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.util.*;
import java.io.*;
import javafx.util.Pair;
 
public class One {
 
    static BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    static StringBuilder out = new StringBuilder();
    static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
    static PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));
 
    static int I(String s) {
        return Integer.parseInt(s);
    }
 
    static long L(String s) {
        return Long.parseLong(s);
    }
 
    static double D(String s) {
        return Double.parseDouble(s);
    }
 
    static String[] SA() throws IOException {
        return bf.readLine().split(" ");
    }
 
    public static void main(String[] args) throws IOException {
        int t = I(bf.readLine());
        while (t-- > 0) {
               long n = I(bf.readLine());
            StringTokenizer in = new StringTokenizer(bf.readLine());
           long x=0l;
           for(int i=0;i<n;i++){
           x+=L(in.nextToken());
           }
          long mod=x%n;
           
             out.append(mod*(n-mod)+"\n");
        }
        System.out.println(out);
 
    }
 
}