 6\n4 3\n1 2\n5 4\n6 7\n9 1 5 8 7 3 4 6 10\n",
"10 3\n10 5\n3 2\n6 8\n1 5\n10 4\n6 1\n9 8\n2 9\n7 3\n3 10 1\n",
"15 2\n7 12\n13 11\n6 8\n2 15\n10 5\n5 1\n13 5\n5 4\n14 3\n8 9\n8 4\n4 7\n12 14\n5 2\n7 4\n",
"26 22\n20 4\n2 7\n7 19\n5 9\n20 23\n22 18\n24 3\n8 22\n16 10\n5 2\n7 15\n22 14\n25 4\n25 11\n24 13\n8 24\n13 1\n20 8\n22 6\n7 26\n16 12\n16 5\n13 21\n25 17\n2 25\n16 4 7 24 10 12 2 23 20 1 26 14 8 9 3 6 21 13 11 18 22 17\n",
"36 5\n36 12\n11 12\n14 12\n25 24\n27 26\n23 24\n20 19\n1 2\n3 2\n17 18\n33 34\n23 1\n32 31\n12 15\n25 26\n4 5\n5 8\n5 6\n26 29\n1 9\n35 33\n33 32\n16 1\n3 4\n31 30\n16 17\n19 21\n1 30\n7 5\n9 10\n13 12\n19 18\n10 11\n22 19\n28 26\n29 12 11 17 33\n",
"17 12\n5 2\n4 3\n8 17\n2 4\n2 8\n17 12\n8 10\n6 11\n16 7\n4 14\n15 13\n6 9\n4 6\n15 16\n16 5\n13 1\n4 8 1 9 3 12 15 10 13 6 14 16\n",
"10 4\n2 3\n4 2\n8 9\n6 5\n8 1\n5 1\n9 10\n7 5\n1 2\n4 10 2 5\n",
"10 9\n3 9\n4 8\n10 1\n2 3\n5 6\n8 3\n1 2\n5 4\n6 7\n9 1 5 8 7 3 4 6 10\n",
"10 3\n10 5\n3 2\n4 8\n1 5\n10 4\n6 1\n9 8\n2 9\n7 3\n3 10 1\n",
"13 11\n4 11\n2 7\n4 13\n8 12\n8 9\n8 6\n3 8\n4 1\n2 10\n1 5\n3 4\n3 2\n10 4 5 6 1 2 3 9 13 7 12\n",
"26 22\n20 16\n2 7\n7 19\n5 9\n20 23\n22 18\n24 3\n16 22\n16 10\n5 2\n7 15\n22 14\n25 4\n25 11\n24 13\n8 24\n13 1\n20 8\n22 6\n7 26\n16 12\n16 5\n13 21\n25 17\n2 25\n16 4 7 24 10 12 2 23 20 1 26 14 8 9 3 6 21 13 11 18 22 17\n",
"36 5\n36 33\n11 12\n14 12\n25 24\n27 26\n23 24\n20 19\n1 2\n3 2\n17 18\n33 34\n23 1\n32 31\n12 15\n25 26\n4 5\n5 8\n5 6\n13 29\n1 9\n35 33\n33 32\n16 1\n3 4\n31 30\n16 17\n19 21\n1 30\n7 5\n9 10\n13 12\n19 18\n10 11\n22 19\n28 26\n29 12 11 17 33\n",
"43 13\n7 28\n17 27\n39 8\n21 3\n17 20\n17 2\n9 6\n35 23\n43 22\n7 41\n5 24\n26 11\n21 43\n41 17\n16 5\n25 15\n39 10\n18 7\n37 33\n39 13\n39 14\n10 12\n1 21\n2 25\n14 36\n12 7\n16 34\n24 4\n25 40\n5 29\n37 31\n3 32\n22 14\n16 35\n5 37\n10 38\n25 19\n9 1\n26 42\n43 26\n10 30\n33 9\n28 6 42 38 27 32 8 11 36 7 41 29 19\n",
"53 30\n41 42\n27 24\n13 11\n10 11\n32 33\n34 33\n37 40\n21 22\n21 20\n46 47\n2 1\n31 30\n29 30\n11 14\n42 43\n50 51\n34 35\n36 35\n24 23\n48 47\n41 1\n28 29\n45 44\n16 15\n5 4\n6 5\n18 19\n9 8\n37 38\n11 12\n39 37\n49 48\n50 49\n43 44\n50 53\n3 4\n50 52\n24 25\n7 6\n46 45\n2 3\n17 18\n31 32\n19 20\n7 8\n15 1\n36 37\n23 22\n9 10\n17 16\n24 26\n28 1\n38 52 41 35 53 43 3 29 36 4 23 20 46 5 40 30 49 25 16 48 17 18 21 9 45 44 15 13 14 2\n",
