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.util.StringTokenizer;

import java.io.IOException;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.math.BigDecimal;

public class S2 {
	
	static class Reader {
		
		static BufferedReader reader;
		static StringTokenizer tokenizer;
		
		static void init(InputStream input) {
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer("");
		}
		
		static String next() throws IOException {
			while(!tokenizer.hasMoreTokens()) {
				tokenizer = new StringTokenizer(reader.readLine());
			}
			return tokenizer.nextToken();
		}
		
		static int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
		
		static long nextLong() throws IOException {
			return Long.parseLong(next());
		}
		
	}
	
	private static void arrInp(int n1) throws IOException {
		// TODO Auto-generated method stub
		arr = new long[n1];
		for(int i=0; i<n1; i++) {
			long a = Reader.nextLong();
		//	System.err.println(a+" "+i);
			arr[i] = a;
		}
	}

	static long[] merge(long[] a, long[] b) {
		int m = a.length;
		int n = b.length;
		long [] c = new long[n+m];
		
		int j=0, k=0;
		while(j+k<m+n) {
			if(j>=m) {
				c[j+k] = b[k];
				k++;
			}
			else if(k>=n) {
				c[j+k] = a[j];
				j++;
			}
			else {
				if(a[j]<b[k]) {
					c[j+k] = a[j];
					j++;
				}
				else if(a[j]==b[k]) {
					if(a[j]<b[k]) {
						c[j+k] = a[j];
						j++;
					}
					else {
						c[j+k] = b[k];
						k++;
					}
				}
				else {
					c[j+k] = b[k];
					k++;
				}
			}
		}
		return c;
	}
	
	static long[] Msort(long[] unsorted){
		int l = unsorted.length;
		
		if(l<=1) {
			return unsorted;
		}
		
		else {
			long[] Msorted = new long[l];
			long[] m1 = new long[l/2];
			long[] m2 = new long[l-(l/2)];
			
			for(int i=0; i<l; i++) {
				if(i<l/2) {
					m1[i] = unsorted[i];
				}
				else {
					m2[i-(l/2)] = unsorted[i];
				}
			}
			
			Msorted = merge(Msort(m1), Msort(m2));		
			
			return Msorted;
		}
		
	}
	
	static Node[] merge(Node[] a, Node[] b) {
		int m = a.length;
		int n = b.length;
		Node [] c = new Node[n+m];
		
		int j=0, k=0;
		while(j+k<m+n) {
			if(j>=m) {
				c[j+k] = b[k];
				k++;
			}
			else if(k>=n) {
				c[j+k] = a[j];
				j++;
			}
			else {
				if(a[j].compareTo(b[k])<0) {
					c[j+k] = a[j];
					j++;
				}
				else {
					c[j+k] = b[k];
					k++;
				}
			}
		}
		return c;
	}
	
	static Node[] Msort(Node[] unsorted){
		int l = unsorted.length;
		
		if(l<=1) {
			return unsorted;
		}
		
		else {
			Node[] Msorted = new Node[l];
			Node[] m1 = new Node[l/2];
			Node[] m2 = new Node[l-(l/2)];
			
			for(int i=0; i<l; i++) {
				if(i<l/2) {
					m1[i] = unsorted[i];
				}
				else {
					m2[i-(l/2)] = unsorted[i];
				}
			}
			
			Msorted = merge(Msort(m1), Msort(m2));		
			
			return Msorted;
		}
		
	}
	
	private static class Node implements Comparable<Node> {
		
		public long x;
		public long y;
		
		public Node(int xi, int yi) {
			// TODO Auto-generated constructor stub
			x=xi;
			y=yi;
		}
		
		public void swap() {
			long c=x;
			x=y;
			y=c;
		}
		
		@Override
		public int compareTo(Node o) {
			// TODO Auto-generated method stub
			return (int) (this.x - o.x);
		}
		@Override
		public String toString() {
			// TODO Auto-generated method stub
			return (" x:"+x+" y:"+y);
		}
	}

	private static long inf = 1<<27;
	private static long ans;
	private static long n;
	private static long k;
	private static long[] arr;
	private static long[] L;
	private static long[] R;
	private static char[] str;
	private final static long fd = 1000000007;
	private static boolean bruh;

	public static void main(String[] args) throws IOException {
				
		ans = 0;
		
		Reader.init(System.in);
		
		OutputStream out = new BufferedOutputStream(System.out);
		
		int tc=1;
		tc = Reader.nextInt();
		
		main_loop:
		for(int tn=0; tn<tc; tn++) {
			
			ans=0;
			bruh = false;
			n=tn+1;
			n = Reader.nextInt();
			
		//	k = Reader.nextInt();
			int n1 = (int) n;	
			arrInp(n1);
			
			int j=n1;
			
			long sum=0;
			for(int i=0; i<n1; i++) {
				sum+=arr[i];
			}
			
			if(sum%n==0) {
				long x = sum/n;
				
				
				
				for(int i=0; i<n1; i++) {
					if(arr[i]>x) {
						ans++;
					}
				}
				
			}
			else {
				ans=-1;
			}
			
//			if(bruh) {
//				out.write(("YES").getBytes());
//			}
//			else {
//				out.write(("NO").getBytes());
//			}
			
		//	out.write(("YES").getBytes());
		//	out.write(("NO").getBytes());
			
			out.write((ans+" ").getBytes());
			out.write(("\n").getBytes());
			
		}
		
		out.flush();
		out.close();
		
	}
}
