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;

public class Main {

	public static void main(String[] args) {
		try (Scanner s = new Scanner(System.in)) {
			int n = s.nextInt();
			int[] array = new int[n];
			for (int i = 0; i < n; i++) {
				array[i] = s.nextInt();
			}
			Arrays.sort(array);
			int start = array[0];
			int end = array[n - 1];
			int min = Integer.MAX_VALUE;
			for (int i = start; i <= end; i++) {
				int sum = 0;
				for (int j = 0; j < n; j++) {
					sum += pow2(array[j] - i);
				}
				if (min > sum) {
					min = sum;
				}
			}
			System.out.println(min);
		}
	}
	private static int pow2(int x) {
		return x * x;
	}
}
