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.*;
import java.lang.*;
// import java.math.*;
import java.io.*;
public class Main
{
    public static int mod=(int)(1e9) + 7;

    public static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    public static PrintWriter ot=new PrintWriter(System.out);

    public static int[] take_arr(int n){
        int a[]=new int[n];
        try {
            String s[]=br.readLine().trim().split(" ");
            for(int i=0;i<n;i++)
            a[i]=Integer.parseInt(s[i]);
        } catch (Exception e) {
            e.printStackTrace();
        }
        return a;
    }
	public static void main (String[] args) throws java.lang.Exception
	{
		try{
         
            int t=Integer.parseInt(br.readLine().trim());
            int cno=1;
            
            while(t-->0)
            {
                
                String qq[]=br.readLine().trim().split(" ");
                int n=Integer.parseInt(qq[0]);
                // int m=Integer.parseInt(qq[1]);
                int a[]=take_arr(n);
                Arrays.sort(a);
                int low=0,high=n-1;
                while(low<high)
                {
                    if((a[low]+a[high])%2==0)
                    {
                        int temp=(a[low]+a[high])/2;
                        a[low++]=temp;
                        a[high--]=temp;
                    }
                    else
                    {
                        int temp=(a[low]+a[high])/2;
                        a[low++]=temp;
                        a[high--]=temp+1;
                    }
                }
                Arrays.sort(a);
                ot.println(a[n-1]-a[0]);
            }
            ot.close();
            br.close();
        }catch(Exception e){
            e.printStackTrace();
            return;
        }
    }
 
}