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.BufferedReader;
import java.util.StringTokenizer;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.PrintWriter;
public class B {


   

    public static void main(String[] args) {
        
        FastReader fr = new FastReader();
        PrintWriter out = new PrintWriter(System.out, true);
        int cases = fr.nextInt();
        for(int c = 0; c < cases; c++) {
            int size = fr.nextInt();
            long total = 0;
            for(int i = 0; i < size; i++) {
                total += fr.nextLong();
            }
            if(total % size == 0) {
                out.write("0\n");
            } else{
                long up = total/size+1;
                
                if (up == 1) {
                    out.write((size - total)*(size - (size - total)) + "\n");
                } else {
                    long num = ((up*size) - total);
                    out.write(((size-num) * num) + "\n");
                }
            }
            
        }
        out.close();
    }

    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            this.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;
        }
    }
}
