Square



Description

Given a set of sticks of various lengths, is it possible to join them end-to-end to form a square?

 

Input

The first line of input contains N, the number of test cases. Each test case begins with an integer 4 <= M <= 20, the number of sticks. M integers follow; each gives the length of a stick - an integer between 1 and 10,000.

 

Output

For each case, output a line containing "yes" if is is possible to form a square; otherwise output "no".

 

Sample Input

 3
4 1 1 1 1
5 10 20 30 40 50
8 1 7 2 6 4 4 3 5 

 

Sample Output

 yes
no
yes 



#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int a[25];
int vis[25];
int n,sum;
int dfs(int d, int w, int cnt)
{
    if(d == sum)
    {
        w = 0;
        d = 0;
        cnt++;
        if(cnt == 4)
            return 1;
    }
    for(int i=w; i<n; i++)
    {
        if(!vis[i])
        {
            vis[i] = 1;
            if((d+a[i] <= sum ) && dfs(d+a[i], i+1, cnt))
                return 1;
            vis[i] = 0;
        }
    }
    return 0;
}
int main()
{
    int T;
    cin>>T;
    while(T--)
    {
        cin>>n;
        sum = 0;
        memset(vis, 0, sizeof(vis));
        memset(a, 0, sizeof(a));
        for(int i=0; i<n; i++)
        {
            cin>>a[i];
            sum += a[i];
        }
        int flag = 0;
        if(sum % 4 ==0)
        {
            sum /= 4;
            flag = dfs(0, 0, 0);
        }
        if(flag)
        {
            cout<<"yes"<<endl;
        }
        else
        {
            cout<<"no"<<endl;
        }
    }
}