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.Arrays;
import java.util.Scanner;


public class Main {
    
    public static void main(String[] args) {
 
       Scanner sc = new Scanner(System.in);

       int N = sc.nextInt();
       
       int a[] = new int[N];
       
       for(int i = 0 ; i < N;i++){
           a[i] = sc.nextInt();           
       }
                     
       int min = Integer.MAX_VALUE;
               
       for(int i = -100; i <= 100;i++){
          int sum = 0;
          for(int j = 0 ;j < N;j++){
              sum+= (a[j]-i)*(a[j]-i);
          }          
          min = Math.min(min,sum);
       }
              
       System.out.println(min);
       
    }      
}