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
//package src;

import java.util.Scanner;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.TreeMap;
import java.rmi.server.Skeleton;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Stack;

public class cc {
	static Scanner scn = new Scanner(System.in);
	//static int max = Integer.MIN_VALUE;
	static int mod=1000000007;
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		int t=scn.nextInt();
		while(t-->0)
		{
			int n=scn.nextInt();
			int arr[]=new int[n],sum=0;
			for(int i=0;i<n;i++)
			{
				arr[i]=scn.nextInt();
				sum+=arr[i];
				
			}
			if(sum%n!=0)
				System.out.println("-1");
			else
			{
				int d=sum/n,count=0;
				for(int i=0;i<n;i++)
				{
					if(arr[i]>d)
						count++;
				}
				System.out.println(count);
			}
		}
		
		
	}
	
	
	public static boolean palind(String str)
	{
		int n=str.length();
		boolean bl=true;
		for(int i=0;i<=n/2;i++)
		{
			if(str.charAt(i)!=str.charAt(n-i-1))
			{
				bl=false;
				break;
			}
		}
		return bl;
	}
	

	public static int gcd(int a, int b) {
		if (a == 0)
			return b;
		int l = gcd(b % a, a);
		return l;
	}
}

class kuch
{
	int fir,sec;
	kuch(int a,int b)
	{
		this.fir=a;
		this.sec=b;
		
	}
	@Override
	public int hashCode() {
		// TODO Auto-generated method stub
		
		return fir*7+sec*7;
	}
	@Override
	public boolean equals(Object other) {   //learn this again
		if (this == other)
			return true;

		if (other instanceof kuch) {
			kuch pt = (kuch) other;

			return pt.fir == this.fir && pt.sec == this.sec;
		} else
			return false;
	}
}
class makepair
{
	int a,step;
	 makepair(int a ,int b) {
		this.a=a; 
		this.step=b;
	}
}
class sort implements Comparator<kuch>
{

	@Override
	public int compare(kuch o1, kuch o2) {
		// TODO Auto-generated method stub
		int a=o1.sum-o2.sum;
		if(a<0)
			return 1;
		else
			return -1;
		
	}
	
}
