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
import java.util.*;
public class Main {

    public static void main(String __[]) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[N];
        int equal_checker = 1;
        double total = 0;
        int total_cost = 0;
        for(int x = 0; x<N; x++){
            a[x]= sc.nextInt();
            total += a[x];
        }


            double equal_integer = (Math.round(total / N));
            for(int y : a){
                total_cost += Math.pow((y- equal_integer),2);
            }
            System.out.println(total_cost);

    }
}
