poj3480 John （nim博弈变形--SJ定理）

John

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 2940		Accepted: 1432

Description

Little John is playing very funny game with his younger brother. There is one big box filled with M&Ms of different colors. At first John has to eat several M&Ms of the same color. Then his opponent has to make a turn. And so on. Please note that each player has to eat at least one M&M during his turn. If John (or his brother) will eat the last M&M from the box he will be considered as a looser and he will have to buy a new candy box.

Both of players are using optimal game strategy. John starts first always. You will be given information about M&Ms and your task is to determine a winner of such a beautiful game.

Input

The first line of input will contain a single integer T – the number of test cases. Next T pairs of lines will describe tests in a following format. The first line of each test will contain an integer N – the amount of different M&M colors in a box. Next line will contain N integers A_i, separated by spaces – amount of M&Ms of i-th color.

Constraints:
1 <= T <= 474,
1 <= N <= 47,
1 <= A_i <= 4747

Output

Output T lines each of them containing information about game winner. Print “John” if John will win the game or “Brother” in other case.

Sample Input

2
3
3 5 1
1
1

Sample Output

John
Brother

Source

Southeastern Europe 2007

题意：在一般的nim博弈上稍作修改，就是最后取完的输，其他一样；

分析：这就牵扯到一个牛逼的定理了....SJ定理，然后就和基础nim一样了。

       我们提出定理里的两个限制：1、SG函数为不为0。2、有没有某单一游戏的SG函数大于1。

      通过这两个限制，我们可以组合出4种情况：

     （1）SG==0，有某单一游戏的SG>1。

     （2）SG!=0，有某单一游戏的SG>1。（必胜SJ）

     （3）SG==0，无某单一游戏的SG>1。(必胜SJ)

     （4）SG!=0，无某单一游戏的SG>1。

 

 

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