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.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class _1543_B {

    private static final FastScanner in = new FastScanner();
    private static final PrintWriter out = new PrintWriter(System.out);
    private static final PrintWriter err = new PrintWriter(System.err);

    public static void solve() {
        int n = in.nextInt();
        int[] cars = in.nextIntArray(n);
        long sum = 0;
        for (int c : cars) {
            sum += c;
            sum %= n;
        }

        out.println(sum * (n - sum));
    }

    // Boilerplate
    public static void main(String[] args) {
        int t = in.nextInt();
        while (t-- > 0) {
            solve();
        }

        err.close();
        out.close();
    }

    @SuppressWarnings("unused")
    static class FastScanner {

        StringTokenizer tok = new StringTokenizer("");
        BufferedReader in;

        FastScanner() {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (!tok.hasMoreElements()) {
                try {
                    tok = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tok.nextToken();
        }

        String nextLine() {
            String line;
            try {
                line = in.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

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

        List<Integer> nextIntegerList(int n) {
            ArrayList<Integer> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextInt());
            }
            return list;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

        List<Long> nextLongList(int n) {
            ArrayList<Long> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextLong());
            }
            return list;
        }

        ArrayList<Integer>[] nextGraph(int n, int m) {
            @SuppressWarnings("unchecked")
            ArrayList<Integer>[] adj = (ArrayList<Integer>[]) new ArrayList[n];

            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }

            for (int i = 0; i < m; i++) {
                int v = nextInt();
                int t = nextInt();
                adj[v - 1].add(t - 1);
                adj[t - 1].add(v - 1);
            }

            return adj;
        }
    }
}