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.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int numbers = sc.nextInt();
		int[] values = new int[numbers];
		int sum = 0;
		for (int i = 0; i < numbers; i++) {
			values[i] = sc.nextInt();
			sum += values[i];
		}
		
		// finding the average
		int averageCeil = (int) Math.ceil(sum * 1.0/numbers);
		int averageFloor = (int) Math.floor(sum * 1.0/numbers);
		
		// computing the cost
		int totalcostceil = 0; 
		int totalcostfloor = 0;
		for (int i = 0; i < numbers; i++) {
			int ceil = (values[i] - averageCeil) * (values[i] - averageCeil);
			int floor = (values[i] - averageFloor) * (values[i] - averageFloor);
			totalcostceil += ceil;
			totalcostfloor += floor;
		}
		System.out.println(Math.min(totalcostceil, totalcostfloor));
	}
}
