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.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		ArrayList<Integer> a = new ArrayList<Integer>();

		int N = scanner.nextInt();
		for (int i = 0 ; i < N ; i++) {
			a.add(scanner.nextInt());
		}
		double average = (double)a.stream().mapToInt(x -> x).sum() / N;

		System.out.println(calc_cost(a, (int)Math.round(average)));

		scanner.close();
	}

	private static int calc_cost(ArrayList<Integer> a, int rewrite_num) {
		return a.stream().map(i -> (int)Math.pow((rewrite_num - i), 2))
				.mapToInt(x -> x)
				.sum();
	}
}
