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 sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] ar = new int[n];
        int total = 0;
        for(int i = 0; i < n; i++){
            ar[i] = sc.nextInt();
            total += ar[i];
        }
        int a = total / n;
        int b = a + 1;
        long costa = 0;
        long costb = 0;
        for(int i = 0; i < n; i++){
                costa += (ar[i] - a) * (ar[i] - a);
                costb += (ar[i] - b) * (ar[i] - b);
        }
        if(costa < costb)
                System.out.println(costa);
        else{
                System.out.println(costb);
        }

    }
}
