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];
		}


		int avg = (int) Math.round((double)sum / n);
		/*int closest = -1;
		int closestIndex = -1;
		int dif = sum;
		for (int i = 0; i < n; i++) {
			int curDif = Math.abs(avg - a[i]);
			if (curDif < dif) {
				closest = a[i];
				closestIndex = i;
				dif = curDif;
			}
		}
		*/


		int ans = 0;
		for (int i = 0; i < n; i++) {
			ans += Math.pow(a[i] - avg, 2);
		}

		System.out.println(ans);
	}
}