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.
  /*  Karmanye vadhikaraste Ma Phaleshu Kadachana | Ma Karmaphalaheturbhurma Te Sangostvakarmani ||*/
//----------------------------------------------------------------------------------------------------------------//

/* this is begining have to survive more and go through long journey*/ 
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#include<bits/stdc++.h>
using namespace std;
#define pb push_back
#define vi vector<int>
#define vii vector<vi>
#define vll vector<long long>
#define mx(v) *max_element(v.begin(),v.end())
#define mn(v) *min_element(v.begin(),v.end())
#define st(v) sort(v.begin(),v.end())
#define bg .begin()
#define ed .end()
#define fi first
#define sc second
#define fr(i,l,u) for(i=l;i<u;i++)
#define rfr(i,l,u) for(i=l;i>u;i--)
#define ll long long int
#define lld long long double
#define uld unsigned long long int
#define pii pair<int,int>
#define flash ios_base::sync_with_stdio(0);cin.tie(NULL);
#define mod 1000000007
 
 void solve()
{
    ll n,i,x,sum=0,rem=0;
    cin>>n;
    vi v;
    fr(i,0,n)
    {
        cin>>x;
        sum+=x;
    }
    rem=sum%n;
    cout<<(n-rem)*rem<<endl;
    
    
}      
int main()
{
     int t;
   cin>>t;
   while(t--) solve();

}