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 CP {
    public static void main(String[] args) throws IOException{
        FastReader sc = new FastReader();
        int t = sc.Int();
        for(;t > 0;t--){
            int n = sc.Int();
            int arr[] = new int[n];
            for(int i = 0;i < n;i++){
                arr[i] = sc.Int();
            }
            Arrays.sort(arr);
            for(int i = 0,j = n - 1;i < j;i++,j--){
                int d = arr[j] - arr[i];
                if(d % 2 == 0){
                    arr[i] += d / 2;
                    arr[j] -= d / 2;
                }
                else{
                    arr[i] += (d + 1) / 2;
                    arr[j] -= (d + 1) / 2 + 1;
                }
            }
            Arrays.sort(arr);
            System.out.println(arr[n-1] - arr[0]);
        }
        sc.close();
    }
}

class FastReader {
    private BufferedReader br;
    private StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public String next() throws IOException {
        for (; st == null || !st.hasMoreTokens();) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

    public String nextLine() throws IOException {
        return br.readLine();
    }

    public int Int() throws IOException {
        return Integer.parseInt(next());
    }

    public long Long() throws IOException {
        return Long.parseLong(next());
    }

    public double Double() throws IOException {
        return Double.parseDouble(next());
    }

    public float Float() throws IOException {
        return Float.parseFloat(next());
    }

    public char Char() throws IOException {
        return next().charAt(0);
    }

    public void close() throws IOException {
        br.close();
    }
}