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];
      int sum = 0;
      int k = 0;
      int sum2 = 0;
      for(int i = 0;i < n;i++){
        a[i]=sc.nextInt();
        sum += a[i];
        sum2 += a[i]*a[i];
      }
      if((double)sum/n-sum/n >= sum/n+1-(double)sum/n)k = sum/n+1;
      else k=sum/n;
      System.out.println(n*k*k-2*k*sum+sum2);
    }
}