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.*;

public class Main {

  public static void main (String[] args) {

    Scanner sc = new Scanner(System.in);
    
    int N = sc.nextInt();
    int[] a = new int[N]; 
    for (int i = 0; i < N; i++) {
      a[i] = sc.nextInt();
    }
 
    sc.close();

    int answer = 2001000;

    for (int i = -100; i <= 100; i++) {
      
      int cost = 0;
      
      for (int j = 0; j < N; j++) {
        cost += Math.pow(Math.abs(i - a[j]),2);
      }

      answer = Math.min(answer, cost);

    }

    System.out.println(answer);

  }

}