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 MyClass
    {
        public static void main(String []args) throws IOException
        {
            BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
            BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
            int t = Integer.parseInt(br.readLine());
            while(t-->0)
            {
                int n = Integer.parseInt(br.readLine());
                String s[] = br.readLine().split(" ");
                int arr[] = new int[n];
                int sum = 0;
                for(int i=0;i<n;i++)
                {
                    arr[i] = Integer.parseInt(s[i]);
                    sum+=arr[i];
                }
                if(sum%n!=0)
                {
                    System.out.println("-1");
                }
                else
                {
                    int avg = sum/n;
                    int count = 0;
                    for(int i=0;i<n;i++)
                    {
                        if(arr[i]>avg)
                            count++;
                    }
                    System.out.println(count);
                }
            }
        }
    }