Problem Statement  
Alice likes lotteries. Her favorite lottery is Pyaterochka, which is very popular in Belarus. Each ticket in this lottery is a rectangular grid with N rows and 5 columns, where each cell contains an integer between 1 and 5*N, inclusive. All integers within a single ticket are distinct.
After the tickets are distributed, the lottery organizers randomly choose 5 distinct integers, each between 1 and 5*N, inclusive. Each possible subset of 5 integers has the same probability of being chosen. These integers are called the winning numbers. A ticket is considered a winner if and only if it has a row which contains at least 3 winning numbers. Alice will buy a single ticket. Each possible ticket has the same probability of being sold. Return the probability that she will buy a winning ticket.  
Definition  
 
Notes  
  Your return value must have an absolute or relative error less than 1e9.  
Constraints  
  N will be between 1 and 100, inclusive.  
Examples  
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