"12 9\n11 12\n1 10\n1 7\n5 6\n8 7\n9 8\n4 5\n1 4\n2 3\n1 2\n10 11\n4 9 11 2 5 12 8 6 7\n",
"54 8\n33 9\n39 36\n22 14\n24 13\n8 50\n34 52\n47 2\n35 44\n16 54\n34 25\n1 3\n39 11\n9 17\n43 19\n10 40\n47 38\n5 37\n21 47\n37 12\n16 6\n37 7\n32 26\n39 42\n54 10\n1 18\n37 8\n9 1\n8 24\n10 33\n33 53\n5 4\n21 30\n9 31\n24 28\n24 49\n16 5\n34 35\n21 48\n47 43\n13 34\n39 16\n10 27\n22 32\n43 22\n13 46\n33 23\n44 15\n1 21\n8 41\n43 45\n5 29\n35 20\n13 51\n40 50 33 14 48 25 44 9\n",
"28 6\n25 21\n9 18\n25 1\n16 5\n9 11\n28 19\n5 2\n20 16\n20 13\n2 23\n5 25\n8 24\n14 27\n3 15\n24 28\n8 10\n22 14\n14 17\n13 9\n3 22\n22 26\n16 7\n3 8\n25 3\n3 12\n14 4\n9 6\n28 27 22 24 20 16\n",
"10 2\n5 1\n1 3\n3 4\n5 2\n5 10\n1 9\n3 8\n4 7\n2 6\n3 4\n",
"2 1\n2 1\n2\n",
"19 11\n8 9\n10 13\n16 15\n6 4\n3 2\n17 16\n4 7\n1 14\n10 11\n15 14\n4 3\n10 12\n4 5\n2 1\n16 19\n8 1\n10 9\n18 16\n10 14 18 12 17 11 19 8 1 6 9\n",
"36 5\n36 12\n11 12\n14 12\n25 11\n27 26\n23 24\n20 19\n1 2\n3 2\n17 18\n33 34\n23 1\n32 31\n12 15\n25 26\n4 5\n5 8\n5 6\n26 29\n1 9\n35 33\n33 32\n16 1\n3 4\n31 30\n16 17\n19 21\n1 30\n7 5\n9 10\n13 12\n19 18\n10 11\n22 19\n28 26\n29 12 11 17 33\n",
"43 13\n7 28\n17 27\n39 8\n21 3\n17 20\n17 2\n9 6\n35 23\n43 22\n7 41\n5 24\n26 11\n21 43\n41 17\n16 5\n25 15\n39 10\n18 7\n37 33\n39 13\n39 14\n10 12\n1 21\n2 25\n14 36\n12 7\n16 34\n24 4\n25 40\n1 29\n7 31\n3 32\n22 14\n16 35\n5 37\n10 38\n25 19\n9 1\n26 42\n43 26\n10 30\n33 9\n28 6 42 38 27 32 8 11 36 7 41 29 19\n",
"31 29\n10 14\n16 6\n23 22\n25 23\n2 27\n24 17\n20 8\n5 2\n8 24\n16 5\n10 26\n8 7\n5 29\n20 16\n13 9\n13 21\n24 30\n13 1\n10 15\n23 3\n25 10\n2 25\n29 13\n25 11\n8 12\n30 28\n20 18\n5 4\n23 19\n16 31\n13 14 3 30 5 6 26 22 25 1 23 7 31 12 16 28 17 2 8 18 24 4 20 21 15 11 9 29 10\n",
"21 20\n16 9\n7 11\n4 12\n2 17\n17 7\n5 2\n2 8\n4 10\n8 19\n6 15\n2 12\n12 18\n16 5\n20 16\n6 14\n5 3\n5 21\n20 1\n17 13\n6 4\n6 4 18 11 14 1 19 15 10 8 9 17 16 3 20 13 2 5 12 21\n",
