{"trustable":false,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"MD","content":"两个人玩游戏,轮流操作,对象是给定的 $n$ 个数 $[a_1, a_2, ..., a_n]$:\n* 每次选中一个素数 $p$ 和一个次数 $k$,满足 $p^k$ 是某个数 $a_i$ 的因子,然后把所有 $a_i \\bmod p^k \u003d 0$ 的 {$a_i$} 们都更新成 $a_i \u003d a_i / p^k$ 。\n\n谁不能操作谁输掉游戏。 \n问先手还是后手胜利。\n\n---\n\n\u003cp\u003eMojtaba and Arpa are playing a game. They have a list of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e numbers in the game.\u003c/p\u003e\n\u003cp\u003eIn a player\u0027s turn, he chooses a number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csup class\u003d\"upper-index\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/sup\u003e\u003c/span\u003e (where \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e is a prime number and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e is a positive integer) such that \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csup class\u003d\"upper-index\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/sup\u003e\u003c/span\u003e divides at least one number in the list. For each number in the list divisible by \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003csup class\u003d\"upper-index\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/sup\u003e\u003c/span\u003e, call it \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e, the player will delete \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e and add \u003cimg align\u003d\"middle\" class\u003d\"tex-formula\" src\u003d\"CDN_BASE_URL/cabd3ace973fc5b7e2fcac24b886f71e?v\u003d1684196860\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e to the list. The player who can not make a valid choice of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e loses.\u003c/p\u003e\n\u003cp\u003eMojtaba starts the game and the players alternatively make moves. Determine which one of players will be the winner if both players play optimally.\u003c/p\u003e"}},{"title":"Input","value":{"format":"MD","content":"\u003cp\u003eThe first line contains a single integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 100\u003c/span\u003e)\u0026nbsp;— the number of elements in the list.\u003c/p\u003e\n\u003cp\u003eThe second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e\u003c/span\u003e)\u0026nbsp;— the elements of the list.\u003c/p\u003e"}},{"title":"Output","value":{"format":"MD","content":"\u003cp\u003eIf Mojtaba wins, print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eMojtaba\u003c/span\u003e\", otherwise print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eArpa\u003c/span\u003e\" (without quotes).\u003c/p\u003e\n\u003cp\u003eYou can print each letter in any case (upper or lower).\u003c/p\u003e"}},{"title":"Sample 1","value":{"format":"MD","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\n1 1 1 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eArpa\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 2","value":{"format":"MD","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\n1 1 17 17\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eMojtaba\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 3","value":{"format":"MD","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\n1 1 17 289\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eArpa\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 4","value":{"format":"MD","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\u003e5\n1 2 3 4 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eArpa\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"MD","content":"\u003cp\u003eIn the first sample test, Mojtaba can\u0027t move.\u003c/p\u003e\n\u003cp\u003eIn the second sample test, Mojtaba chooses \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e \u003d 17\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 1\u003c/span\u003e, then the list changes to \u003cspan class\u003d\"tex-span\"\u003e[1, 1, 1, 1]\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eIn the third sample test, if Mojtaba chooses \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e \u003d 17\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 1\u003c/span\u003e, then Arpa chooses \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e \u003d 17\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 1\u003c/span\u003e and wins, if Mojtaba chooses \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e \u003d 17\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 2\u003c/span\u003e, then Arpa chooses \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e \u003d 17\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e \u003d 1\u003c/span\u003e and wins.\u003c/p\u003e"}}]}