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<iostream>
#include<algorithm>


using namespace std;

int main(){
    int n,a[100],ans = 99999999;
    cin >> n;
    for(int i=0;i<n;i++)cin >> a[i];
    for(int i=-100;i<=100;i++){
        int sum=0;
        for(int j=0;j<n;j++){
            sum += (a[j]-i)*(a[j]-i);
        }
        ans = min(ans,sum);
    }
    cout << ans << endl;
}