"15 7\n5 4\n12 5\n7 13\n10 11\n3 8\n6 12\n3 15\n1 3\n5 14\n13 9\n1 10\n6 1\n12 7\n10 2\n4 10 8 13 1 7 9\n",
"17 12\n5 2\n7 3\n8 17\n2 4\n2 8\n17 12\n8 10\n6 11\n16 7\n4 14\n15 13\n6 9\n4 6\n15 16\n16 5\n9 1\n4 8 1 9 3 12 15 10 13 6 14 16\n",
"5 4\n2 3\n2 1\n4 5\n4 3\n4 2 5 1\n",
"10 5\n4 5\n9 1\n1 2\n7 1\n5 1\n10 1\n7 3\n6 3\n5 8\n5 2 7 4 1\n",
"5 1\n1 2\n2 3\n3 4\n3 5\n4\n",
"29 6\n16 9\n20 13\n24 3\n24 28\n22 12\n10 11\n10 26\n22 4\n10 27\n5 1\n2 23\n23 5\n16 7\n8 24\n7 19\n7 17\n8 10\n20 16\n20 25\n24 20\n23 15\n22 29\n2 8\n7 22\n2 21\n23 14\n19 18\n19 6\n19 17 18 27 29 4\n",
"4 2\n1 3\n2 1\n2 4\n3 4\n",
"19 11\n8 9\n10 13\n16 15\n6 4\n3 2\n17 16\n4 7\n1 14\n10 11\n15 14\n4 3\n10 12\n4 5\n2 1\n16 19\n8 1\n10 9\n18 16\n10 14 18 12 17 11 19 8 2 3 9\n",
"10 9\n2 9\n4 8\n10 1\n2 3\n5 6\n4 3\n1 2\n5 4\n6 7\n9 1 5 8 7 3 4 6 10\n",
"10 3\n10 5\n3 2\n5 8\n1 5\n10 4\n6 1\n9 8\n2 9\n7 3\n3 10 1\n",
"15 2\n7 12\n13 11\n6 8\n2 15\n10 9\n5 1\n13 5\n5 4\n14 3\n7 9\n8 4\n4 7\n12 14\n5 2\n7 4\n",
"26 22\n20 4\n2 7\n7 19\n5 9\n20 23\n13 18\n24 3\n8 22\n16 10\n5 2\n7 15\n22 14\n25 4\n25 11\n24 13\n8 24\n13 1\n20 8\n22 6\n7 26\n16 12\n16 5\n13 21\n25 17\n2 25\n16 4 7 24 10 12 2 23 20 1 26 14 8 9 3 6 21 13 11 18 22 17\n",
"43 13\n7 28\n17 27\n39 8\n21 3\n17 20\n17 2\n9 6\n35 23\n43 22\n7 41\n5 24\n26 11\n21 43\n41 17\n16 5\n25 15\n39 10\n18 7\n37 33\n39 13\n39 14\n10 12\n1 21\n2 25\n14 36\n12 7\n16 34\n24 4\n25 40\n5 29\n7 31\n3 32\n22 14\n16 35\n5 37\n10 38\n25 19\n9 1\n26 42\n43 26\n10 30\n33 9\n28 6 42 38 27 32 8 11 36 7 41 29 19\n",
"53 30\n41 42\n27 24\n13 11\n10 11\n32 33\n34 33\n37 40\n21 22\n21 20\n46 47\n2 1\n31 30\n29 30\n11 14\n42 43\n50 51\n34 35\n36 35\n24 23\n48 47\n41 1\n28 29\n45 44\n16 15\n5 4\n6 5\n18 19\n9 8\n37 38\n11 12\n39 37\n49 48\n50 49\n43 44\n50 53\n3 4\n50 52\n24 25\n7 6\n46 45\n2 3\n17 18\n31 32\n19 20\n7 8\n15 1\n36 37\n23 22\n9 10\n17 16\n24 26\n28 1\n38 52 41 35 53 43 3 29 36 4 23 20 46 6 40 30 49 25 16 48 17 18 21 9 45 44 15 13 14 2\n",
