Problem Statement 
 A derangement of n numbers is a permutation of those numbers in which none of the numbers appears in its original place. For example, the numbers {1,2,3} can be deranged into {2,3,1} and {3,1,2}. We can modify this slightly for n numbers that are not necessarily distinct by saying that no number in the derangement can be in the place that a number of the same value was in in the original ordering. So the numbers {1,1,2,2,3} could be deranged into {2,2,1,3,1}, {2,2,3,1,1}, {2,3,1,1,2}, and {3,2,1,1,2}. Create a class Deranged with a function numDerangements that takes a int[] nums and return the number of derangements of nums. 

Definition 
 Class:  Deranged  Method:  numDerangements  Parameters:  int[]  Returns:  long  Method signature:  long numDerangements(int[] nums)  (be sure your method is public) 




Notes 
  The return value will fit in a 64bit unsigned integer. 

Constraints 
  nums will contain between 1 and 15 elements, inclusive. 
  nums will only contain values between 0 and the number of elements in nums  1, inclusive. 

Examples 
0)  
 
1)  
  Returns: 1  The only derangement is {1,1,1,0,0,0}. 


2)  
  Returns: 0  There is no way to arrange the numbers such that no 1 is where a 1 was originally. 


3)  
 {0,0,0,0,0,0,0,1,1,1,1,1,1,1,2} 
 Returns: 14  

4)  
 
5)  
 {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14} 
 Returns: 481066515734  
