{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e .input, .output {border: 1px solid #888888;} .output {margin-bottom:1em;position:relative;top:-1px;} .output pre,.input pre {background-color:#EFEFEF;line-height:1.25em;margin:0;padding:0.25em;} .title {background-color:#FFFFFF;border-bottom: 1px solid #888888;font-family:arial;font-weight:bold;padding:0.25em;} @media print{div.print-content article.node .node-blog .clearfix div.item-body p a{display:none}.compact-problemset div.ttypography{margin:0!important}.compact-problemset .problem-statement p{margin-bottom:.75em!important;page-break-inside:avoid}.compact-problemset .problem-frames{column-count:2}.compact-problemset .problem-statement .input,.compact-problemset .problem-statement .output{page-break-inside:avoid}.compact-problemset .problem-statement .output{page-break-inside:avoid}.compact-problemset .problem-statement{margin:.25em;font-family:helvetica neue,Helvetica,Arial,sans-serif;line-height:1.45em;font-size:1.4rem}.compact-problemset #header{display:none}.compact-problemset .problem-statement .time-limit,.compact-problemset .problem-statement .memory-limit{display:inline}.compact-problemset .problem-statement .time-limit::after{content:\", \"}.compact-problemset .problem-statement .property-title{display:none}.compact-problemset .problem-statement .input-file,.compact-problemset .problem-statement .output-file{display:none}.compact-problemset .problem-statement .sample-tests .section-title,.compact-problemset .problem-statement .note .section-title{display:none}.compact-problemset .input-output-copier{display:none}}.problem-statement{margin:.5em;font-family:helvetica neue,Helvetica,Arial,sans-serif;line-height:1.5em;font-size:1.4rem}.problem-statement .epigraph{}.problem-statement .epigraph-text{margin-left:67%;width:33%}.problem-statement .epigraph-source{border-top:1px solid #888;text-align:right}.problem-statement .lstlisting{padding:.5em}.problem-statement .tex-tabular{margin:1em 0;border-collapse:collapse;border-spacing:0;border:initial!important}.problem-statement .tex-tabular *{border:initial!important}.problem-statement .tex-tabular tr:hover *{background:initial}.problem-statement .tex-tabular .tex-tabular-border-left{border-left:1px #ccc solid!important}.problem-statement .tex-tabular .tex-tabular-border-right{border-right:1px #ccc solid!important}.problem-statement .tex-tabular .tex-tabular-border-top{border-top:1px #ccc solid!important}.problem-statement .tex-tabular .tex-tabular-border-bottom{border-bottom:1px #ccc solid!important}.problem-statement .tex-tabular .tex-tabular-text-align-left{text-align:left}.problem-statement .tex-tabular .tex-tabular-text-align-center{text-align:center}.problem-statement .tex-tabular .tex-tabular-text-align-right{text-align:right}.problem-statement .tex-tabular td{padding:.4em;vertical-align:middle}.problem-statement p{margin:0 0 1em!important}.problem-statement .header{margin-bottom:1em;text-align:center}.problem-statement .header .title{font-size:150%;margin-bottom:.5em}.problem-statement .header .title{font-size:150%;font-family:helvetica neue,Helvetica,Arial,sans-serif}.problem-statement ul{list-style:disc;list-style-type:disc;list-style-position:outside;margin-top:1em!important;margin-bottom:1em!important}.problem-statement ol{list-style:decimal;list-style-type:decimal;list-style-position:outside;margin-top:1em!important;margin-bottom:1em!important}.problem-statement li{line-height:1.5em;margin-left:3em}.problem-statement .property-title{display:inline;padding-right:4px}.problem-statement .property-title:after{content:\":\"}.problem-statement .time-limit,.problem-statement .memory-limit,.problem-statement .input-file,.problem-statement .output-file{margin:0 auto}.problem-statement .legend{margin-bottom:1em}.problem-statement .section-title{font-family:helvetica neue,Helvetica,Arial,sans-serif;font-size:115%;font-weight:700}.problem-statement .input-specification,.problem-statement .output-specification,.problem-statement .sample-tests,.problem-statement .author,.problem-statement .resource,.problem-statement .date{}.problem-statement .output-specification{margin-bottom:1em}.problem-statement .sample-tests .sample-test{}.problem-statement .sample-tests .input,.problem-statement .sample-tests .output{border:1px solid #888}.problem-statement .sample-tests .output{margin-bottom:1em;position:relative;top:-1px}.problem-statement .sample-tests pre{line-height:1.25em;padding:.25em;margin:0;background-color:#efefef}.problem-statement .sample-tests{font-family:Consolas,lucida console,andale mono,bitstream vera sans mono,courier new,Courier;font-size:.9em}.problem-statement .sample-tests .title{font-size:1.3em;padding:.25em;border-bottom:1px solid #888;text-transform:lowercase;font-weight:700}.problem-statement .test{margin-bottom:3em}.problem-statement .test-title{font-weight:700}.problem-statement .test-stem,.problem-statement .test-explanation-note{margin:.5em 0}.problem-statement input[type\u003dsubmit]{margin-top:.5em;margin-right:1em;padding:0 1em}.problemindexholder{position:relative}div .problem-statement-overlay{position:absolute;top:0;left:0;height:100%;width:100%;background-color:#000;z-index:50;opacity:.2}.load-answers-waiting-indicator{position:absolute;top:49%;left:49%}.problem-statement input[type\u003dradio]{margin-right:.5em}.problem-statement input[type\u003dcheckbox]{margin-right:.5em}.problem-statement input[type\u003dtext]{width:20em}.problem-statement textarea{width:20em;height:7em}.problem-statement .test-form{line-height:1.75em}.problem-statement .test-form{line-height:1.75em}.tex-formula{font-family:times new roman,sans-serif;vertical-align:middle;margin:0;border:medium;position:relative;bottom:2px}.tex-span{font-size:125%;font-family:times new roman,sans-serif;white-space:nowrap}.tex-font-size-tiny{font-size:70%}.tex-font-size-script{font-size:75%}.tex-font-size-footnotes{font-size:85%}.tex-font-size-small{font-size:85%}.tex-font-size-normal{font-size:100%}.tex-font-size-large-1{font-size:115%}.tex-font-size-large-2{font-size:130%}.tex-font-size-large-3{font-size:145%}.tex-font-size-huge-1{font-size:175%}.tex-font-size-huge-2{font-size:200%}.tex-font-style-rm{}.tex-font-style-sf{font-family:helvetica neue,Helvetica,Arial,sans-serif}.tex-font-style-tt{font-size:110%;font-family:courier new,monospace}.tex-font-style-md{}.tex-font-style-bf{font-weight:700}.tex-font-style-up{}.tex-font-style-it{font-style:italic}.tex-font-style-sl{font-style:italic}.tex-font-style-sc{text-transform:uppercase}.tex-font-style-striked{text-decoration:line-through}.tex-font-style-underline{text-decoration:underline}.tex-graphics{display:block}.tex-font-style-part{font-size:187.5%;font-weight:700;font-family:Tahoma,Arial,Helvetica,sans-serif}.tex-font-style-chapter{font-size:162.5%;font-weight:700;font-family:Tahoma,Arial,Helvetica,sans-serif}.tex-font-style-section{font-size:137.5%;font-weight:700}.tex-font-style-subsection{font-size:125%;font-weight:700}.tex-font-style-subsubsection{font-size:112.5%;font-weight:700}.tex-font-style-paragraph{font-size:100%;font-weight:700}.tex-font-style-subparagraph{font-size:100%;font-style:italic}.problem-statement .tex-tabular .tex-graphics{max-width:100%}.problem-statement .tex-tabular td\u003ep{margin-bottom:0!important} \u003c/style\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\u003cspan class\u003d\"tex-font-style-it\"\u003eRock... Paper!\u003c/span\u003e\u003c/p\u003e\n\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\n\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\n\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\n\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\n\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\n\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\n\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":"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\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":"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\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\n\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"}}]}