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 S {
    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());
        }

        float nextFloat() {
            return Float.parseFloat(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return str;
        }

        char nextChar() {

            char c = ' ';
            try {
                c = (char) br.read();
            } catch (Exception e) {
                e.printStackTrace();
            }
            return c;
        }
    }

    public static void main(String[] args) {

        FastReader sc = new FastReader();

        int ntc = sc.nextInt();

        while(ntc -- > 0){

            int n = sc.nextInt();

            int [] a =new int[n];

            int sum  = 0;

            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
                sum += a[i];
            }

            if(sum % n != 0)
            {
                System.out.println(-1);
            }else {

                int avg = sum/n;

                int def = 0;

                List<Integer> donors = new ArrayList<>();

                for (int i = 0; i < n; i++) {
                    if(a[i] <= avg){
                        def +=avg - a[i];
                    }else if(a[i] > avg){
                       donors.add(a[i] - avg);
                    }

                }

                int cnt = 0;

                Collections.sort(donors, Collections.reverseOrder());

                for(int i = 0; i<donors.size(); i++){
                    if(def <= donors.get(i)){
                        cnt++;
                        break;
                    }else {
                        def -=donors.get(i);
                        cnt++;
                    }
                }

                System.out.println(cnt);
            }


        }

    }
}
