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();
    }
    Arrays.sort(a);
    int sum = 0;
    int min = Integer.MAX_VALUE;
    for(int j = a[0];j <= a[n - 1];j++){
      sum = 0;
      for(int i = 0;i < n;i++){
        sum += (j - a[i]) * (j - a[i]);
      }
      if(min > sum){
        min = sum;
      }
    }
    System.out.println(min);
  }
}