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 debug(String str) {
        System.out.println(str);
    }

    public static void main(String[] args) {

        int N;

        long[] A;


        try (Scanner sc = new Scanner(System.in)) {
            N = sc.nextInt();
            A = new long[N];
            for (int i = 0; i < A.length; i++) {
                A[i] = sc.nextLong();

            }

        }
        long result = 0;
        long sum = 0;
        for (int i = 0; i < A.length; i++) {
            sum += A[i];
        }
        long average = Math.round((double)sum / N);
        for (int i = 0; i < A.length; i++) {
            result += (average - A[i]) * (average - A[i]);
        }

        System.out.println(result);
    }


}
