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.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        int num[] = new int[n];
        int total = 0;
        for (int i = 0; i < n; i++) {
            int m = sc.nextInt();
            num[i] = m;
            total += m;
        }

        int average = total / n;

        int ans1 = 0, ans2 = 0;
        for (int i = 0; i < n; i++) {
            if(num[i] != average) {
                ans1 += Math.pow(num[i] - average, 2);
            }
            if(num[i] != (average + 1)) {
                ans2 += Math.pow(num[i] - (average + 1), 2);
            }
        }

        System.out.println(Math.min(ans1, ans2));
    }
}