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.Arrays;
import java.util.Scanner;

public class SolnA {
	static boolean checkPerfectSquare(double number)    
	{    
		double sqrt=Math.sqrt(number);     
		return ((sqrt - Math.floor(sqrt)) == 0);   
	}
	static boolean checkPerfectCube(double number)    
	{    
		double cbrt=Math.cbrt(number);     
		return ((cbrt - Math.floor(cbrt)) == 0);   
	}
	public static int reverseInt(int i) {
		int n = 0;
		while(i!=0) {
			n=n*10+i%10;
			i=i/10;
		}
		return n;
	}
	public static Long reverseLong(long i) {
		long n = 0;
		while(i!=0) {
			n=n*10+i%10;
			i=i/10;
		}
		return n;
	}
	public static long gcdl(long a,long b) {
		if(b==0)	return a;
		return gcdl(b,a%b);
	}
	public static long gcdi(int a,int b) {
		if(b==0)	return a;
		return gcdi(b,a%b);
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t>0) {
			t--;
			run(sc);
		}
		sc.close();
	}
	public static void run(Scanner sc) {
		int n=sc.nextInt();
		int[] a = new int[n];
		for(int i=0;i<n;i++) {
			a[i]=sc.nextInt();
		}
		Arrays.sort(a);
		int i=0,j=n-1;
		while(i<=j&&a[i]<a[j]) {
			int diff = a[j]-a[i];
			a[i]=a[i]+diff/2;
			a[j]=a[j]-diff/2;
			i++;
			j--;
		}
		int max = Integer.MIN_VALUE;
		int min = Integer.MAX_VALUE;
		for(int k=0;k<n;k++) {
			max=Math.max(max, a[k]);
			min = Math.min(min, a[k]);
		}
		System.out.println(max-min);
	}
}
