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.Scanner;

public class Main {
  static final int INF = Integer.MAX_VALUE / 2;
  static int n;
  static int[] a;

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    n = sc.nextInt();
    a = new int[n];
    for(int i = 0; i < n; i++){
      a[i] = sc.nextInt();
    }

    int min = INF;
    for(int i = -100; i <= 100; i++){
      int sum = 0;
      for(int j = 0; j < n; j++){
        sum += (a[j] - i) * (a[j] - i);
      }
      min = Math.min(min, sum);
    }

    System.out.println(min);
  }
}