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 Codeforces {
    final static long mod = 1000000007;

    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while (t-- > 0) {
            int n = sc.nextInt();
            int[] a = new int[n];
            long sum = 0;
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
                sum += a[i];
            }

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

            long req = sum / n;

            Arrays.sort(a);

            int c = 0;

            for (int i = n - 1; i >= 0; i--) {
                if (a[i] <= req) {
                    break;
                }
                c++;
            }

            System.out.println(c);

        }
    }

    public static int diglen(Long y) {
        int a = 0;
        while (y != 0L) {
            y /= 10;
            a++;

        }
        return a;
    }

    static class FastReader {

        BufferedReader br;
        StringTokenizer st; // StringTokenizer() is used to read long strings

        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());
        }

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

    public class Pair implements Comparable<Pair> {
        public final int index;
        public final int value;

        public Pair(int index, int value) {
            this.index = index;
            this.value = value;
        }

        @Override
        public int compareTo(Pair other) {
            // multiplied to -1 as the author need descending sort order
            return -1 * Integer.valueOf(this.value).compareTo(other.value);
        }
    }

    static String reverseString(String str) {
        StringBuilder input = new StringBuilder();
        return input.append(str).reverse().toString();
    }

    static long factorial(int n, int b) {
        if (n == b)
            return 1;

        return n * factorial(n - 1, b);
    }

    static int lcm(int ch, int b) {
        return ch * b / gcd(ch, b);
    }

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

    static double ceil(double n, double k) {
        return Math.ceil(n / k);
    }

    static int sqrt(double n) {
        return (int) Math.sqrt(n);
    }

}
