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 N = Integer.parseInt(sc.nextLine());
    String[] S = sc.nextLine().split(" ");
    
    int[] nums = new int[N];
    int sum = 0;
    for(int i = 0; i < N; i++){
      nums[i] = Integer.parseInt(S[i]);
      sum += nums[i];
    }
    
    double a = (double)sum / N;
    int n = (int)Math.round(a);
    
    int ans = 0;
    for(int i = 0; i < N; i++){
      ans += ((nums[i] - n) * (nums[i] - n));
    }
    System.out.println(ans);
  }
}