"53 30\n41 42\n27 24\n13 11\n10 11\n32 33\n34 33\n37 40\n21 22\n21 20\n46 47\n2 1\n31 30\n29 30\n18 14\n42 43\n50 51\n34 35\n36 35\n24 23\n48 47\n41 1\n28 29\n45 44\n16 15\n5 4\n6 5\n18 19\n9 8\n37 38\n11 12\n39 37\n49 48\n50 49\n43 44\n50 53\n3 4\n50 52\n24 25\n7 6\n46 45\n2 3\n17 18\n31 32\n19 20\n7 8\n15 1\n36 37\n23 22\n9 10\n17 16\n24 26\n28 1\n38 52 41 35 53 43 3 29 36 4 23 20 46 6 40 30 49 25 16 48 17 18 21 9 45 44 15 13 14 2\n",
"10 4\n2 3\n4 2\n8 9\n6 5\n8 1\n5 2\n9 10\n7 5\n1 2\n4 10 2 5\n"
],
"outputs": [
"2\n3",
"2\n4",
"1\n5",
"1\n16",
"3\n6",
"4\n1",
"3\n46",
"1\n18",
"1\n32",
"5\n6",
"1\n37",
"1\n0",
"12\n21",
"4\n14",
"1\n20",
"19\n41",
"12\n1",
"3\n1",
"6\n66",
"4\n34",
"3\n70",
"1\n8",
"13\n74",
"1\n5",
"2\n6",
"4\n0",
"6\n16",
"3\n53",
"14\n21",
"4\n16",
"6\n1",
"27\n13",
"2\n6",
"4\n6",
"3\n2",
"3\n1",
"1\n0",
"4\n6",
"11\n18",
"7\n11\n",
"3\n7\n",
"4\n1\n",
"1\n36\n",
"12\n21\n",
"1\n20\n",
"4\n7\n",
"7\n10\n",
"1\n7\n",
"5\n17\n",
"1\n37\n",
"29\n14\n",
"19\n40\n",
"13\n72\n",
"6\n14\n",
"14\n26\n",
"20\n13\n",
"3\n1\n",
"2\n0\n",
"6\n22\n",
"29\n16\n",
"6\n37\n",
"3\n46\n",
"1\n32\n",
"8\n13\n",
"1\n22\n",
"1\n4\n",
"2\n5\n",
"4\n0\n",
"4\n16\n",
"3\n3\n",
"11\n18\n",
"7\n11\n",
"1\n7\n",
"4\n1\n",
"1\n36\n",
"19\n40\n",
"13\n72\n",
"13\n72\n",
"4\n7\n"
]
}
|
Ari the monster is not an ordinary monster. She is the hidden identity of Super M, the Byteforces’ superhero. Byteforces is a country that consists of n cities, connected by n - 1 bidirectional roads. Every road connects exactly two distinct cities, and the whole road system is designed in a way that one is able to go from any city to any other city using only the given roads. There are m cities being attacked by humans. So Ari... we meant Super M have to immediately go to each of the cities being attacked to scare those bad humans. Super M can pass from one city to another only using the given roads. Moreover, passing through one road takes her exactly one kron - the time unit used in Byteforces.
<image>
However, Super M is not on Byteforces now - she is attending a training camp located in a nearby country Codeforces. Fortunately, there is a special device in Codeforces that allows her to instantly teleport from Codeforces to any city of Byteforces. The way back is too long, so for the purpose of this problem teleportation is used exactly once.
