HDU 1564 Play a game

Description

New Year is Coming! 
ailyanlu is very happy today! and he is playing a chessboard game with 8600. 
The size of the chessboard is n*n. A stone is placed in a corner square. They play alternatively with 8600 having the first move. Each time, player is allowed to move the stone to an unvisited neighbor square horizontally or vertically. The one who can't make a move will lose the game. If both play perfectly, who will win the game?

Input

The input is a sequence of positive integers each in a separate line. 
The integers are between 1 and 10000, inclusive,(means 1 <= n <= 10000) indicating the size of the chessboard. The end of the input is indicated by a zero.

Output

Output the winner ("8600" or "ailyanlu") for each input line except the last zero. 
No other characters should be inserted in the output.

Sample Input

2 0

Sample Output

8600

博弈，看着猜猜大概可以想到是奇数和偶数的区别

至于如何证明的话，​​看这里吧​​

#include<set>
#include<map>
#include<ctime>
#include<cmath>
#include<stack>
#include<queue>
#include<bitset>
#include<cstdio>
#include<string>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<functional>
#define rep(i,j,k) for (int i = j; i <= k; i++)
#define per(i,j,k) for (int i = j; i >= k; i--)
using namespace std;
typedef long long LL;
const int low(int x) { return x&-x; }
const double eps = 1e-8;
const int INF = 0x7FFFFFFF;
const int mod = 1e9 + 7;
const int N = 1e5 + 10;
int T, n, m, a, b, c;

int main()
{
  while (scanf("%d", &n), n)
  {
    printf("%s\n", (n & 1) ? "ailyanlu" : "8600");
  }
  return 0;
}