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 main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[]a = new int[N];
		int sum = 0;
		for(int i = 0; i < N; i++) {
			a[i] = sc.nextInt();
			sum += a[i];
		}
		sc.close();
		int x = sum / N;
		int ans1 = 0;
		int ans2 = 0;
		for(int i = 0; i < N; i++) {
			int t1 = x - a[i];
			int t2 = x + 1 - a[i];
			ans1 += t1 * t1;
			ans2 += t2 * t2;
		}
		System.out.println(Math.min(ans1, ans2));
	}
}