Highway 201 is the most busy street in Rockport. Traffic cars cause a lot of hindrances to races, especially when there are a lot of them. The track which passes through this highway can be divided into n sub-tracks. You are given an array a where a_i represents the number of traffic cars in the i-th sub-track. You define the inconvenience of the track as ∑_{i=1}^{n} ∑_{j=i+1}^{n} \lvert a_i-a_j\rvert, where |x| is the absolute value of x. 

You can perform the following operation any (possibly zero) number of times: choose a traffic car and move it from its current sub-track to any other sub-track.

Find the minimum inconvenience you can achieve.

Input

The first line of input contains a single integer t (1≤ t≤ 10 000) — the number of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 2⋅ 10^5).

The second line of each test case contains n integers a_1, a_2, …, a_n (0≤ a_i≤ 10^9).

It is guaranteed that the sum of n over all test cases does not exceed 2⋅ 10^5.

Output

For each test case, print a single line containing a single integer: the minimum inconvenience you can achieve by applying the given operation any (possibly zero) number of times.

Example

Input


3
3
1 2 3
4
0 1 1 0
10
8 3 6 11 5 2 1 7 10 4


Output


0
4
21

Note

For the first test case, you can move a car from the 3-rd sub-track to the 1-st sub-track to obtain 0 inconvenience.

For the second test case, moving any car won't decrease the inconvenience of the track.
import java.io.*;
import java.util.*;
public class Codeforces10 {
    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());}

        String nextLine(){
            String str = "";
            try {
                str=br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    
    public static void main(String[] args)throws IOException {
        FastReader sc = new FastReader();
        BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out));
        //t -> test cases;
        int t = sc.nextInt();
        while(t-->0){
            int n = sc.nextInt();
            long s[] = new long[n];
            long sum = 0;
            for(int i=0; i<n; i++){
               s[i] = sc.nextInt();
               sum+=s[i];
            }
            long mod = sum%n;
            long incon = mod*(n-mod);
            output.write(incon+"\n");
        }
        output.flush();
    }
}
