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.io.*;
import java.util.*;

public class A {

    static int gcd(int a, int b){
        if(a==0) return b;
        else return gcd(b%a, a);
    }
    static int lcm(int a, int b){
        return (a/gcd(a,b))*b;
    }

    static boolean isVow(char c){
        return c=='a'||c=='e'||c=='i'||c=='o'||c=='u';
    }

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        Scanner in = new Scanner(System.in);
        int T = fs.nextInt();
        for (int tt = 0; tt < T; tt++) {
            int  n = fs.nextInt();
            int sum=0;
            int[] arr = new int[n];
            for(int i=0;i<n;i++){
                int tm = fs.nextInt();
                arr[i] = tm;
                sum+=tm;
            }
            if(sum%n==0){
                System.out.println(0);
                continue;
            }
            sort(arr);
            int l=0,r=n-1;
            int max=arr[0], min=arr[n-1];
            while(l<r){
                if((arr[l]+arr[r])%2==0){
                    arr[l] = (arr[l]+arr[r])>>1;
                    arr[r] = (arr[l]+arr[r])>>1;
                }
                else{
                    arr[l] = (arr[l]+arr[r])>>1;
                    arr[r] = arr[l]+1;
                }
                max = Math.max(max, arr[l]);
                min = Math.min(min, arr[l]);
                l++;
                r--;
            }
            if(l==r){
                max = Math.max(max, arr[l]);
                min = Math.min(min, arr[l]);
            }
            System.out.println(max-min);
        }
    }

    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    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());
        }
    }

}