{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n section pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"Problem Statement","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003e\u003cvar\u003e\\(N\\)\u003c/var\u003e players will participate in a tennis tournament. We will call them Player \u003cvar\u003e\\(1\\)\u003c/var\u003e, Player \u003cvar\u003e\\(2\\)\u003c/var\u003e, \u003cvar\u003e\\(\\ldots\\)\u003c/var\u003e, Player \u003cvar\u003e\\(N\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eThe tournament is round-robin format, and there will be \u003cvar\u003e\\(N(N-1)/2\\)\u003c/var\u003e matches in total.\r\nIs it possible to schedule these matches so that all of the following conditions are satisfied? If the answer is yes, also find the minimum number of days required.\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eEach player plays at most one matches in a day.\u003c/li\u003e\r\n\u003cli\u003eEach player \u003cvar\u003e\\(i\\)\u003c/var\u003e \u003cvar\u003e\\((1 \\leq i \\leq N)\\)\u003c/var\u003e plays one match against Player \u003cvar\u003e\\(A_{i, 1}, A_{i, 2}, \\ldots, A_{i, N-1}\\)\u003c/var\u003e in this order.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Constraints","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(3 \\leq N \\leq 1000\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq A_{i, j} \\leq N\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(A_{i, j} \\neq i\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(A_{i, 1}, A_{i, 2}, \\ldots, A_{i, N-1}\\)\u003c/var\u003e are all different.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Input","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eInput is given from Standard Input in the following format:\u003c/p\u003e\r\n\u003cpre\u003e\u003cvar\u003e\\(N\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(A_{1, 1}\\)\u003c/var\u003e \u003cvar\u003e\\(A_{1, 2}\\)\u003c/var\u003e \u003cvar\u003e\\(\\ldots\\)\u003c/var\u003e \u003cvar\u003e\\(A_{1, N-1}\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(A_{2, 1}\\)\u003c/var\u003e \u003cvar\u003e\\(A_{2, 2}\\)\u003c/var\u003e \u003cvar\u003e\\(\\ldots\\)\u003c/var\u003e \u003cvar\u003e\\(A_{2, N-1}\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(:\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(A_{N, 1}\\)\u003c/var\u003e \u003cvar\u003e\\(A_{N, 2}\\)\u003c/var\u003e \u003cvar\u003e\\(\\ldots\\)\u003c/var\u003e \u003cvar\u003e\\(A_{N, N-1}\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eIf it is possible to schedule all the matches so that all of the conditions are satisfied, print the minimum number of days required; if it is impossible, print \u003ccode\u003e-1\u003c/code\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 1","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n2 3\r\n1 3\r\n1 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eAll the conditions can be satisfied if the matches are scheduled for three days as follows:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eDay \u003cvar\u003e\\(1\\)\u003c/var\u003e: Player \u003cvar\u003e\\(1\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(2\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eDay \u003cvar\u003e\\(2\\)\u003c/var\u003e: Player \u003cvar\u003e\\(1\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(3\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eDay \u003cvar\u003e\\(3\\)\u003c/var\u003e: Player \u003cvar\u003e\\(2\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(3\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eThis is the minimum number of days required.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 2","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4\r\n2 3 4\r\n1 3 4\r\n4 1 2\r\n3 1 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eAll the conditions can be satisfied if the matches are scheduled for four days as follows:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eDay \u003cvar\u003e\\(1\\)\u003c/var\u003e: Player \u003cvar\u003e\\(1\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(2\\)\u003c/var\u003e, Player \u003cvar\u003e\\(3\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(4\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eDay \u003cvar\u003e\\(2\\)\u003c/var\u003e: Player \u003cvar\u003e\\(1\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(3\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eDay \u003cvar\u003e\\(3\\)\u003c/var\u003e: Player \u003cvar\u003e\\(1\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(4\\)\u003c/var\u003e, Player \u003cvar\u003e\\(2\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(3\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eDay \u003cvar\u003e\\(4\\)\u003c/var\u003e: Player \u003cvar\u003e\\(2\\)\u003c/var\u003e vs Player \u003cvar\u003e\\(4\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eThis is the minimum number of days required.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 3","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n2 3\r\n3 1\r\n1 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e-1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eAny scheduling of the matches violates some condition.\u003c/p\u003e\u003c/section\u003e\r\n"}}]}