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 A_Closing_The_Gap {
    static final FastScanner scan = new FastScanner();
    static PrintWriter out = new PrintWriter(System.out);
    public static void main (String[] args) {
        int t = scan.nextInt();
        while (t-- > 0) {
            mitul();
        }
        out.close();
    }
    static void mitul() {
        int n = scan.nextInt();
        int[] arr = scan.readArray(n);
        Arrays.sort(arr);
        int i = 0, j = n - 1;
        while (i < j) {
            int diff = arr[j] - arr[i];
            if (diff % 2 == 0) {
                arr[i] = arr[j] = (arr[i] + arr[j]) / 2;
            }
            else {
                arr[i] += diff / 2;
                arr[j] -= diff / 2;
            }
            i++;
            j--;
        }
        Arrays.sort(arr);
        out.println(arr[n-1] - arr[0]);
    }
    static void printArray (int[] arr) {
        for (int i=0; i<arr.length; i++) {
            out.print(arr[i] + " ");
        }
        out.println();
    }
    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();
        }
 
        String nextLine(){
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
 
            return "";
        }
 
        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());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}