# Mind Blown!?!?!?

Among $$100$$ points in a plane, no three collinear, exactly $$4026$$ pairs are connected by line segments. Each point is then randomly assigned an integer from $$1$$ to $$100$$ inclusive, each equally likely, such that no integer appears more than once. Find the expected value of the number of segments which join two points whose labels differ by at least $$50$$.

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