Problem Statement  
*** You may only submit a given problem once  no resubmissions will be accepted. *** Suppose there is a universal set called U containing the integers between 1 and size inclusive. You will be given some subsets of U. A subset of U is a set of numbers that are in U. The set can contain no numbers (empty set), every number in U, or anything in between. Each subset will be given as a String containing a single spacedelimited list of the numbers in the set. The Borel Field B (also called sigmaalgebra) generated by subsets is the smallest collection of sets satisfying the following statements:
 
Definition  
 
Constraints  
  size will be between 1 and 10 inclusive.  
  subsets will contain between 1 and 50 elements inclusive.  
  Each element of subsets will contain between 0 and 50 characters inclusive.  
  Each element of subsets will either be an empty string, or a single spacedelimited list of integers. Each integer in the list will be between 1 and size inclusive, and will have no leading zeros.  
  Each element of subsets will not have any leading or trailing spaces.  
Examples  
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