Problem Statement  
You have a group of nonzero digits, which are not necessarily unique. If you can insert '0' digits wherever you wish, there are an infinite number of integers which have exactly those nonzero digits. For example, given the group of digits {1, 2}, you can create the numbers 12, 21, 102, 120, 201, 210, 1002, 1020, etc. Given a potentially large number n in String format, return how many numbers that use the same exact nonzero digits are less than it. Leading zeros are not allowed.  
Definition  
 
Constraints  
  n will have between 1 and 50 characters, inclusive.  
  n will consist only of digit characters ('0'  '9').  
  n will not start with a '0'.  
  There will be at most 2^63  1 integers with the same nonzero digits as n that are less than n  
Examples  
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