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 n = sc.nextInt();
		int[] a = new int[n];
		int b = 0;

		for(int i=0; i<n; i++){
			a[i] = sc.nextInt();
			b += a[i];
		}

		int mid = 0;
		if(b<0){
			mid = (int)((double)b/n - 0.5);
		}else{
			mid = (int)((double)b/n + 0.5);
		}
		int cost = 0;

		for(int i=0; i<n; i++){
			cost += Math.pow(a[i]-mid, 2);
		}

		System.out.println(cost);
	}
}