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 scan = new Scanner(System.in);
        int N = scan.nextInt();
        int[] nums = new int[N];

        for(int i=0; i<N ;i++){
            nums[i] = scan.nextInt();
        }

        int min = Integer.MAX_VALUE;
        for(int i=-100;i<=100;i++){
            int sumSquare = 0;
            for(int j=0;j<N;j++){
                sumSquare +=  (nums[j] - i) * (nums[j] - i);
            }

            if(sumSquare < min){
                min = sumSquare;
            }
        }

        System.out.println(min);
    }
}