You are working for a company and asked to create a perfect metro map where there will be as many stops as possible. But there are two constraints which limits the number of tracks (railroads) and maximum number of stations between one station to another one:
- There are at most $3$ tracks (railway) from one stop to others since it is not wanted to dig the underground too much and have the least amount of railways.
- The maximum number of stations between destination and departure stations is limited as $1$. So you can go from one station to another one with only seeing other $1$ different stations. In other words, if you move from one station (departure), there has to be at most $1$ stations between departure to destination.
- The tracks on the map can overlap to each other, since it is underground you can adjust the depth of the tunnels accordingly.
For example, if this question is asked for at most $3$ tracks with the maximum number of stations between stations as $0$ (no station between destination and departure stops), the answer would be 4 stations at most as seen below: