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 void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int[] a = new int[N];
        int sum = 0;
        for(int i=0; i<N; i++) {
            a[i] = Integer.parseInt(sc.next());
            sum += a[i];
        }
        double av = (double)sum / (double)N;
        long v = Math.round(av);
        
        long ans = 0;
        for(int i=0; i<N; i++) {
            ans += Math.pow(a[i]-v, 2);
        }
        System.out.println(ans);
    }
}
