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.io.BufferedReader;
import java.io.InputStreamReader;

class Main{
  public static void main(String[] args) throws Exception{
    BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    int n = Integer.parseInt(bf.readLine());
    String[] list = bf.readLine().split(" ");

    float sum = 0;
    for (String s : list){
      sum = sum + Integer.parseInt(s);
    }

    int num = Math.round(sum / n);

    int ans = 0;

    for (String s : list){
      ans = ans + (Integer.parseInt(s) - num) * (Integer.parseInt(s) - num);
    }
    System.out.println(ans);
    bf.close();
  }
}