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) throws Exception{
		
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		double[] x = new double[n];
		double sum = 0;
		long ave;
		
		for(int i=0; i<n; i++){
			x[i] = sc.nextDouble();
			sum += x[i];
		}
		
		ave = Math.round(sum / n);
		
		int ans = 0;
		for(int i=0; i<n; i++){
			ans += Math.pow(x[i]-ave, 2);
		}
		
		System.out.println(ans);
		

		sc.close();
	}
}
