Game

提示：扫一扫查出行
【扫一扫了解最新限行尾号】
复制提示

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

Total Submission(s): 50 Accepted Submission(s): 44

Problem Description

Bob and Alice are playing a new game. There are n boxes which have been numbered from 1 to n. Each box is either empty or contains several cards. Bob and Alice move the cards in turn. In each turn the corresponding player should choose a non-empty box A and choose another box B that B<A && (A+B)%2=1 && (A+B)%3=0. Then, take an arbitrary number (but not zero) of cards from box A to box B. The last one who can do a legal move wins. Alice is the first player. Please predict who will win the game.

Input

The first line contains an integer T (T<=100) indicating the number of test cases. The first line of each test case contains an integer n (1<=n<=10000). The second line has n integers which will not be bigger than 100. The i-th integer indicates the number of cards in the i-th box.

Output

For each test case, print the case number and the winner's name in a single line. Follow the format of the sample output.

Sample Input

2

2

1 2

7

1 3 3 2 2 1 2

Sample Output

Case 1: Alice

Case 2: Bob

Author

hanshuai@whu

Source

The 5th Guangting Cup Central China Invitational Programming Contest

Recommend

notonlysuccess

/*

题意：1到n的盒子里，是空的或者装着卡片，每人轮流移动卡片，Alice先手，移动卡片的规则：每次选择一个A，然后选择一个B

    要求 B<A&&(A+B)%2==1&&(A+B)%3==0,从A中抽取任意一张卡片放到B中，谁不能移动了，就输了。

初步思路：这个就是先将能移动的盒子对找出来，然后统计能移动的牌

#错误：上面的想法不完善，只是一方面的认为卡片会从一上一级向下一级移动。

#补充：阶梯博弈，实际上卡片是在3的余数上进行转移的。

#感悟：手残用了数组，开小了，wa了两发才发现

*/

#include<bits/stdc++.h>

using namespace std;

int n;

int x;

int res=;

int t;

void init(){

    res=;

}

int main(){

    // freopen("in.txt","r",stdin);

    scanf("%d",&t);

    for(int ca=;ca<=t;ca++){

        init();

        scanf("%d",&n);

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

            scanf("%d",&x);

            if(i%==||i%==||i%==)

                res^=x;

        }

        if(res) printf("Case %d: Alice\n",ca);

        else printf("Case %d: Bob\n",ca);

    }

    return ;

}