The database of mini-facebook only has space for the data of 100 participants. These 100 participants want to establish as many mini-facebook friendships among them as possible. However, mini-facebook has introduced the following set of ground rules:
- Mini-facebook friendships are always symmetric.
- Mini-facebook only accepts one mini-facebook friendship or mini-facebook un-friend request per second. If two or more requests arrive simultaneously, they are all rejected.
- Any mini-facebook friendship request must consist of four distinct participants $A,B,C,D$ (ordered) so that none of the four pairs $AB$, $BC$, $CD$, $DA$ are currently mini-facebook friends. Mini-facebook will then establish the new friendship $AD$.
- Any mini-facebook un-friend request must consist of two distinct participants $A,B$ that are currently friends. Mini-facebook will then delete the new friendship $AB$.
Question: What is the maximum number of mini-facebook friendships that can exist simultaneoulsy at any moment in time?