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 CodeForce;
import java.util.*;

import java.util.Scanner;

public class sdfdf {
	static long mod=1000000007;
	static String r;
	public static void main(String[] args) {
		Scanner sc= new Scanner(System.in);
		int test=sc.nextInt();
		while(test-->0) {
			int n=sc.nextInt();
			int[] arr=new int[n];
			for(int i=0;i<n;i++) {
				arr[i]=sc.nextInt();
				
			}
			int sum=0;
			for(int i=0;i<n;i++) {
				sum+=arr[i];
			}
			if(sum%n!=0) {
				System.out.println(-1);
			}
			else {
				int count=0;
				int val=sum/n;
				Arrays.sort(arr);
				for(int i=0;i<n;i++) {
					if(arr[i]>val)count++;
				}
				System.out.println(count);
			}
		}
		}

	
	public static void swap(int a, int b) {
		int temp=a;
		a=b;
		b=temp;
	}
	
	public static boolean checkPallindrome(String str){
		boolean ok=true;
		int low=0;int high=str.length()-1;
		while(low<high){
			if(str.charAt(low)==str.charAt(high)){
				ok=false;
				break;
			}

			low++;high--;
		}
		return ok;
	}
	public static int[] primeArray(int n){
			boolean prime[] = new boolean[n + 1];
			for (int i = 0; i <= n; i++)
				prime[i] = true;

			for (int p = 2; p * p <= n; p++)
			{
				if (prime[p] == true)
				{
					for (int i = p * p; i <= n; i += p)
						prime[i] = false;
				}
			}
			int[] primeArray =new int[n+1];int pos=0;
			for(int i=0;i<n;i++) {
				if(prime[i]==true) {
					primeArray[pos++]=i;
				}
			}
			return primeArray;
			
		}

	
	public static boolean checkPrime(int n) {
		for(int i=2;i*i<n;i++) {
			if(n%i==0)return false;
		}
		return true;
	}

	public static int GCD2(int a, int b) {
		if(a==0)return b;
		if(b==0)return a;
		if(a>b)return GCD2(a%b,b);
		else return GCD2(b%a,a);
	}
	public static void sort(int[] arr,int strt,int lst) {
		if(lst>arr.length-1) {
			lst=arr.length-1;
		}
		while(strt<=lst) {
			int temp=arr[strt];
			arr[strt]=arr[lst];
			arr[lst]=temp;
			strt++;lst--;
		}
		
	}
	
	
	

}