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.*;
import java.util.stream.*;

public class Main
{
  public static void main(String[] args)
  {
    Scanner sc = new Scanner(System.in);
    String line = sc.nextLine();
    int nums_cnt = Integer.parseInt(line);
    line = sc.nextLine();
    int[] numbers_ary = Stream.of(line.split(" ")).mapToInt(Integer::parseInt).toArray();
    
    int sum = Arrays.stream(numbers_ary).sum();
    
    int value = (int)(Math.round((double)sum / nums_cnt));
    sum = 0;
    for(int i : numbers_ary)
    {
      sum += (int)Math.pow((i - value),2);
    }
    
    System.out.println(sum);
    
  }
}