There are n block towers in a row, where tower i has a height of a_i. You're part of a building crew, and you want to make the buildings look as nice as possible. In a single day, you can perform the following operation:

  * Choose two indices i and j (1 ≤ i, j ≤ n; i ≠ j), and move a block from tower i to tower j. This essentially decreases a_i by 1 and increases a_j by 1. 



You think the ugliness of the buildings is the height difference between the tallest and shortest buildings. Formally, the ugliness is defined as max(a)-min(a). 

What's the minimum possible ugliness you can achieve, after any number of days?

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t cases follow.

The first line of each test case contains one integer n (2 ≤ n ≤ 100) — the number of buildings.

The second line of each test case contains n space separated integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^7) — the heights of the buildings.

Output

For each test case, output a single integer — the minimum possible ugliness of the buildings.

Example

Input


3
3
10 10 10
4
3 2 1 2
5
1 2 3 1 5


Output


0
0
1

Note

In the first test case, the ugliness is already 0.

In the second test case, you should do one operation, with i = 1 and j = 3. The new heights will now be [2, 2, 2, 2], with an ugliness of 0.

In the third test case, you may do three operations: 

  1. with i = 3 and j = 1. The new array will now be [2, 2, 2, 1, 5], 
  2. with i = 5 and j = 4. The new array will now be [2, 2, 2, 2, 4], 
  3. with i = 5 and j = 3. The new array will now be [2, 2, 3, 2, 3]. 

The resulting ugliness is 1. It can be proven that this is the minimum possible ugliness for this test.

import java.util.Arrays;
import java.util.Scanner;

public class JavaApplication485 {

    public static void main(String[] args) {
        Scanner kb=new Scanner(System.in);
       
       int T=kb.nextInt();
       for(int t=0;t<T;t++)
       {  //System.out.println("hello");
           int n=kb.nextInt();
           int arr[]=new int[n];
           
           for(int i=0;i<n;i++)
               arr[i]=kb.nextInt();
           
           Arrays.sort(arr);
           
           int j=0;
           int i=0;
           if(n%2!=0)
           {
                j=(n/2)+1;
                i=j-2;
           }
           else
           {
               j=n/2;
               i=j-1;
           }
           
           while(i>=0&&j<=(n-1))
           {
               int fac=0;
               int diff=arr[j]-arr[i];
               
               
               if(diff!=0)
                fac=diff/2;
               
               arr[i]=arr[i]+fac;
               arr[j]=arr[j]-fac;
               
               i--;
               j++;
               
           }
           
           Arrays.sort(arr);
                      
      //     System.out.println("Array is ");
         //  for(int k=0;k<arr.length;k++)
         //      System.out.print(arr[k]+" ");
         System.out.println((arr[n-1]-arr[0]));

         
           
           
       }
    }
    
}

