{"raw_statement":[{"iden":"statement","content":"_Rock... Paper!_\n\nAfter 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.\n\nA positive integer _n_ is decided first. Both Koyomi and Karen independently choose _n_ distinct positive integers, denoted by _x_1, _x_2, ..., _x__n_ and _y_1, _y_2, ..., _y__n_ respectively. They reveal their sequences, and repeat until **all of 2_n_ integers become distinct**, which is the only final state to be kept and considered.\n\nThen they count the number of ordered pairs (_i_, _j_) (1 ≤ _i_, _j_ ≤ _n_) such that the value _x__i_ _xor_ _y__j_ equals to one of the 2_n_ integers. Here _xor_ means the [bitwise exclusive or](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation on two integers, and is denoted by operators _^_ and/or _xor_ in most programming languages.\n\nKaren claims a win if the number of such pairs is even, and Koyomi does otherwise. And you're here to help determine the winner of their latest game."},{"iden":"input","content":"The first line of input contains a positive integer _n_ (1 ≤ _n_ ≤ 2 000) — the length of both sequences.\n\nThe second line contains _n_ space-separated integers _x_1, _x_2, ..., _x__n_ (1 ≤ _x__i_ ≤ 2·106) — the integers finally chosen by Koyomi.\n\nThe third line contains _n_ space-separated integers _y_1, _y_2, ..., _y__n_ (1 ≤ _y__i_ ≤ 2·106) — the integers finally chosen by Karen.\n\nInput guarantees that **the given 2_n_ integers are pairwise distinct**, that is, no pair (_i_, _j_) (1 ≤ _i_, _j_ ≤ _n_) exists such that one of the following holds: _x__i_ = _y__j_; _i_ ≠ _j_ and _x__i_ = _x__j_; _i_ ≠ _j_ and _y__i_ = _y__j_."},{"iden":"output","content":"Output one line — the name of the winner, that is, \"_Koyomi_\" or \"_Karen_\" (without quotes). Please be aware of the capitalization."},{"iden":"examples","content":"Input\n\n3\n1 2 3\n4 5 6\n\nOutput\n\nKaren\n\nInput\n\n5\n2 4 6 8 10\n9 7 5 3 1\n\nOutput\n\nKaren"},{"iden":"note","content":"In the first example, there are 6 pairs satisfying the constraint: (1, 1), (1, 2), (2, 1), (2, 3), (3, 2) and (3, 3). Thus, Karen wins since 6 is an even number.\n\nIn the second example, there are 16 such pairs, and Karen wins again."}],"translated_statement":[{"iden":"statement","content":"_Rock... Paper!_\n\n在Karen找到了石头剪刀布的确定性胜负策略后，她的弟弟Koyomi提出了一种新的替代游戏。游戏规则如下：\n\n首先确定一个正整数 $n$。Koyomi和Karen各自独立地选择 $n$ 个互不相同的正整数，分别记为 $x_1, x_2, ..., x_n$ 和 $y_1, y_2, ..., y_n$。他们展示各自的序列，并重复此过程，直到 *所有 $2n$ 个整数互不相同*，此时为唯一保留并考虑的最终状态。