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 {

    Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        new Main().run();
    }

    void run() {

        int n = sc.nextInt();
        int[] arr = new int[n];
        for (int i=0; i<n; i++) arr[i] = sc.nextInt();
        Arrays.sort(arr);

        int res = Integer.MAX_VALUE;

        for (int i=arr[0]; i<=arr[arr.length-1]; i++) {
            int tmp = 0;
            for (int j=0; j<arr.length; j++) {
                tmp += (int)Math.pow(i - arr[j], 2);
            }
            res = Math.min(res, tmp);
        }

        System.out.println(res);


    }

}

