{"trustable":true,"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":"HTML","content":"\u003cp\u003e\u003cspan class\u003d\"tex-font-style-it\"\u003eRock... Paper!\u003c/span\u003e\u003c/p\u003e\u003cp\u003eAfter Karen have found the deterministic winning (losing?) strategy for rock-paper-scissors, her brother, Koyomi, comes up with a new game as a substitute. The game works as follows.\u003c/p\u003e\u003cp\u003eA positive integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e is decided first. Both Koyomi and Karen independently choose \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e distinct positive integers, denoted by \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e respectively. They reveal their sequences, and repeat until \u003cspan class\u003d\"tex-font-style-bf\"\u003eall of \u003cspan class\u003d\"tex-span\"\u003e2\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers become distinct\u003c/span\u003e, which is the only final state to be kept and considered.\u003c/p\u003e\u003cp\u003eThen they count the number of ordered pairs \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ei\u003c/i\u003e, \u003ci\u003ej\u003c/i\u003e)\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ei\u003c/i\u003e, \u003ci\u003ej\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e) such that the value \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e \u003cspan class\u003d\"tex-font-style-tt\"\u003exor\u003c/span\u003e \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e equals to one of the \u003cspan class\u003d\"tex-span\"\u003e2\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers. Here \u003cspan class\u003d\"tex-font-style-tt\"\u003exor\u003c/span\u003e means the \u003ca href\u003d\"https://en.wikipedia.org/wiki/Bitwise_operation#XOR\"\u003ebitwise exclusive or\u003c/a\u003e operation on two integers, and is denoted by operators \u003cspan class\u003d\"tex-font-style-tt\"\u003e^\u003c/span\u003e and/or \u003cspan class\u003d\"tex-font-style-tt\"\u003exor\u003c/span\u003e in most programming languages.\u003c/p\u003e\u003cp\u003eKaren claims a win if the number of such pairs is even, and Koyomi does otherwise. And you\u0027re here to help determine the winner of their latest game.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of input contains a positive 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 ≤ 2 000\u003c/span\u003e) — the length of both sequences.\u003c/p\u003e\u003cp\u003eThe second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ex\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\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 2·10\u003csup class\u003d\"upper-index\"\u003e6\u003c/sup\u003e\u003c/span\u003e) — the integers finally chosen by Koyomi.\u003c/p\u003e\u003cp\u003eThe third line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e space-separated integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ey\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\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 2·10\u003csup class\u003d\"upper-index\"\u003e6\u003c/sup\u003e\u003c/span\u003e) — the integers finally chosen by Karen.\u003c/p\u003e\u003cp\u003eInput guarantees that \u003cspan class\u003d\"tex-font-style-bf\"\u003ethe given \u003cspan class\u003d\"tex-span\"\u003e2\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers are pairwise distinct\u003c/span\u003e, that is, no pair \u003cspan class\u003d\"tex-span\"\u003e(\u003ci\u003ei\u003c/i\u003e, \u003ci\u003ej\u003c/i\u003e)\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ei\u003c/i\u003e, \u003ci\u003ej\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e\u003c/span\u003e) exists such that one of the following holds: \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e \u003d \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e; \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e ≠ \u003ci\u003ej\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e \u003d \u003ci\u003ex\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e; \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ei\u003c/i\u003e ≠ \u003ci\u003ej\u003c/i\u003e\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e \u003d \u003ci\u003ey\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ej\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput one line — the name of the winner, that is, \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eKoyomi\u003c/span\u003e\" or \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eKaren\u003c/span\u003e\" (without quotes). Please be aware of the capitalization.\u003c/p\u003e"}},{"title":"Examples","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\n1 2 3\n4 5 6\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eKaren\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e5\n2 4 6 8 10\n9 7 5 3 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eKaren\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first example, there are \u003cspan class\u003d\"tex-span\"\u003e6\u003c/span\u003e pairs satisfying the constraint: \u003cspan class\u003d\"tex-span\"\u003e(1, 1)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(1, 2)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(2, 1)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(2, 3)\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e(3, 2)\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e(3, 3)\u003c/span\u003e. Thus, Karen wins since \u003cspan class\u003d\"tex-span\"\u003e6\u003c/span\u003e is an even number.\u003c/p\u003e\u003cp\u003eIn the second example, there are \u003cspan class\u003d\"tex-span\"\u003e16\u003c/span\u003e such pairs, and Karen wins again.\u003c/p\u003e"}}]}