# Brilliant Space Station

**Discrete Mathematics**Level 5

Brilliant Space Station has 99 rooms. Any two of the 99 rooms are connected by a tunnel directly; however, only 99 of the tunnels are two-way tunnels (the traffic is allowed to travel in both directions), and the rest of the tunnels are one-way tunnels (the traffic is only allowed to travel in one direction). If four of the rooms can be connected in a way that it is possible to travel from any one of the rooms to another one of the rooms, we call that a "four-room group". You being the designer of Brilliant Space Station, what is the maximum number of "four-room groups" that you can make?

**Note:** For 4 rooms to be a "four-room group", you cannot visit any room outside the group to get to another room in the group, i.e. you must be able to travel **directly** from one room to another.