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, i, j;
  int mn=10000000;
  cin>>N;
  vector<int> a(N);
  
  for(i=0; i<N; i++) cin>>a[i];
  
  for(i=-100; i<=100; i++){
    int Sum=0;
    for(j=0; j<N; j++){
      Sum+=pow(i-a[j], 2);
    }
    mn=min(Sum, mn);
  }
  cout<<mn<<endl;
  return 0;
}