Problem Statement 
 You are trying to predict the outcome of a race between n runners, numbered from 0 to n  1.You are given two int[]s, first and second. It is guaranteed that for all i, the runner numbered first[i] will always beat the runner numbered second[i]. Determine how many final orderings are possible, modulo 1,000,003. If the information is contradictionary, return 0. Runners are never tied. 

Definition 
 Class:  RaceOrdering  Method:  countOrders  Parameters:  int, int[], int[]  Returns:  int  Method signature:  int countOrders(int n, int[] first, int[] second)  (be sure your method is public) 




Constraints 
  n will be between 1 and 30, inclusive. 
  first and second will each contain between 0 and 15 elements, inclusive. 
  first and second will contain the same number of elements. 
  Each element of first and second will be between 0 and n  1, inclusive. 
  first[i] does not equal second[i] for all i between 0 and m  1, inclusive, where m is the number of elements in first and second. 

Examples 
0)  
  Returns: 3  Contestant 1 beat contestant 2, so the valid orders are 012, 102 and 120. 


1)  
  Returns: 8  Contestant 0 beat contestants 1 and 2, but there is no information on contestant 3. The valid orderings are 3012, 3021, 0312, 0321, 0132, 0231, 0123 and 0213. 


2)  
  Returns: 0  There is no way to satisfy this cycle. 


3)  
 