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 = sc.nextInt();
        int[] as = new int[N];
        for (int i = 0; i < N; i++) {
            as[i] = sc.nextInt();
        }
        System.out.println( solve(N, as) );
    }

    private static int solve(int N, int[] as) {
        int min = Integer.MAX_VALUE;

        for (int n = -100; n <= 100; n++) {
            min = Math.min( calc(n, as), min );
        }
        return min;
    }

    private static int calc(int n, int[] as) {
        int cost = 0;
        for (int a : as) {
            int diff = a - n;
            cost += diff * diff;
        }
        return cost;
    }
}