The map below displays the train network of Beastville, including the stations X and Y, and the lines a, b, c, d, e, and f. There is a station where any two lines intersect, and on every line, trains stop at each station.
Grogg wants to travel from station X to station Y, with the following conditions:
* Once Grogg leaves station X, he never returns to station X.
* Once Grogg arrives at station Y, he never leaves station Y.
* Grogg travels along each line at most once.
How many different routes can Grogg take?