Polycarp has n friends, the i-th of his friends has a_i candies. Polycarp's friends do not like when they have different numbers of candies. In other words they want all a_i to be the same. To solve this, Polycarp performs the following set of actions exactly once: 

  * Polycarp chooses k (0 ≤ k ≤ n) arbitrary friends (let's say he chooses friends with indices i_1, i_2, …, i_k); 
  * Polycarp distributes their a_{i_1} + a_{i_2} + … + a_{i_k} candies among all n friends. During distribution for each of a_{i_1} + a_{i_2} + … + a_{i_k} candies he chooses new owner. That can be any of n friends. Note, that any candy can be given to the person, who has owned that candy before the distribution process. 



Note that the number k is not fixed in advance and can be arbitrary. Your task is to find the minimum value of k.

For example, if n=4 and a=[4, 5, 2, 5], then Polycarp could make the following distribution of the candies: 

  * Polycarp chooses k=2 friends with indices i=[2, 4] and distributes a_2 + a_4 = 10 candies to make a=[4, 4, 4, 4] (two candies go to person 3). 



Note that in this example Polycarp cannot choose k=1 friend so that he can redistribute candies so that in the end all a_i are equal.

For the data n and a, determine the minimum value k. With this value k, Polycarp should be able to select k friends and redistribute their candies so that everyone will end up with the same number of candies.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4). Then t test cases follow.

The first line of each test case contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5).

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^4).

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case output: 

  * the minimum value of k, such that Polycarp can choose exactly k friends so that he can redistribute the candies in the desired way; 
  * "-1" if no such value k exists. 

Example

Input


5
4
4 5 2 5
2
0 4
5
10 8 5 1 4
1
10000
7
1 1 1 1 1 1 1


Output


2
1
-1
0
0
import java.io.*;
import java.util.*;

public class B {
	public static void main(String[] args) {
		FastReader in = new FastReader();
		
		int T = in.nextInt();
		while(T-- > 0) {
			int n = in.nextInt();
			int sum = 0;
			int[] a = new int[n];
			for(int i = 0; i < n; i++) {
				a[i] = in.nextInt();
				sum += a[i];
			}

			if(sum % n != 0) System.out.println(-1);
			else {
				int f = sum/n;

				int ans = 0;
				for(int i = 0; i < n; i++) {
					if(a[i]>f)
						ans++;
				}

				System.out.println(ans);
			}
		}
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		public FastReader() { 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 size) {
			int[] arr = new int[size];
			for(int i = 0; i < size; i++)
				arr[i] = Integer.parseInt(next());
			return arr;
		}
		int[][] read2dArray(int rows, int cols) {
			int[][] arr = new int[rows][cols];
			for(int i = 0; i < rows; i++) {
				for(int j = 0; j < cols; j++)
					arr[i][j] = Integer.parseInt(next());
			}
			return arr;
		}
	}
}