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.*;
public class Main{
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

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

        int[] nextArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }
        long[] nextArray(long n) {
            long[] a = new long[(int) n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
    static class FastWriter extends PrintWriter {
        FastWriter(){
            super(System.out);
        }
        void println(int[] array) {
            for(int i=0; i<array.length; i++) {
                print(array[i]+" ");
            }
            println();
        }
        void println(long [] array) {
            for(int i=0; i<array.length; i++) {
                print(array[i]+" ");
            }
            println();
        }
    }
    static int MOD=998244353;
    public static void main(String[] args){
        FastScanner in = new FastScanner();
        FastWriter out = new FastWriter();
        int t=in.nextInt();
        //int t=1;
        while (t-->0){
            int n=in.nextInt();
            int[] ar=in.nextArray(n);
            long total=0L;
            for (int i = 0; i < n; i++) {
                total+=ar[i];
            }
            long rem=total%n;
            out.println(rem*(long)(n-rem));
        }
        out.close();
    }
    //Arrays.sort(a, (o1, o2) -> (o1[0] - o2[0]));
    static int subarray_lessthan_k(int[] A,int n,int k){
        int s=0,e=0,sum=0,cnt=0;
        while(e<n){
            sum+=A[e];
            while(s<=e&&sum>k){
                sum-=A[s++];
            }
            cnt+=e-s+1;
            e++;
        }
        return cnt;
    }
    static int totalPrimeFactors(int n) {
        int cnt=0;
        while (n%2==0) {
            cnt++;
            n /= 2;
        }
        int num= (int) Math.sqrt(n);
        for (int i = 3; i <= num; i+= 2) {
            while (n%i == 0) {
                cnt++;
                n /= i;
                num=(int)Math.sqrt(n);
            }
        }
        if (n > 2){
            cnt++;
        }
        return cnt;
    }
    static char get(int i){
        return (char)(i+'a');
    }
    static boolean distinct(int num){
        HashSet<Integer> set=new HashSet<>();
        int len=String.valueOf(num).length();
        while (num!=0){
            set.add(num%10);
            num/=10;
        }
        return set.size()==len;
    }
    static int maxSubArraySum(int a[],int st,int en) {
        int max_s = Integer.MIN_VALUE, max_e = 0,ind=0,ind1=1;
        for (int i = st; i <= en; i++) {
            max_e+= a[i];
            if (max_s < max_e){
                max_s = max_e;
                ind=ind1;
            }
            if (max_e < 0){
                max_e = 0;
                ind1=i+1;
            }
        }
        if(st==0){
            return max_s;
        }
        if(ind==1){
            return a[0]+2*max_s;
        }else {
            return 2*max_s+maxSubArraySum(a,0,ind-1);
        }
        //return max_s;
    }
    static void segmentedSieve(ArrayList<Integer> res,int low, int high) {
        if(low < 2){
            low = 2;
        }
        ArrayList<Integer> prime = new ArrayList<>();
        simpleSieve(high, prime);
        boolean[] mark = new boolean[high - low + 1];
        for (int i = 0; i < mark.length; i++){
            mark[i] = true;
        }
        for (int i = 0; i < prime.size(); i++) {
            int loLim = (low / prime.get(i)) * prime.get(i);
            if (loLim < low){
                loLim += prime.get(i);
            }
            if (loLim == prime.get(i)){
                loLim += prime.get(i);
            }
            for (int j = loLim; j <= high; j += prime.get(i)) {
                mark[j - low] = false;
            }
        }
        for (int i = low; i <= high; i++) {
            if (mark[i - low]){
                res.add(i);
            }
        }
    }
    static void simpleSieve(int limit, ArrayList<Integer> prime) {
        int bound = (int)Math.sqrt(limit);
        boolean[] mark = new boolean[bound + 1];
        for (int i = 0; i <= bound; i++){
            mark[i] = true;
        }
        for (int i = 2; i * i <= bound; i++) {
            if (mark[i]) {
                for (int j = i * i; j <= bound; j += i){
                    mark[j] = false;
                }
            }
        }
        for (int i = 2; i <= bound; i++) {
            if (mark[i]){
                prime.add(i);
            }
        }
    }
    static int highestPowerOf2(int n) {
        if (n < 1){ return 0; }
        int res = 1;
        for (int i = 0; i < 8 * Integer.BYTES; i++) {
            int curr = 1 << i;
            if (curr > n){ break; }
            res = curr;
        }
        return res;
    }
    static int reduceFraction(int x, int y) {
        int d= gcd(x, y);
        return x/d+y/d;
    }
    static boolean subset(int[] ar,int n,int sum){
        if(sum==0){
            return true;
        }
        if(n<0||sum<0){
            return false;
        }
        return subset(ar,n-1,sum)||subset(ar,n-1,sum-ar[n]);
    }
    static boolean isPrime(int n){
        if(n<=1) return false;
        for(int i = 2;i<=Math.sqrt(n);i++){
            if (n % i == 0) return false;
        }
        return true;
    }
    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }
    static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }
    static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }
    static boolean isPowerOfTwo(long n) {
        if(n==0){
            return false;
        }
        while (n%2==0){
            n/=2;
        }
        return n==1;
    }
    static boolean isPerfectSquare(int x){
        if (x >= 0) {
            int sr = (int)Math.sqrt(x);
            return ((sr * sr) == x);
        }
        return false;
    }
    static int lower_bound(int[] arr, int x) {
        int low_limit = 0, high_limit = arr.length, mid;
        while (low_limit < high_limit) {
            mid = (low_limit + high_limit) / 2;
            if (arr[mid] >= x){
                high_limit = mid;
            }else{
                low_limit = mid + 1;
            }
        }
        return low_limit;
    }
    static int upper_bound(int[] arr, int x) {
        int low_limit = 0, high_limit = arr.length, mid;
        while (low_limit < high_limit) {
            mid = (low_limit + high_limit) / 2;
            if (arr[mid] > x){
                high_limit = mid;
            }else{
                low_limit = mid + 1;
            }
        }
        return low_limit;
    }
    static int binarySearch(int[] ar,int n,int num){
        int low=0,high=n-1;
        while (low<=high){
            int mid=(low+high)/2;
            if(ar[mid]==num){
                return mid;
            }else if(ar[mid]>num){
                high=mid-1;
            }else {
                low=mid+1;
            }
        }
        return -1;
    }
    static int fib(int n) {
        long F[][] = new long[][]{{1,1},{1,0}};
        if (n == 0){
            return 0;
        }
        power(F, n-1);
        return (int)F[0][0];
    }
    static void multiply(long F[][], long M[][]) {
        long x =  (F[0][0]*M[0][0])%1000000007 + (F[0][1]*M[1][0])%1000000007;
        long y =  (F[0][0]*M[0][1])%1000000007 + (F[0][1]*M[1][1])%1000000007;
        long z =  (F[1][0]*M[0][0])%1000000007 + (F[1][1]*M[1][0])%1000000007;
        long w =  (F[1][0]*M[0][1])%1000000007 + (F[1][1]*M[1][1])%1000000007;
        F[0][0] = x%1000000007;
        F[0][1] = y%1000000007;
        F[1][0] = z%1000000007;
        F[1][1] = w%1000000007;
    }
    static void power(long F[][], int n) {
        if( n == 0 || n == 1){
            return;
        }
        long M[][] = new long[][]{{1,1},{1,0}};
        power(F, n/2);
        multiply(F, F);
        if (n%2 != 0){
            multiply(F, M);
        }
    }
}