\n\n然后，他们统计满足条件的有序对 $(i, j)$（$1 ≤ i, j ≤ n$）的数量，使得值 $x_i$ _xor_ $y_j$ 等于这 $2n$ 个整数中的某一个。这里 _xor_ 表示两个整数的按位异或运算，在大多数编程语言中用操作符 _^_ 和/或 _xor_ 表示。\n\n如果这样的对的数量为偶数，Karen获胜；否则Koyomi获胜。你的任务是帮助确定他们最新一局游戏的胜者。\n\n输入的第一行包含一个正整数 $n$（$1 ≤ n ≤ 2 000$）——两个序列的长度。\n\n第二行包含 $n$ 个用空格分隔的整数 $x_1, x_2, ..., x_n$（$1 ≤ x_i ≤ 2·10^6$）——Koyomi最终选择的整数。\n\n第三行包含 $n$ 个用空格分隔的整数 $y_1, y_2, ..., y_n$（$1 ≤ y_i ≤ 2·10^6$）——Karen最终选择的整数。\n\n输入保证给定的 $2n$ 个整数两两互不相同，即不存在任何一对 $(i, j)$（$1 ≤ i, j ≤ n$）满足以下任一条件：$x_i = y_j$；$i ≠ j$ 且 $x_i = x_j$；$i ≠ j$ 且 $y_i = y_j$。\n\n请输出一行——胜者的姓名，即 \"_Koyomi_\" 或 \"_Karen_\"（不含引号）。请注意大小写。\n\n在第一个例子中，有 $6$ 个满足条件的对：$(1, 1)$、$(1, 2)$、$(2, 1)$、$(2, 3)$、$(3, 2)$ 和 $(3, 3)$。因此，由于 $6$ 是偶数，Karen获胜。\n\n在第二个例子中，有 $16$ 个这样的对，Karen再次获胜。"},{"iden":"input","content":"输入的第一行包含一个正整数 $n$（$1 ≤ n ≤ 2 000$）——两个序列的长度。第二行包含 $n$ 个用空格分隔的整数 $x_1, x_2, ..., x_n$（$1 ≤ x_i ≤ 2·10^6$）——Koyomi最终选择的整数。第三行包含 $n$ 个用空格分隔的整数 $y_1, y_2, ..., y_n$（$1 ≤ y_i ≤ 2·10^6$）——Karen最终选择的整数。输入保证给定的 $2n$ 个整数两两互不相同，即不存在任何一对 $(i, j)$（$1 ≤ i, j ≤ n$）满足以下任一条件：$x_i = y_j$；$i ≠ j$ 且 $x_i = x_j$；$i ≠ j$ 且 $y_i = y_j$。"},{"iden":"output","content":"请输出一行——胜者的姓名，即 \"_Koyomi_\" 或 \"_Karen_\"（不含引号）。请注意大小写。"},{"iden":"examples","content":"输入\n3\n1 2 3\n4 5 6\n输出\nKaren\n\n输入\n5\n2 4 6 8 10\n9 7 5 3 1\n输出\nKaren"},{"iden":"note","content":"在第一个例子中，有 $6$ 个满足条件的对：$(1, 1)$、$(1, 2)$、$(2, 1)$、$(2, 3)$、$(3, 2)$ 和 $(3, 3)$。因此，由于 $6$ 是偶数，Karen获胜。在第二个例子中，有 $16$ 个这样的对，Karen再次获胜。"}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n \\in \\mathbb{Z}^+ $ with $ 1 \\leq n \\leq 2000 $.  \nLet $ X = \\{x_1, x_2, \\dots, x_n\\} \\subset \\mathbb{Z}^+ $ and $ Y = \\{y_1, y_2, \\dots, y_n\\} \\subset \\mathbb{Z}^+ $ be two sets of distinct positive integers such that $ X \\cap Y = \\emptyset $ and all $ 2n $ elements in $ X \\cup Y $ are pairwise distinct.  \nLet $ S = X \\cup Y $.\n\n**Constraints**  \n1. $ 1 \\leq x_i \\leq 2 \\cdot 10^6 $ for all $ i \\in \\{1, \\dots, n\\} $  \n2. $ 1 \\leq y_j \\leq 2 \\cdot 10^6 $ for all $ j \\in \\{1, \\dots, n\\} $  \n3. $ |S| = 2n $ and all elements in $ S $ are distinct.\n\n**Objective**  \nCompute the number of ordered pairs $ (i, j) \\in \\{1, \\dots, n\\}^2 $ such that:  \n$$\nx_i \\oplus y_j \\in S\n$$  \nwhere $ \\oplus $ denotes bitwise XOR.  \nLet $ C = \\left| \\left\\{ (i,j) \\mid x_i \\oplus y_j \\in S \\right\\} \\right| $.  \nOutput \"Koyomi\" if $ C $ is odd, \"Karen\" if $ C $ is even.","simple_statement":null,"has_page_source":false}