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.*;
import java.time.*;
import static java.lang.Math.*;

@SuppressWarnings("unused")
public class A {
	static boolean DEBUG = false;

	public static void main(String[] args) throws IOException {
		Instant start = Instant.now();
		if (args.length == 2) {
			System.setIn(new FileInputStream(new File("D:\\program\\javaCPEclipse\\CodeForces\\src\\input.txt")));
			// System.setOut(new PrintStream(new File("output.txt")));
			System.setErr(new PrintStream(new File("D:\\program\\javaCPEclipse\\CodeForces\\src\\error.txt")));
			DEBUG = true;
		}
		Reader fs = new Reader();
		PrintWriter pw = new PrintWriter(System.out);
		int t = fs.nextInt();
		while (t-- > 0) {
			int n = fs.nextInt();
			int a[] = fs.readArray(n);
			sort(a);
			for (int i = 0; i < n + n; i++) {
				if (a[0] < a[n - 1]) {
					a[0]++;
					a[n - 1]--;
					sort(a);
				} else {
					break;
				}
			}
			log(a);
			pw.println(abs(a[0] - a[n - 1]));
		}
		Instant end = Instant.now();
		if (DEBUG) {
			pw.println(Duration.between(start, end));
		}
		pw.close();
	}

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

	static void log(Object o) {
		if (DEBUG)
			System.err.println(o);
	}

	static void log(int a[]) {
		if (DEBUG)
			System.err.println(Arrays.toString(a));
	}

	static void log(char a[]) {
		if (DEBUG)
			System.err.println(Arrays.toString(a));
	}

	static void log(String a) {
		if (DEBUG)
			System.err.print(a + " -> ");
	}

	static <T> void log(T a[]) {
		if (DEBUG) {
			System.err.print("[");
			for (T x : a)
				System.err.print(x + " ");
			System.err.println("]");
		}
	}

	static <T> void log(ArrayList<T> a) {
		if (DEBUG) {
			System.err.print("[");
			for (T x : a) {
				System.err.print(x + " ");
			}
			System.err.println("]");
		}
	}

	static <T, V> void log(Map<T, V> mp) {
		if (DEBUG) {
			System.err.print(mp);
		}
	}

	public static void print(long a, long b, long c, PrintWriter pw) {
		pw.println(a + " " + b + " " + c);
		return;
	}

	static class Reader {
		BufferedReader br;
		StringTokenizer st;

		public Reader() {
			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;
		}

		int[] readArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		int[][] read2Array(int n, int m) {
			int a[][] = new int[n][m];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					a[i][j] = nextInt();
				}
			}
			return a;
		}
	}
}