You are to help Super M, by calculating the city in which she should teleport at the beginning in order to end her job in the minimum time (measured in krons). Also, provide her with this time so she can plan her way back to Codeforces.
Input
The first line of the input contains two integers n and m (1 ≤ m ≤ n ≤ 123456) - the number of cities in Byteforces, and the number of cities being attacked respectively.
Then follow n - 1 lines, describing the road system. Each line contains two city numbers ui and vi (1 ≤ ui, vi ≤ n) - the ends of the road i.
The last line contains m distinct integers - numbers of cities being attacked. These numbers are given in no particular order.
Output
First print the number of the city Super M should teleport to. If there are many possible optimal answers, print the one with the lowest city number.
Then print the minimum possible time needed to scare all humans in cities being attacked, measured in Krons.
Note that the correct answer is always unique.
Examples
Input
7 2
1 2
1 3
1 4
3 5
3 6
3 7
2 7
Output
2
3
Input
6 4
1 2
2 3
2 4
4 5
4 6
2 4 5 6
Output
2
4
Note
In the first sample, there are two possibilities to finish the Super M's job in 3 krons. They are:
<image> and <image>.
However, you should choose the first one as it starts in the city with the lower number.
|
{
"inputs": [
"3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 1002237 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 16 27 11\n12 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 44 27 11\n12 21 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n0\n4 16 27 11\n12 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 15\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 1002237 1100000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 15\n12 11 34 2\n7 26 10 16\n14 16 19 12\n17 31 27 6\n2\n322297 1000000 600000 0\n0 1002237 1100000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n30 38 33 6\n0\n4 4 27 11\n15 18 34 2\n7 26 14 16\n14 12 19 12\n17 28 0 21\n2\n322297 1000100 418950 0\n0 600000 1000000 300000\n0",
"3\n4 28 4 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 44 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 1164792 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 22\n12 11 34 2\n7 26 10 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 1002237 1100000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n28 24 33 14\n5\n4 27 27 11\n12 21 34 2\n7 26 14 25\n14 16 19 12\n17 28 93 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 40 33 14\n5\n4 27 27 11\n12 21 34 2\n7 26 14 25\n14 16 19 12\n17 28 93 21\n0\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n1\n322297 1000000 828907 0\n0 552212 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 50 21\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-2 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 55 22\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 1002237 1000000 300000\n0",
"3\n4 28 27 17\n15 20 21 5\n19 42 33 14\n5\n4 28 27 11\n12 11 66 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 1026026 1000001 300000\n0",
"3\n4 28 47 11\n23 20 42 5\n30 38 33 6\n0\n4 4 27 11\n15 18 34 2\n7 26 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 600000 1000000 127946\n0",
"3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 16 44 2\n7 26 14 16\n14 16 19 12\n17 28 27 4\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n11 24 17 14\n5\n4 28 27 11\n12 16 44 2\n7 26 14 16\n14 16 19 12\n17 28 27 4\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 21 5\n19 42 33 14\n5\n4 28 27 11\n12 11 66 2\n7 26 27 5\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 1026026 1000001 300000\n0",
"3\n4 28 27 17\n21 8 42 5\n19 40 33 14\n5\n4 27 27 11\n8 21 34 2\n7 26 14 25\n14 16 19 12\n17 44 93 21\n2\n322297 1000000 390784 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n0 6 42 5\n30 38 33 7\n0\n4 4 27 11\n15 18 44 2\n7 26 14 16\n14 12 19 12\n17 28 0 21\n2\n322297 1000100 14190 0\n0 600000 1000000 300000\n0",
