Two friends were spending their bank holiday on a cycling trip. 
Stopping for a rest at a village inn, they consulted a route map below.
They started from the town in the top left-hand corner marked A. 
There are one hundred and twenty such towns, all connected by straight roads. 

Now they discovered that there are exactly 1,365 different routes by which they may reach their destination, always travelling either due south or due east. 

Which town is their destination?