Comprehension:
Given above is the schematic map of the metro lines in a city with rectangles denoting terminal stations (e.g. A), diamonds denoting junction stations (e.g. R) and small filled-up circles denoting other stations. Each train runs either in east-west or north-south direction, but not both. All trains stop for $2$ minutes at each of the junction stations on the way and for $1$ minute at each of the other stations. It takes $2$ minutes to reach the next station for trains going in east-west direction and $3$ minutes to reach the next station for trains going in north-south direction. From each terminal station, the first train starts at $6$ am; the last trains leave the terminal stations at midnight. Otherwise, during the service hours, there are metro service every $15$ minutes in the north-south lines and every $10$ minutes in the east-west lines. A train must rest for at least $15$ minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction. (All questions are related to this metro service only. Assume that if someone reaches a station exactly at the time a train is supposed to leave, (s)he can catch that train.)
What is the minimum number of trains that are required to provide the service in this city?