least air exti there with 經典的 args determine nes

John

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.

InputThe 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 Ai, separated by spaces – amount of M&Ms of i-th color.

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

OutputOutput 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
 

對於N堆的糖，一種情況下是每堆都是1，那麽誰輸誰贏看堆數就知道；
對於不都是1的話，若這些堆是奇異局勢，或說他們是非奇異局勢，但非奇異局勢皆可以轉換到奇異局勢。

經典的尼姆問題是誰哪拿到最後一個則誰贏，本題是拿最後一個的輸。
下面分析第二種情況：
1.初始給的是奇異局勢的話，則先取者拿到最後一個為輸。
2.初始給的是非奇異局勢的話，則先取者為贏。
	對於任何奇異局勢(a,b,c),都有a^b^c=0(^是代表異或).
非奇異局勢(a,b,c)(a<b<c)轉換為奇異局勢，只需將c變成a^b,即從c中減去c-(a^b)即可

import java.util.*;

public class Main {
    
    static Scanner sc = new Scanner(System.in);
    
    public static void main(String[] args){
        
        int t, n, x, f, ans, i;
        t = sc.nextInt();
        while((t--) != 0){
            n = sc.nextInt();
            ans = 0; f = 0;
            for(i = 1; i <= n; i++){
                x = sc.nextInt();
                ans ^= x;
                if(x > 1) f = 1;
            }
            if(f == 0){
                if((n & 1) != 0) System.out.println("Brother");
                else System.out.println("John");
            }
            else{
                if(ans == 0) System.out.println("Brother");
                else System.out.println("John");
            }
        }
    }
}

John 尼姆博弈