Problem Statement  
There are N boxes numbered 0 through N1. Every box except for one contains carrots, but Rabbit Hanako does not know which box is the empty one. Each box has the same probability of being empty.
Hanako wants to find the empty box without opening it. Fortunately, she has some clues. Some of the boxes contain information about the content of other boxes, and she knows which boxes contain such information. You are given a String[] information, where the jth character of the ith element is 'Y' if opening the ith box will reveal whether or not the jth box contains carrots, or 'N' if the ith box contains no such information. Return the probability that she can find the empty box without opening it, assuming she behaves optimally.  
Definition  
 
Constraints  
  information will contain between 1 and 50 elements, inclusive.  
  Each element of information will contain exactly N characters, where N is the number of elements of information.  
  The ith character of the ith element of information will be 'Y'.  
  Each character in information will be 'Y' or 'N'.  
Examples  
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