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

    }
}
