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.lang.*;
import java.io.*;

public class Main {
//    public static PrintWriter out;
//
//    public static class MyScanner {
//        BufferedReader br;
//        StringTokenizer st;
//
//        public MyScanner() {
//            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 void main(String[] args) throws IOException {
        BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        int T=Integer.parseInt(in.readLine());
        while(T-->0)
        {
            int N=Integer.parseInt(in.readLine());
            String[] str=in.readLine().split(" ");
            int[] arr=new int[N];
            long sum=0;
            for(int i=0;i<N;i++)
            {
                int val=Integer.parseInt(str[i]);
                arr[i]=val;
                sum+=val;
            }
            if(sum%N!=0)
            {
                System.out.println(-1);

            }
            else if(N==1)
            {
                System.out.println(0);
            }
            else
            {
                int count=0;
                sum=sum/N;
                for(int val:arr)
                {
                    if(val>sum)
                    {
                        count++;
                    }
                }
                System.out.println(count);
            }

        }
    }
}



