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.*;

class Main {
        public static void main(String args[]) {
                int N;
                int[] A;
                try (Scanner sc = new Scanner(System.in)) {
                        N = sc.nextInt();
                        A = new int[N];
                        for (int i = 0; i < N; i++) {
                                A[i] = sc.nextInt();
                        }
                } catch (Exception e) {
                        return;
                }
                long ans  = 1L << 60;
                for (int j = -100; j <= 100; j++) {
                        int memo = 0;
                        for (int i = 0; i < N; i++) {
                                memo += (A[i] - j) * (A[i] - j);
                        }
                        ans = Math.min(memo, ans);
                }
                System.out.println(ans);
        }
}