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 scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = scan.nextInt();
		}
		int[] cost = new int[210];
		for (int j = -100; j <= 100; j++) {
			for (int i = 0; i < n; i++) {
				cost[j+100] += Math.pow(a[i]-j, 2);
			}
		}
		final int INF = Integer.MAX_VALUE / 10;
		int min = INF;
		for (int i = 0; i < 201; i++) {
					if (cost[i] < min) {
						min = cost[i];
					}
				}
		System.out.println(min);
	}
}
