A11195. The Artful Expedient
编程题
普及/提高-
知识点
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 $2n$ 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 $2n$ 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.
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.
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 $2n$ 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 $2n$ 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.
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.
输入格式
The first line of input contains a positive integer $n$ ( $1<=n<=2000$ ) — the length of both sequences.
The second line contains $n$ space-separated integers $x_{1},x_{2},...,x_{n}$ ( $1<=x_{i}<=2·10^{6}$ ) — the integers finally chosen by Koyomi.
The third line contains $n$ space-separated integers $y_{1},y_{2},...,y_{n}$ ( $1<=y_{i}<=2·10^{6}$ ) — the integers finally chosen by Karen.
Input guarantees that the given $2n$ 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 $y_{i}=y_{j}$ .
The second line contains $n$ space-separated integers $x_{1},x_{2},...,x_{n}$ ( $1<=x_{i}<=2·10^{6}$ ) — the integers finally chosen by Koyomi.
The third line contains $n$ space-separated integers $y_{1},y_{2},...,y_{n}$ ( $1<=y_{i}<=2·10^{6}$ ) — the integers finally chosen by Karen.
Input guarantees that the given $2n$ 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.
In the second example, there are $16$ such pairs, and Karen wins again.