|There are N boxes numbered 0 through N-1. 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 j-th character of the i-th element is 'Y' if opening the i-th box will reveal whether or not the j-th box contains carrots, or 'N' if the i-th box contains no such information.
Return the probability that she can find the empty box without opening it, assuming she behaves optimally.
|-||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 i-th character of the i-th element of information will be 'Y'.|
|-||Each character in information will be 'Y' or 'N'.|