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.math.*;
import java.util.Scanner;

public class q1 {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int t= sc.nextInt();//sc.nextLine();
        for(int i=0; i<t; i++){
            int n= sc.nextInt();//sc.nextLine();
            int[] arr= new int[n];
            for(int j=0; j<n; j++){
                arr[j]= sc.nextInt();
                System.out.println(arr[j]);
            }

            while(!(ugly(arr)[2] == 0 || ugly(arr)[2] ==1)) {
                arr[ugly(arr)[0]]-- ;
                arr[ugly(arr)[1]]++ ;

            }
            System.out.println(ugly(arr)[2]);

        }

    }
    static int[] ugly(int[] arr){
        int n= arr.length;
        int max = arr[0];
        int min = arr[0];
        int a=0, b=0;
        for(int i=1; i<n; i++){
            if(arr[i] > max){
                a = i;
                max = arr[i];
            }
            if(arr[i] < min) {
                b = i;
                min = arr[i];
            }
        }
        int[] ret= new int[3];
        ret[0] = a;
        ret[1] = b;
        ret[2] = max-min;
        return ret;
    }
}