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) {
    final Scanner scanner = new Scanner(System.in);

    scanner.nextLine();
    final int[] n = Arrays.stream(scanner.nextLine().split(" "))
        .mapToInt(Integer::parseInt)
        .toArray();

    final int x = Arrays.stream(n).sum() / n.length;

    int cost0 = 0;
    int cost1 = 0;
    for (int i = 0; i < n.length; i++) {
      cost0 += (n[i] - x) * (n[i] - x);
      cost1 += (n[i] - (x + 1)) * (n[i] - (x + 1));
    }

    System.out.println(Math.min(cost0, cost1));
  }
}