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 scanner = new Scanner(System.in);
		int n = Integer.parseInt(scanner.nextLine());
		String[] inputs = scanner.nextLine().split(" ");
		int[] nums = new int[inputs.length];
		for (int i = 0; i < inputs.length; i++) {
			nums[i] = Integer.parseInt(inputs[i]) + 100;
		}
		int ave = (int) ((double) Arrays.stream(nums).sum() / n + 0.5d);
		int sum = 0;
		for (int num: nums) {
			sum += (num - ave) * (num - ave);
		}
		System.out.println(sum);
	}
}
