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 stdin =new Scanner(System.in);
		int n=stdin.nextInt();
		int a[]=new int [n];
		int i;
		for(i=0;i<n;i++){
			a[i]=stdin.nextInt();
		}
		int max=-300,min=300;
		for(i=0;i<n;i++){
			if(max<a[i])
				max=a[i];
			if(min>a[i])
				min=a[i];
		}
		int min2=Integer.MAX_VALUE;
		int p=0;
		for(i=min;i<=max;i++){
			p=0;
			for(int j=0;j<n;j++)
				p+=(a[j]-i)*(a[j]-i);

			if(p<min2)
				min2=p;
		}

		System.out.println(min2);
	}
}
