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;
int main(){
  int n;
  cin >> n;
  vector<int> a(n);
  int sum=0,ave1,ave2,s=0,t=0;
  for(int i=0;i<n;i++){
    cin >> a[i];
    sum+=a[i];
  }
  ave1=sum/n;
  ave2=(sum+n-1)/n;
  for(int i=0;i<n;i++){
    s+=(a[i]-ave1)*(a[i]-ave1);
    t+=(a[i]-ave2)*(a[i]-ave2);
  }
  cout << min(s,t) << endl;
}