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 CodeForces {
	// For fast input output
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			try {
				br = new BufferedReader(
						new FileReader("input.txt"));
				PrintStream out = new PrintStream(new FileOutputStream("output.txt"));
				System.setOut(out);
			} catch (Exception e) {
				br = new BufferedReader(new InputStreamReader(System.in));
			}
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	// end of fast i/o code
	public static void main(String[] args) {
		FastReader in = new FastReader();
		OutputStream op = System.out;
		PrintWriter out = new PrintWriter(op);
		int t = in.nextInt();
		for (int i = 1; i <= t; i++) {
			int  n=in.nextInt();
			int arr[]=new int[n];
			for(int j = 0; j < n; j++)
				arr[j]=in.nextInt();
			helper(n,arr,out);
			out.println();
		}
		out.close();

	}

public static void helper(int n,int arr[],PrintWriter o) 
	{
		Arrays.sort(arr);
		if(n==2)
			{
				o.print(arr[1]-arr[0]);
				return;
			}
		o.print(Math.min(arr[n/2]-arr[n/2-1],arr[n/2+1]-arr[n/2]));
	}
}