Magical Bamboos

in a magical forest, there exists N bamboos that don't quite get cut down the way you would expect.

Originally, the height of the ith bamboo is equal to hi. In one move, you can push down a bamboo and decrease its height by one, but this move magically causes all the other bamboos to increase in height by one.

If you can do as many moves as you like, is it possible to make all the bamboos have the same height?

Input

The first line of input is T – the number of test cases.

The first line of each test case contains an integer N (1 ≤ N ≤ 105) - the number of bamboos.

The second line contains N space-separated integers hi (1 ≤ hi ≤ 105) - the original heights of the bamboos.

Output

For each test case, output on a single line "yes” (without quotes), if you can make all the bamboos have the same height, and "no" otherwise.

 

Example

input

Copy

2
3
2 4 2
2
1 2

output

Copy

yes
no

<span style="color:#880000">题意：每次找最大的数减一，其他的数加一，要是每个数相等，就YES。规律是每个数相差偶数就YES</span>

#include <iostream>
#include <stdio.h>
#include <algorithm>
using namespace std;
bool cmp(int a,int b)
{
    return a>b;
}
int main()
{
    int t,n,i,x,s,a[100000];
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        for(i=0;i<n;i++)
        {
            scanf("%d",&a[i]);
        }
        sort(a,a+n,cmp);
        for(i=1;i<n;i++)
        {
            if((a[i]-a[i-1])%2!=0)
                break;
        }
        if(i==n)
            printf("yes\n");
        else
            printf("no\n");
    }
    return 0;
}