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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
//import java.util.*;
public class cp1 {
	
//	public long gcd(long a,long b) {
//    	if(b==0) {
//    		return a;
//    	}
//    	long m=a%b;
//    	return gcd(b,m);
//    }
	
	public static void main(String[] args)throws Exception {
		
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		cp1 cp1=new cp1();
		int t1=Integer.parseInt(br.readLine());
		while(t1-->0) {
			int n=Integer.parseInt(br.readLine());
			String A[]=br.readLine().split(" ");
			long a[]=new long[n];
			for(int i=0;i<n;i++) {
				a[i] =Long.parseLong(A[i]);
			}
			Arrays.sort(a);
			while(a[n-1]-a[0]>1) {
			for(int i=0;i<(n-1)/2;i++) {
				if(a[n-i-1]-a[i]>1) {
					long temp=((a[n-i-1]-a[i])/2);
					a[i]=a[i]+temp;
					a[n-1-i]=a[n-1-i]-temp;
				}
			}
			Arrays.sort(a);}
			if(a[n-1]-a[0]==0) {
				System.out.println("0");
			}
			else if(a[n-1]-a[0]==1) {
				System.out.println("1");
			}
			for(int i=0;i<n;i++) {
				System.out.print(a[i]+" ");
			}
			System.out.println();
		
		}
			}
	}


