Problem Statement 
 Given a positive integer N, let P(N) denote the product of all digits in the decimal representation of N. For example, P(4256) = 4 * 2 * 5 * 6 = 240, P(2112) = 2 * 1 * 1 * 2 = 4 and P(100) = 1 * 0 * 0 = 0.
Consider the infinite sequence S = (P(1), P(2), P(3), ...). Given a int[] prod containing exactly M elements, find the first occurrence of (prod[0], prod[1], ..., prod[M1]) in S as a consecutive subsequence. In other words, return the smallest positive index X such that P(X + i) = prod[i] for all i between 0 and M1, inclusive. The constraints will guarantee that at least one such X exists. 

Definition 
 Class:  ProductsOfDigits  Method:  firstOccurrence  Parameters:  int[]  Returns:  long  Method signature:  long firstOccurrence(int[] prod)  (be sure your method is public) 




Notes 
  It can be shown that under the constraints of this problem, the return value will always fit within a 64bit signed integer datatype. 

Constraints 
  prod will contain between 1 and 50 elements, inclusive. 
  Each element of prod will be between 0 and 1,000,000,000, inclusive. 
  There will be at least one occurrence of (prod[0], ..., prod[M1]) in S as a consecutive subsequence, where M is the number of elements in prod. 

Examples 
0)  
  Returns: 1  Since P(1) = 1, P(2) = 2, ..., P(5) = 5, we have that S starts with an occurrence of (1, 2, 3, 4, 5). 


1)  
  Returns: 9  P(9) = 9, P(10) = 0, P(11) = 1. 


2)  
  Returns: 100  All numbers between 100 and 103, inclusive, have a 0 in their decimal representations. 


3)  
 
4)  
 {108864, 127008, 145152, 163296, 0, 22680, 45360, 68040, 90720} 
 Returns: 789946  

5)  
 
6)  
 