|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.
|-||Your return value must have an absolute or relative error less than 1e-9.|
|-||N will be between 1 and 100, inclusive.|