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.awt.Desktop;




import java.io.BufferedReader;


import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.net.URI;
import java.net.URISyntaxException;
import java.sql.Array;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;

import java.util.LinkedHashMap;
import java.util.LinkedHashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;
import java.util.Vector;

import org.w3c.dom.Node;





public  class codechef3 {
static class comp implements Comparator<String>
{

	
	
	
	@Override
	public int compare(String o1, String o2) {
		if(o1.length()>o2.length())
			return 1;
		else if(o1.length()<o2.length())
			return -1;
		else return o1.compareTo(o2);
	 
	}
	
	}
      //=======================================================
	  //sorting Pair
   static class comp1 implements Comparator<Pair<Integer,Integer>>
   {

	@Override
	public int compare(Pair<Integer, Integer> o1, Pair<Integer, Integer> o2) {
		if(o1.k>o2.k)
			return 1;
		else return -1;
	
	}

	
	
	}
        //======================================================= 
	   
   //Creating Pair class  
         //----------------------------------------------------------------------
	    
       static class Pair<Integer,Intetger>
       {
    	   int k=0;
    	   int v=0;
    	   public Pair(int a,int b)
    	   {
    		   k=a;
    		   v=b;
    	   }
    	   public int getKey()
    	   {
    		   return k;
    		   
    	   }
    	   
    	   
       }
    
     //--------------------------------------------------------------------------
	
		 //gcd of two number
		 
		 
		    
		 //--------------------------------------------------------------------------------------------
		 
		 //lcm of two number
		
		    
		    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; 
		        } 
		    } 
	
		    
		  //-------------------------------------------------------------------------------------------
	
		    public static int gcd(int a,int b)
			{
				return b==0?a:gcd(b,a%b);
			}
		     
		 
		    
		    
		    
		    
			public static void main(String[] args) 
		    {
		    	
		    	StringBuilder sb=new StringBuilder();
		    	FastReader s=new FastReader(); 
		         
		    	
		    	int t=s.nextInt();
		    	while(t-->0)
		    	{
		      
		    		int n=s.nextInt();
		    		int[] a=new int[n];
		    		
		    		long sum=0;
		    		for(int i=0;i<n;i++)
		    		{
		    			a[i]=s.nextInt();
		    			sum+=a[i];
		    		}
		      long sum1=sum/n;
		      if(sum%n!=0)
		      {
		    	  System.out.println("-1");
		    	  continue;
		      }
		    		int count=0;
		    		Arrays.sort(a);
		    	for(int i=n-1;i>=0;i--)
		    	{
		    		if(a[i]<=sum1)
		    			break;
		    		count++;
		    			
		    	}
		    	System.out.println(count);
		    		
		    		
		    		
		           
		    	}
			}
		
		    
		    

}