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.lang.reflect.Array;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static void A() {
        int n = sc.nextInt();
        int[] arr = sc.readArray(n);
        Functions.sort(arr);
        int sum = 0;
        for(int i=0; i<arr.length; i++) sum+=arr[i];
        if(sum%n != 0) {
            p.writeln(-1);
            return;
        }
        sum/=n;
        for(int i=0; i<arr.length; i++) {
            if(sum < arr[i]) {
                p.writeln(n-i);
                return;
            }
        }
        p.writeln(0);
    }

    public static void B() {

    }

    public static void C() {

    }

    public static void solve() {
        A();
//        B();
//        C();
    }

    public static void main(String[] args) {
        int t = 1;
        t = sc.nextInt();
        while (t-- != 0) {
            solve();
        }
        p.print();
    }


    static Integer MOD = (int) 1e9 + 7;
    static FastReader sc = new FastReader();
    static Print p = new Print();

    static class Functions {

        static void sort(int[] a) {
            ArrayList<Integer> l = new ArrayList<>();
            for (int i : a) l.add(i);
            Collections.sort(l);
            for (int i = 0; i < a.length; i++) a[i] = l.get(i);
        }

        public static long mod_add(long a, long b) {
            return (a % MOD + b % MOD + MOD) % MOD;
        }

        public static long pow(long a, long b) {
            long res = 1;
            while (b > 0) {
                if ((b & 1) != 0)
                    res = mod_mul(res, a);
                a = mod_mul(a, a);
                b >>= 1;
            }
            return res;
        }

        public static long mod_mul(long a, long b) {
            long res = 0;
            a %= MOD;
            while (b > 0) {
                if ((b & 1) > 0) {
                    res = mod_add(res, a);
                }
                a = (2 * a) % MOD;
                b >>= 1;
            }
            return res;
        }

        public static long gcd(long a, long b) {
            if (a == 0) return b;
            return gcd(b % a, a);
        }

        public static long factorial(long n) {
            long res = 1;
            for (int i = 1; i <= n; i++) {
                res = (i % MOD * res % MOD) % MOD;
            }
            return res;
        }

        public static int count(int[] arr, int x) {
            int count = 0;
            for (int val : arr) if (val == x) count++;
            return count;
        }

    }

    static class Print {
        StringBuffer strb = new StringBuffer();

        public void write(Object str) {
            strb.append(str);
        }

        public void writes(Object str) {
            strb.append(str).append(" ");
        }

        public void writeln(Object str) {
            strb.append(str).append("\n");
        }

        public void writeln() {
            strb.append('\n');
        }

        public void writes(int[] arr) {
            for (int val : arr) {
                write(val);
                write(' ');
            }
        }

        public void writes(long[] arr) {
            for (long val : arr) {
                write(val);
                write(' ');
            }
        }

        public void writeln(int[] arr) {
            for (int val : arr) {
                writeln(val);
            }
        }

        public void print() {
            System.out.print(strb);
        }

        public void println() {
            System.out.println(strb);
        }
    }

    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());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        double[] readArrayDouble(int n) {
            double[] a = new double[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

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