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