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.*;

class Main
{
	public static void main ( String[] args )
	{
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		ArrayList<Integer> a = new ArrayList();

		for( int i = 0; i < N; ++i ) a.add(sc.nextInt());

		int ans = 1 << 30;
		for( int i = -100; i <= 100; ++i ){
			int tmp = 0;
			for( int j = 0; j < N; ++j ){
				tmp += (a.get(j)-i)*(a.get(j)-i);
			}
			ans = Math.min(tmp, ans);
		}
		System.out.println(ans);
	}
}
