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;

/**
 * https://abc043.contest.atcoder.jp/tasks/arc059_a
 */
public class Main {

	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] a = new int[N];
		for(int i=0; i<N; i++) a[i] = sc.nextInt();
		sc.close();
		
		int ans = Integer.MAX_VALUE;
		for(int i=-100; i<=100; i++){
			int cost = 0;
			for(int j=0; j<N; j++){
				cost += (i-a[j])*(i-a[j]);
			}
			ans = Math.min(ans, cost);
		}
		
		System.out.println(ans);

	}

}