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;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = Integer.parseInt(sc.next());
    int[] numbers = new int[n];
    
    int ave_1 = 0;
    int ave_2 = 0;
    for(int i=0; i<n; i++){
      numbers[i] = Integer.parseInt(sc.next());
      ave_1 += numbers[i];
      ave_2 += numbers[i];
    }
    ave_1 /= n;
    ave_2 /= n;
    ave_2++;
    
    int judge_1 = 0;
    int judge_2 = 0;
    for(int j=0; j<n; j++){
      judge_1 += (numbers[j]-(ave_1))*(numbers[j]-(ave_1));
      judge_2 += (numbers[j]-(ave_2))*(numbers[j]-(ave_2));
    }
    
    System.out.println(Math.min(judge_1, judge_2));
  }
}