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.io.*;

public class CFsolve2 {
  public static void main(String[] args) {
    FastScanner input = new FastScanner();
    int t = input.nextInt();
    while(t-- > 0){
      int n = input.nextInt();
      int[]arr = new int[n];

      for(int i = 0; i<n; i++)
        arr[i] = input.nextInt();

      Arrays.sort(arr);
      int i = 0, j = arr.length-1;

      while(i<=j){
        int left = arr[i];
        int right = arr[j];

        while(left != right){
          left+=1;
          right-=1;
        }
        i++;
        j--;
      }

      int min = 0;
      for(i = 0; i<=arr.length-2;i++){
       if(arr[i] != arr[i+1]) {
         min = Math.abs(arr[i]-arr[i+1]);
         break;
       }
      }
      System.out.println(min);
    }
    }
  }

   class FastScanner {
    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st=new StringTokenizer("");
    String next() {
      while (!st.hasMoreTokens())
        try {
          st=new StringTokenizer(br.readLine());
        } catch (IOException e) {
          e.printStackTrace();
        }
      return st.nextToken();
    }

    int nextInt() {
      return Integer.parseInt(next());
    }
    int[] readArray(int n) {
      int[] a=new int[n];
      for (int i=0; i<n; i++) a[i]=nextInt();
      return a;
    }
    byte nextByte(){
      return Byte.parseByte(next());
    }
    long nextLong() {
      return Long.parseLong(next());
    }
}

