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;
  int ans = 0;
  cin >> N;
  float ave = 0;
  vector<int> a(N);
  for(int i = 0; i < N; i++){
    cin >> a.at(i);
    ave += a.at(i);
  }
  ave = round(ave / N);
  
  for(int i = 0; i < N; i++)
    ans += (a.at(i) - ave) * (a.at(i) - ave);
  cout << ans << endl;
}
