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;
import java.util.List;
import java.util.ArrayList;

public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);

        int N = scan.nextInt();
        if ( N<1 || N>100) {
            System.exit(-1);
        }
        int sum = 0;
        List<Integer> nums = new ArrayList<Integer>();
        for(int i=0; i<N; i++) {
            int num = scan.nextInt();
            if ( num < -100 || num > 100) {
                System.exit(-2);
            }
            nums.add(new Integer(num));
            sum += num;
        }
        int avg = Math.round((float)sum/N);
        int cost = 0;
        for (Integer num: nums) {
            cost += Math.pow(num.intValue() - avg, 2);
        }

        System.out.println(cost);
    }
}