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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int N = Integer.parseInt(br.readLine());
		String[] n = br.readLine().split(" ");
		Integer[] num = new Integer[N];

		double sum = 0;

		for (int i = 0; i < N; i++) {
			n.toString().split(" ");
			num[i] = Integer.parseInt(n[i]);
			sum += num[i];
		}

		for (int i = 0; i < N; i++) {
		}

		double ave = Math.round(sum / N);

		int cost = 0;

		for (int i = 0; i < N; i++) {
			cost +=  Math.pow((num[i] - ave), 2);
		}
		System.out.println(cost);

	}

}
