# Country Connected By One Way Roads

Discrete Mathematics Level pending

The country of Indiapolis has $$2015$$ towns. Each pair of towns is connected by a one way road, i.e. given any two towns $$A$$ and $$B$$, one can either directly travel from $$A$$ to $$B$$ or from $$B$$ to $$A$$ via that road but not both. A triple of towns $$(A, B, C)$$ is called good if one can directly travel from $$A$$ to $$B$$, then from $$B$$ to $$C$$, and then from $$C$$ to $$A$$. Let $$N$$ be the maximum possible number of good triples of towns. Find the last three digits of $$N-280$$.

Details and assumptions
- Each pair of cities are connected by exactly road.
- Traveling directly from city $$A$$ to $$B$$ means traveling from $$A$$ to $$B$$ via the road that connects them. The problem statement says that given two cities $$A$$ and $$B$$, one can either directly travel from $$A$$ to $$B$$ or from $$B$$ to $$A$$, but not both.
- You're not allowed to change roads when you're not in a city.
- This problem is not original.

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