"3\n4 37 4 11\n15 20 42 5\n24 24 33 14\n5\n4 28 43 11\n12 11 31 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 18\n15 20 42 5\n7 20 33 14\n0\n4 4 27 11\n12 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000000 1123821 0\n0 600000 1000100 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n25 24 33 14\n5\n4 28 27 15\n12 11 40 3\n7 45 14 16\n14 27 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 1002237 1100000 332079\n0",
"3\n4 37 4 11\n22 20 42 5\n24 24 33 14\n5\n4 28 43 11\n12 11 31 2\n7 26 14 16\n14 16 19 12\n17 28 41 6\n2\n322297 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n1 28 10 11\n12 8 34 2\n-1 26 14 16\n14 16 19 12\n17 28 27 21\n0\n322297 1000000 600000 0\n0 947852 1000100 300000\n0",
"3\n4 37 4 11\n22 20 42 5\n24 20 33 14\n5\n4 28 43 11\n12 11 31 2\n7 26 14 16\n14 16 19 12\n17 28 41 6\n2\n322297 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 18\n15 20 42 3\n19 41 55 22\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n0\n322297 1000000 600000 0\n0 1002237 1000000 300000\n0",
"3\n4 28 10 11\n23 20 64 5\n30 38 33 6\n0\n4 4 27 10\n15 18 34 3\n7 26 14 16\n14 12 19 12\n17 28 1 21\n2\n322297 1000100 418950 0\n0 1015084 1000101 300000\n0",
"3\n4 28 40 17\n21 8 42 5\n19 40 33 14\n5\n2 27 27 11\n9 21 34 2\n7 26 14 25\n14 16 19 12\n17 44 93 21\n2\n322297 1000000 390784 -1\n0 600000 1000100 300000\n0",
"3\n4 22 27 11\n17 22 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n1\n322297 1000000 828907 -1\n0 506177 1000010 363840\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 50 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 50 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1001000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n5 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000100 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 16 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 66 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 44 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 50 14\n5\n4 28 27 15\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 9\n11 24 33 14\n5\n5 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 66 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 600000 1000001 300000\n0",
"3\n4 28 27 17\n15 20 36 5\n19 24 50 14\n5\n4 28 27 15\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 9\n11 24 33 14\n5\n5 28 27 11\n12 11 34 2\n7 26 19 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 1002237 1100000 300000\n0",
"3\n4 28 27 17\n15 20 21 5\n19 24 33 14\n5\n4 28 27 11\n12 11 66 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 600000 1000001 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 27 27 11\n12 21 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n0\n4 4 27 11\n12 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 27 27 11\n12 21 34 2\n7 26 14 16\n14 16 19 12\n17 28 93 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 15\n12 11 34 2\n7 26 10 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 1002237 1100000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 24 33 14\n0\n4 4 27 11\n12 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 27 27 11\n12 21 34 2\n7 26 14 25\n14 16 19 12\n17 28 93 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 24 33 14\n0\n4 4 27 11\n15 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 40 33 14\n5\n4 27 27 11\n12 21 34 2\n7 26 14 25\n14 16 19 12\n17 28 93 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 15\n12 11 28 2\n7 26 10 16\n14 16 19 12\n17 31 27 6\n2\n322297 1000000 600000 0\n0 1002237 1100000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 24 33 14\n0\n4 4 27 11\n15 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000100 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 40 33 14\n5\n4 27 27 11\n5 21 34 2\n7 26 14 25\n14 16 19 12\n17 28 93 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 15\n12 11 28 2\n7 26 10 16\n14 16 19 12\n17 31 27 6\n2\n232522 