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;

class Main{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);

		int kosu=sc.nextInt();
		int ave=0;
		int kst=0;
		int kag=0;
		int sum=0;
		int wa=0;
		int[] aa=new int[kosu];
		for(int i=0; i<kosu; i++) {
			aa[i]=sc.nextInt();
			sum+=aa[i];
		}

		if(sum%kosu==0) {
			ave=sum/kosu;
		}
		else {
			kst=sum/kosu;
			kag=(sum+kosu-1)/kosu;
			if(kag*kosu-sum>=sum-kst*kosu) {
				ave=kst;
			}
			else {
				ave=kag;
			}
		}

		for(int i=0; i<kosu; i++) {
			wa+=(aa[i]-ave)*(aa[i]-ave);
		}
		System.out.println(wa);
	}
}