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();
    PrintWriter out = new PrintWriter(System.out);
    while(t-- > 0){
      int n = input.nextInt();
      ArrayList<Integer> list  = new ArrayList<>();
      
      int diff = input.nextInt();
      list.add(diff);
      
      for(int i = 1; i<n; i++) {
        list.add(input.nextInt());
        if(diff!=list.get(i)){
          diff = 1;
        }
      }
      int min = 0;      
      if(diff == 1)
        min = 1;
      
//      Collections.sort(list);
//      int i = 0, j = list.size()-1;
//
//      while(i<=j){
//        int left = list.get(i);
//        int right = list.get(j);
//
//        while(Math.abs(left-right)>1){
//
//          list.set(i,left+1 );
//          list.set(j,right-1);
//          left = list.get(i);
//          right = list.get(j);
//        }
//        i++;
//        j--;
//      }
//
//      int min = 0;
//      for(i = 0; i<=list.size()-2; i++){
//       if(!list.get(i).equals(list.get(i+1))) {
//         min = Math.abs(list.get(i) - list.get(i + 1));
//       }
//      }
      out.println(min);
    }
    out.close();
    }
    static 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;
      }
      long nextLong() {
        return Long.parseLong(next());
      }
    }

}
