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) {
		@SuppressWarnings("resource")
		Scanner scan = new Scanner(System.in);

		int N = scan.nextInt();
		int a[] = new int[N];
		int max = 0;
		int min = 0;
		for (int i = 0; i < N; i++) {
			switch (i) {
			case 0:
				a[i] = scan.nextInt();
				min = a[i];
				max = a[i];
				break;
			default:
				a[i] = scan.nextInt();
				if (max < a[i]) {
					max = a[i];
				} else if (min > a[i]) {
					min = a[i];
				}
				break;
			}
		}
		int minCost = 0;
		for (int i = min; i <= max; i++) {
			int cost = 0;
			for (int j = 0; j < N; j++) {
				int dis = a[j] - i;
				cost += dis * dis;
			}
			if (i == min) {
				minCost = cost;
			} else {
				if (minCost > cost) {
					minCost = cost;
				}
			}
		}
		System.out.println(minCost);
	}

}
