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.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        int[] ary = new int[n];
        int sum = 0;
        int ans = 0;
        for (int i = 0; i < n; i++) {
            int a = Integer.parseInt(sc.next());
            sum += a;
            ary[i] = a;
        }
        sum = (int) Math.round(sum / (n * 1.0));
        for (int i = 0; i < n; i++) {
            ans += Math.pow(sum - ary[i], 2);
        }
        System.out.println(ans);
    }
}