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.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

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

        int N = sc.nextInt();
        int[] a = new int[N];
        for (int i = 0; i < a.length; ++i) {
            a[i] = sc.nextInt();
        }

        System.out.println(solve(a));

        sc.close();
    }

    static int solve(int[] a) {
        return IntStream.rangeClosed(Arrays.stream(a).min().getAsInt(), Arrays.stream(a).max().getAsInt())
                .map(x -> Arrays.stream(a).map(ai -> (ai - x) * (ai - x)).sum()).min().getAsInt();
    }
}