CF869A.The Artful Expedient
普及-
通过率:0%
时间限制:1.00s
内存限制:256MB
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题目描述
Rock... Paper!
After 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.
A 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.
Then 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 operation on two integers, and is denoted by operators ^ and/or xor in most programming languages.
Karen 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.
石头……剪刀!
在凯伦为“石头剪刀布”找到了确定性的必胜(或必败?)策略后,她的弟弟小夜美提出了一个新游戏作为替代。游戏规则如下:
首先确定一个正整数 n。小夜美和凯伦各自独立地选择 n 个互不相同的正整数,分别记为 x1,x2,…,xn 和 y1,y2,…,yn。双方公布各自的序列,并不断重复该过程,直至全部 2n 个整数互不相同——此为唯一被保留并考虑的最终状态。
接着,他们统计满足条件的有序对 (i,j)(其中 1≤i,j≤n)的个数,使得异或值 xi xor yj 等于这 2n 个整数中的某一个。此处 xor 表示两整数间的按位异或运算,在大多数编程语言中用操作符 ^ 和/或 xor 表示。
若满足条件的有序对个数为偶数,则凯伦获胜;否则小夜美获胜。现在,请你帮助判断他们最近一局游戏的胜者。
输入格式
The first line of input contains a positive integer n (1 ≤ n ≤ 2 000) — the length of both sequences.
The second line contains n space-separated integers _x_1, _x_2, ..., x__n (1 ≤ x__i ≤ 2·106) — the integers finally chosen by Koyomi.
The third line contains n space-separated integers _y_1, _y_2, ..., y__n (1 ≤ y__i ≤ 2·106) — the integers finally chosen by Karen.
Input 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.
输入的第一行包含一个正整数 n(1 ≤ n ≤ 2000)—— 表示两个序列的长度。
第二行包含 n 个用空格分隔的整数 x1,x2,...,xn(1 ≤ xi ≤ 2⋅106)—— 表示小夜美最终选定的整数。
第三行包含 n 个用空格分隔的整数 y1,y2,...,yn(1 ≤ yi ≤ 2⋅106)—— 表示卡伦最终选定的整数。
输入保证所给的 2n 个整数两两互不相同,即不存在任何下标对 (i,j)(其中 1 ≤ i,j ≤ n),使得以下任一条件成立:xi = yj;i = j 且 xi = xj;i = j 且 yi = yj。
输出格式
Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.
输出一行——获胜者的名字,即“Koyomi”或“Karen”(不带引号)。请注意大小写。
输入输出样例
输入#1
3 1 2 3 4 5 6
输出#1
Karen
输入#2
5 2 4 6 8 10 9 7 5 3 1
输出#2
Karen
说明/提示
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.
In the second example, there are 16 such pairs, and Karen wins again.
在第一个例子中,有 6 对满足约束条件:(1, 1)、(1, 2)、(2, 1)、(2, 3)、(3, 2) 和 (3, 3)。因此,Karen 获胜,因为 6 是偶数。
在第二个例子中,共有 16 对这样的组合,Karen 再次获胜。
输入解题思路,AI测评打分。不知道怎么写?