1000000 600000 0\n0 1002237 1100000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 38 33 14\n0\n4 4 27 11\n15 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000100 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 40 33 14\n5\n4 27 27 11\n5 21 34 2\n7 26 14 25\n14 16 19 12\n17 28 93 21\n2\n322297 1000000 390784 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 38 33 6\n0\n4 4 27 11\n15 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000100 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 40 33 14\n5\n4 27 27 11\n5 21 34 2\n7 26 14 25\n14 16 19 12\n17 44 93 21\n2\n322297 1000000 390784 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 38 33 6\n0\n4 4 27 11\n15 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 2 21\n2\n322297 1000100 828907 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 40 33 14\n5\n4 27 27 11\n10 21 34 2\n7 26 14 25\n14 16 19 12\n17 44 93 21\n2\n322297 1000000 390784 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 38 33 6\n0\n4 4 27 11\n15 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 2 21\n2\n322297 1000100 418950 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 8\n19 40 33 14\n5\n4 27 27 11\n10 21 34 2\n7 26 14 25\n14 16 19 12\n17 44 93 21\n2\n322297 1000000 390784 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 38 33 6\n0\n4 4 27 11\n15 18 34 2\n7 26 14 16\n14 12 19 12\n17 28 2 21\n2\n322297 1000100 418950 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n19 38 33 6\n0\n4 4 27 11\n15 18 34 2\n7 26 14 16\n14 12 19 12\n17 28 0 21\n2\n322297 1000100 418950 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n30 38 33 6\n0\n4 4 27 11\n15 18 34 2\n7 26 14 16\n14 12 19 12\n17 28 0 21\n2\n322297 1000100 14190 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n30 38 33 6\n0\n4 4 27 11\n15 18 34 2\n7 26 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n0 38 33 6\n0\n4 4 27 11\n15 18 34 2\n7 26 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n0 38 33 6\n0\n4 4 27 11\n15 18 34 1\n7 26 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n0 38 33 4\n0\n4 4 27 11\n15 18 34 1\n7 26 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n0 38 7 4\n0\n4 4 27 11\n15 18 34 1\n7 26 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n0 38 7 4\n0\n4 4 27 11\n15 18 34 1\n7 26 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 1136690 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n0 38 7 4\n0\n4 4 10 11\n15 18 34 1\n7 26 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 1136690 1000000 300000\n0",
"3\n4 28 27 11\n23 20 42 5\n0 38 7 4\n0\n4 4 10 11\n15 18 34 1\n7 43 14 16\n14 12 19 12\n17 22 0 21\n2\n322297 1000100 14190 0\n0 1136690 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 16 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n0 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 552212 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 1\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 49 5\n19 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 50 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-2 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 50 14\n5\n4 26 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n322297 1000000 828907 0\n-1 600000 1001000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n5 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 428458\n0",
"3\n4 28 27 11\n15 20 42 5\n11 24 33 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n2 16 19 12\n17 28 27 21\n2\n322297 1000100 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 66 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1010000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 50 14\n5\n4 28 27 15\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 50 21\n2\n267741 1000000 828907 0\n-1 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 70 9\n11 24 33 14\n5\n5 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 21\n2\n300000 1000000 600000 0\n0 600000 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 55 14\n5\n4 28 27 11\n12 11 34 2\n7 26 14 16\n14 16 19 12\n17 28 27 6\n2\n322297 1000000 600000 0\n0 1002237 1000000 300000\n0",
