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.List;
import java.util.Scanner;

class Main {
	@SuppressWarnings("resource")
	public static void main(String args[]) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		List<Integer> list = new ArrayList<>();
		int sumA = 0;

		for (int i = 0; i < n; i++) {
			list.add(scanner.nextInt());
			sumA += list.get(i);
		}

		int ans = 0;
		int harf = (int) Math.round( (double) sumA / list.size()) ;;
			for (int i : list) {
				ans += (i - harf) * (i - harf);
			}
		

		System.out.println(ans);
	}
}