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 x1, x2, ..., xnand y1, y2, ..., yn 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 xi xor yj equals to one of the 2n integers. Here xormeans 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.

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 x1, x2, ..., xn (1 ≤ xi ≤ 2·106) — the integers finally chosen by Koyomi.

The third line contains n space-separated integers y1, y2, ..., yn (1 ≤ yi ≤ 2·106) — 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: xi = yj; i ≠ j and xi = xj; i ≠ j and yi = yj.

Output one line — the name of the winner, that is, "Koyomi" or "Karen" (without quotes). Please be aware of the capitalization.

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.

这题是一道好题呀，虽然用暴力也能做，但最佳的做法运用到了异或的运算法则。

做题思路：

a^b=c;

a^c=a^b^a=b;

所以如果x与y中分别取一个数a和b求异或值c，如果c在y中，那a^c=b；如果c在x中，那b^c=a;

也就是无论如何，答案一定是偶数。

附ac代码：

#include <cstdio>

int main() {

    puts("Karen");

    return 0;

}

附暴力ac代码：

#include <cstdio>

#include <iostream>

#include <cstring>

#include <string>

#include <algorithm>

using namespace std;

const int maxn = 4000006;

int nua[2005],nub[2005];

int vis[maxn];

int main() {

    int n;

    cin>>n;

    for(int i=0;i<n;++i) {

        cin>>nua[i];

        vis[nua[i]]=1;

    }

    for(int i=0;i<n;++i) {

        cin>>nub[i];

        vis[nub[i]]=1;

    }

    long long cnt = 0;

    for(int i=0;i<n;++i) {

        for(int j=0;j<n;++j) {

            if(vis[nua[i]^nub[j]])

                cnt++;

        }

    }

    if(cnt%2==0) {

        puts("Karen");

    }

    else puts("Koyomi");

    return 0;

}