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.lang.*;
 
public class Main {
  public static void main(String[] args){
    
    Scanner sc = new Scanner(System.in);
    int x = sc.nextInt();
    
    int a[ ] = new int[x]; 
    
    for(int i=0; i<x; i++){
      a[i] =  sc.nextInt();
    }
    
    int min = Integer.MAX_VALUE;
    
    for(int j = -100; j <=100; j++) {
      
      int sum  = 0;

      for(int k=0; k<x; k++){
        sum = sum + (int)Math.pow(a[k]-j, 2);
      }
      
      if(sum<min){
        min = sum;
      }
    }
    
    System.out.println(min);
  }
}