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.
//package com.company;/* package codechef; // don't place package name! */
import java.util.*;
import java.lang.*;
import java.io.*;
public class Solution{
//public class Main {
    public static boolean check = false;
    public static int aa =0;
    public static Set<Long> set = new HashSet<>();
    public static Map<Long, Integer> m = new HashMap<>();
    public static void hehe(long n, long a, long b){
        //System.out.println("Size"+m.size());
        if(n==1){
            //System.out.println("Yes");
            check = true;
            return;
        }
        if(n%a!=0 && n<=b) return;
        if(n%a==0 && !set.contains(n%a)&&a!=1){
            if(check) return;
            hehe(n/a, a, b);
            set.add(n%a);
        }
        if(n>b && !set.contains(n-b)){
            if(check) return;
            hehe(n-b, a,b);
            set.add(n-b);
        }
    }
    public  static void generate(long a, long b, long find, long from){
        System.out.println(from);
        if(a!=1) {
            if (find == a * from) {
                check = true;
                return;
            } else if (find < a * from) {
                return;
            } else {
                generate(a, b, find, a * from);
            }
        }
        if(find == b+from) {
            check = true;
        }
        else if(find <b+from){
            check = true;
            return;
        }
        else {
            generate(a, b, find, b+from);
        }
    }
    public static void main (String[] args) throws java.lang.Exception {
        FastReader sc = new FastReader();
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int testCase = sc.nextInt();
        while (testCase-- > 0) {
            int n = sc.nextInt();
            long[] longArr = new long[n];
            long sum=0;
            for(int i=0; i<n; i++){
                longArr[i] = sc.nextLong();
                sum+=longArr[i];
            }
            long rem = sum - ((n)*(sum/n));
            long emp = n-rem;
            System.out.println(rem*emp);

        }
    }
    // Fast Reader Class
    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; }
    }
}
