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.ArrayList;
public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        ArrayList<Integer> a = new ArrayList<Integer>();
        for(int i = 0;i < N;i++){
            a.add(sc.nextInt());
        }
        long min = 100000000;
        for(int y = -100;y <= 100;y++){
            long sum = 0;
            for(int i = 0;i < N;i++){
                sum += (a.get(i) - y)*(a.get(i) - y);
            }
            min = Math.min(min,sum);
        }
        System.out.println(min);
    }
}
