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.
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define FOR(i, j, k, in) for (int i=j; i<k; i+=in)
#define RFOR(i, j, k, in) for (int i=j; i>=k; i-=in)

#define F(i, n) FOR(i, 0, n, 1)
#define MP make_pair
#define PB push_back

typedef pair<int, int> PII;
typedef vector<int> VI;
typedef vector<string> VS;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef map<int,int> MPII;
typedef set<int> SETI;
typedef multiset<int> MSETI;
typedef queue<int> QI;
typedef stack<int> SI;

const int MAX_N = 1e5 + 1;
const ll MOD = 1e9 + 7;
const ll INF = 1e9;

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    ll t;
    cin >> t;
    while(t--) {
        ll n;
        cin >> n;
        ll sum = 0;
        F(i, n){
            ll temp;
            cin >> temp;
            sum+=temp;
        }
        ll v = sum % n;
        ll ans = v * (n-v);
        cout << ans << endl;
    }
}
