An airport has a system of bus routes to shuttle passengers between terminals. The system is laid out in such a way that:

(a) there are exactly 3 bus stops on each route;

(b) it is possible to travel between any two bus stops without changing routes;

(c) any two distinct bus routes have exactly one bus stop in common.

What is the number of bus routes in the airport?

The diagram shows the fairly trivial case in which each route has just 2 bus stops; in this case, we only need 3 routes to satisfy all the conditions.

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