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
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

import java.util.*;

/**
 *
 * @author xpeng
 */

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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;

public class Main {

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    static StringTokenizer st;
    public static void main(String[] args) throws IOException {
        int t = readInt();
        for (int i = 0; i < t; i++) {
            int n = readInt();
            int[] arr = new int[n];
            int sum=0;
            for (int j = 0; j < n; j++) {
                arr[j]=readInt();
                sum+=arr[j];
            }
            double num=(double)sum/n;
            if (num%1!=0) {
                System.out.println("-1");
            }else{
                int need=0;
                for (int j = 0; j < n; j++) {
                    if (arr[j]<num) {
                        need+=num-arr[j];
                    }
                }
                if (need==0) {
                    System.out.println("0");
                }else{
                    Arrays.sort(arr); 
                    int k=0,have=0;
                    boolean flag=false;
                    for (int j = arr.length-1; j >=0; j--) {
                        have+=arr[j]-num;
                        k++;
                        if (have>=need) {
                            System.out.println(k);
                            flag = true;
                            break;
                        }
                    }
                    if (!flag) {
                        System.out.println("-1");
                    }
                    
                }
            }
        }
    }

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine().trim());
        }
        return st.nextToken();
    }

    static long readLong() throws IOException {
        return Long.parseLong(next());
    }

    static int readInt() throws IOException {
        return Integer.parseInt(next());
    }

    static double readDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static char readCharacter() throws IOException {
        return next().charAt(0);
    }

    static String readLine() throws IOException {
        return br.readLine().trim();
    }
}
