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 int
#define pb push_back
#define vec vector<ll>
#define vpl vector<pair<ll,ll>>
#define vvl vector<vector<ll>>
#define fio ios_base::sync_with_stdio(false)
#define fo(i,n) for(ll i=0;i<n;i++)
#define forv(i,n,N) for(ll i=n;i<N;i++)
#define ford(i,n,N) for(ll i=n;i>=N;i--)
#define fin cin.tie(NULL)
#define fou cout.tie(NULL)
#define mp make_pair
#define F first
#define S second
#define endl "\n"
#define simsort(v) sort(v.begin(),v.end())
#define simsortd(a) sort(a.begin(),a.end(),greater<int>())
#define mod 1000000007

void solve()
{ ll sum=0;
 ll n;cin>>n;vec a(n);fo(i,n){cin>>a[i];sum+=a[i];}
 simsort(a);
 ll cnt=0;
 ll s=sum/n,m=sum%n;ll i=0;
 fo(i,n){if(m>0)a[i]=1;else{a[i]=0;}m--;}
 fo(i,n){
     cnt+=a[n-1-i]*(n-1-i)-a[n-1-i]*i;
 }
 cout<<abs(cnt-0)<<endl;
} 

int main()
{ 
    fio,fin,fou;
   
   ll t=1;
   cin>>t;
  
   for(ll i=1;i<=t;i++)
   {
       solve();
    
   }
}
     