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[] a = new int[n];

		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
		}
		Arrays.sort(a);

		int minsum = Integer.MAX_VALUE;

		for (int i = a[0]; i <= a[n - 1]; i++) {
			int tmpsum = 0;
			for (int j = 0; j < n; j++) {
				tmpsum += Math.abs((a[j] - i) * (a[j] - i));
				//System.out.println("i=" + i + ", j=" + j + ", a[j]=" + a[j] + ", tmpsum=" + tmpsum);
			}
			if (minsum > tmpsum) {
				minsum = tmpsum;
			}
		}

		System.out.print(minsum);

		sc.close();
	}
}