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 number = sc.nextInt();
		int[] integral=new int[number];
		int sum=0;
		int average=0;
		int ans=0;
		for(int i=0; i<number; i++){
			integral[i]=sc.nextInt();
			sum+=integral[i];
		}
		if(sum%number!=0){
			if(((10*(sum%number))/number)>=5){
				average=(sum/number)+1;
			}else{
				average=sum/number;
			}
		}else{
			average=sum/number;
		}
		for(int i = 0; i<number; i++){
			ans+=(integral[i]-average)*(integral[i]-average);
		}
		System.out.println(ans);
	}
}