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.*;
import java.util.stream.Collectors;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int min = Integer.MAX_VALUE;
    int max = 0;
    int ans = Integer.MAX_VALUE;
    ArrayList<Integer> list = new ArrayList<Integer>();
    for (int i = 0; i < N; i++) {
      list.add(sc.nextInt());
      min = Math.min(min, list.get(i));
      max = Math.max(max, list.get(i));
    }
    for (int i = min; i <= max; i++) {
      int total = 0;
      for (int j = 0; j < N; j++) {
        total += Math.pow(i - list.get(j), 2);
      }
      ans = Math.min(ans, total);
    }
    System.out.println(ans);
  }
}
