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 scan = new Scanner(System.in);

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

		int[] cost = new int[201];
		int k = 0;
		for(int i = -100; i <= 100; i++){
			for(int j = 0; j < n; j++){
				cost[k] += (a[j] - i) * (a[j] - i);
			}
			k ++;
		}

		int min = cost[0];
		for(int i = 1; i < 201; i++){
			if(cost[i] < min){
				min = cost[i];
			}
		}
		System.out.println(min);
	}
}
