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.io.*;
import java.util.*;

public class Main
{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    static StreamTokenizer st=new StreamTokenizer(br);
    static PrintWriter pw=new PrintWriter(new OutputStreamWriter(System.out), true);

    static int nextInt() throws IOException
    {
        st.nextToken();
        return (int)st.nval;
    }

    static String nextStr() throws IOException
    {
        st.nextToken();
        return st.sval;
    }

    static int brReadInt() throws IOException
    {
        return Integer.parseInt(br.readLine());
    }

    static long brReadLong() throws IOException
    {
        return Long.parseLong(br.readLine());
    }

    static int[] brReadIntArray(int n) throws IOException
    {
        int[] res=new int[n];
        String[] input=br.readLine().split(" ");
        for(int i=0; i<n; i++)
            res[i]=Integer.parseInt(input[i]);
        return res;
    }

    static int gcd(int a, int b)
    {
        return b==0 ? a : gcd(b, a%b);
    }

    static int INF=0x3f3f3f3f;

    public static void main(String[] args) throws IOException
    {
        int T=nextInt();
        while(T-->0)
        {
            int n=nextInt();
            long[] candies=new long[n];
            long sum=0;
            for(int i=0; i<n; i++)
            {
                candies[i]=nextInt();
                sum+=candies[i];
            }

            if(sum%n!=0)
            {
                pw.println(-1);
                continue;
            }

            long avg=sum/n;
            int ans=0;
            for(int i=0; i<n; i++)
            {
                if(candies[i]>avg)
                    ans++;
            }
            pw.println(ans);
        }
    }
}

class HideArray
{
    int[] preSum;

    HideArray(int[] nums)
    {
        int n=nums.length;
        preSum=new int[n+1];
        for(int i=1; i<=n; i++)
            preSum[i]=preSum[i-1]+nums[i-1];
    }

    int getPreSum(int right)
    {
        return preSum[right];
    }
}