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.*;
import java.io.*;
public class CodeChef {

	public static void main(String[] args) {
		FastReader in = new FastReader();
		int t =in.nextInt();
		while(t-->0) {
	         int n = in.nextInt();
	         int a[] = new int[n];
	         int sum =0;
	         for(int i =0;i<n;i++) {
	        	 a[i] = in.nextInt();
	        	 sum+=a[i];
	         }
	         if(sum%n!=0)
	        	 System.out.println(-1);
	         else {
	        	 int avg = sum/n;
	        	 int res=0;
	        	 for(int i =0;i<n;i++) {
	        		 if(a[i]>avg)
	        			 res++;
	        	 }
	        	 System.out.println(res);
	         }
	         
	         
		}
		
		
	 }
	

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 [] readintarray(int n) {
	            int res [] = new int [n];
	            for(int i = 0; i<n; i++)res[i] = nextInt();
	            return res;
	        }
	        long [] readlongarray(int n) {
	            long res [] = new long [n];
	            for(int i = 0; i<n; i++)res[i] = nextLong();
	            return res;
	        }
	  }
    static boolean isPrime(int n)
    {

    // Check if number is less than
    // equal to 1
     if (n <= 1)
         return false;

    // Check if number is 2
     else if (n == 2)
         return true;

    // Check if n is a multiple of 2
     else if (n % 2 == 0)
         return false;

    // If not, then just check the odds
     for (int i = 3; i <= Math.sqrt(n); i += 2)
     {
        if (n % i == 0)
            return false;
     }
     return true;
    }

   static int getSum(int n)
   {    
       int sum = 0;
       
       while (n != 0)
      {
         sum = sum + n % 10;
         n = n/10;
      }
  
    return sum;
   }

    static int gcd(int a, int b)
   {
    // Everything divides 0
    if (a == 0)
      return b;
    if (b == 0)
      return a;
  
    // base case
    if (a == b)
        return a;
  
    // a is greater
    if (a > b)
        return gcd(a-b, b);
    return gcd(a, b-a);
   }

     static void swap(int[] arr, int i, int j)
    {
       int temp = arr[i];
       arr[i] = arr[j];
       arr[j] = temp;
    }

    static int countDigit(long n)
    {
        return (int)Math.floor(Math.log10(n) + 1);
    }
    static long fastpower(long a,long b,int n ) {
    	long res =1;
    	while(b>0) {
    		if((b&1)!=0) {
    			res = (res* a % n)%n;
    		}
    		a = (a % n*a % n) % n;
    		b = b >> 1;
	            
    	}
    	return res;
    }
    static int catalan(int n)
    {
        int res = 0;
 
        // Base case
        if (n <= 1)
        {
            return 1;
        }
        for (int i = 0; i < n; i++)
        {
            res += catalan(i)
                * catalan(n - i - 1);
        }
        return res;
    }
    static int mod(int a, int m)
    {
        return (a%m + m) % m;
    }
}