"3\n4 28 27 11\n15 20 42 5\n19 24 33 14\n5\n4 16 27 11\n12 11 34 2\n7 26 14 16\n14 12 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n0 600000 1000000 256152\n0",
"3\n4 28 27 17\n15 20 42 5\n19 24 33 14\n5\n4 28 27 11\n12 11 66 2\n11 26 14 16\n14 16 19 12\n17 28 27 21\n2\n322297 1000000 828907 0\n-1 600000 1000001 300000\n0",
"3\n4 28 27 11\n15 20 42 9\n11 24 33 14\n5\n5 28 27 11\n12 11 34 2\n7 26 19 16\n14 16 19 12\n17 28 27 21\n2\n550504 1000000 600000 0\n0 600000 1000000 300000\n0"
],
"outputs": [
"8\n6\n6",
"8\n6\n6\n",
"8\n7\n6\n",
"8\n8\n6\n",
"8\n8\n4\n",
"8\n5\n6\n",
"8\n9\n6\n",
"8\n",
"8\n11\n4\n",
"8\n12\n4\n",
"6\n",
"4\n8\n6\n",
"8\n7\n4\n",
"8\n10\n4\n",
"6\n8\n6\n",
"8\n8\n",
"8\n6\n2\n",
"6\n7\n6\n",
"6\n8\n4\n",
"8\n6\n4\n",
"10\n",
"8\n10\n6\n",
"6\n10\n6\n",
"8\n9\n4\n",
"5\n8\n6\n",
"4\n",
"4\n9\n6\n",
"7\n",
"8\n13\n4\n",
"4\n10\n6\n",
"8\n9\n",
"3\n10\n6\n",
"6\n8\n",
"5\n",
"7\n8\n6\n",
"7\n6\n2\n",
"8\n6\n6\n",
"8\n6\n6\n",
"8\n6\n6\n",
"8\n6\n6\n",
"8\n7\n6\n",
"8\n7\n6\n",
"8\n6\n6\n",
"8\n6\n6\n",
"8\n6\n6\n",
"8\n6\n6\n",
"8\n7\n6\n",
"8\n8\n6\n",
"8\n6\n6\n",
"8\n6\n6\n",
"8\n8\n6\n",
"8\n7\n6\n",
"8\n8\n4\n",
"8\n6\n6\n",
"8\n9\n6\n",
"8\n",
"8\n9\n6\n",
"8\n11\n4\n",
"8\n",
"8\n8\n6\n",
"8\n",
"8\n8\n6\n",
"8\n12\n4\n",
"8\n",
"8\n8\n6\n",
"8\n12\n4\n",
"8\n",
"8\n8\n6\n",
"8\n",
"8\n8\n6\n",
"8\n",
"8\n8\n6\n",
"8\n",
"8\n8\n6\n",
"8\n",
"8\n",
"6\n",
"6\n",
"6\n",
"6\n",
"6\n",
"6\n",
"6\n",
"6\n",
"6\n",
"8\n7\n6\n",
"8\n7\n6\n",
"8\n6\n6\n",
"8\n6\n6\n",
"8\n7\n6\n",
"8\n7\n6\n",
"8\n7\n6\n",
"8\n6\n6\n",
"8\n7\n6\n",
"8\n6\n6\n",
"8\n8\n6\n",
"8\n6\n6\n",
"8\n8\n4\n",
"8\n5\n6\n",
"8\n6\n6\n",
"8\n7\n6\n"
]
}
|
There are a number of rectangles on the x-y plane. The four sides of the rectangles are parallel to either the x-axis or the y-axis, and all of the rectangles reside within a range specified later. There are no other constraints on the coordinates of the rectangles.
The plane is partitioned into regions surrounded by the sides of one or more rectangles. In an example shown in Figure C.1, three rectangles overlap one another, and the plane is partitioned into eight regions.
Rectangles may overlap in more complex ways. For example, two rectangles may have overlapped sides, they may share their corner points, and/or they may be nested. Figure C.2 illustrates such cases.
Your job is to write a program that counts the number of the regions on the plane partitioned by the rectangles.
Input
The input consists of multiple datasets. Each dataset is formatted as follows.
n
l1 t1 r1 b1
l2 t2 r2 b2
:
ln tn rn bn
A dataset starts with n (1 ≤ n ≤ 50), the number of rectangles on the plane. Each of the following n lines describes a rectangle. The i-th line contains four integers, li, ti, ri, and bi, which are the coordinates of the i-th rectangle; (li, ti) gives the x-y coordinates of the top left corner, and (ri, bi) gives that of the bottom right corner of the rectangle (0 ≤ li < ri ≤ 106, 0 ≤ bi < ti ≤ 106, for 1 ≤ i ≤ n). The four integers are separated by a space.
The input is terminated by a single zero.
Output
For each dataset, output a line containing the number of regions on the plane partitioned by the sides of the rectangles.
<image>
Figure C.1. Three rectangles partition the plane into eight regions. This corresponds to the first dataset of the sample input. The x- and y-axes are shown for illustration purposes only, and therefore they do not partition the plane.
<image>
Figure C.2. Rectangles overlapping in more complex ways. This corresponds to the second dataset.
Example
Input
3
4 28 27 11
15 20 42 5
11 24 33 14
5
4 28 27 11
12 11 34 2
7 26 14 16
14 16 19 12
17 28 27 21
2
300000 1000000 600000 0
0 600000 1000000 300000
0
Output
8
6
6
|
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