Evi has N integers a_1,a_2,..,a_N. His objective is to have N equal integers by transforming some of them.

He may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i≠j), he has to pay the cost separately for transforming each of them (See Sample 2).

Find the minimum total cost to achieve his objective.

Constraints

* 1≦N≦100
* -100≦a_i≦100

Input

The input is given from Standard Input in the following format:


N
a_1 a_2 ... a_N


Output

Print the minimum total cost to achieve Evi's objective.

Examples

Input

2
4 8


Output

8


Input

3
1 1 3


Output

3


Input

3
4 2 5


Output

5


Input

4
-100 -100 -100 -100


Output

0
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n,m) for(int i=(n);i<(m);i++)
int main(){
  int N;
  cin>>N;
  int A[N];
  rep(i,0,N) cin>>A[i];
  int ans;
  sort(A,A+N);
  rep(i,A[0],A[N-1]+1){
    int cost=0;
    rep(j,0,N) cost+=(A[j]-i)*(A[j]-i);
    if(i==A[0]) ans=cost;
    else if(cost<ans) ans=cost;
  }
  cout<<ans<<endl;   
}