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 {
    public static Scanner sc = new Scanner(System.in);
    public static void main(String[] args) throws Exception {
        int n = sc.nextInt();
        int[] ary = new int[n];
        
        int min = 100;
        int max = -100;
        for (int i = 0; i < n; i++) {
            int a = sc.nextInt();
            ary[i] = a;
            min = Math.min(min, a);
            max = Math.max(max, a);
        }
        
        long res = 4000000;
        for (int i = min; i <= max; i++) {
            long tmp = 0;
            for (int j = 0; j < n; j++) {
                tmp += Math.pow(ary[j]-i, 2);
            }
            res = Math.min(res, tmp);
        }
        
        System.out.println(res);
    }
}
