+785 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?
