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
//package AtCoder;
import java.util.*;
public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int[] a=new int[n];
		int s=0;
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextInt();
			s=s+a[i];
		}
		s=(s/n)+((s%n==0)?0:1);
		int n1=s;
		int n2=s-1;
		int cost1=0,cost2=0;
		for(int i=0;i<n;i++)
		{
			cost1=cost1+(int)Math.pow((n1-a[i]),2);
			cost2=cost2+(int)Math.pow((n2-a[i]),2);
			
		}
		int cost=Math.min(cost1, cost2);
		System.out.println(cost);

	}

}
