This feels a little like bottom-up DP, I'm not too sure what the actual
name of this pattern is.

It's actually easier than expected. I was considering something crazy
like constructing a graph and doing backtracking, but after some
pen-and-paper work, we can simply get the answer by keep track of a
count, splitting the counts when encountering a splitter, and merging
the count when they overlap.

Rather straightforward: we just need to count the set intersection of
beams and splitters on every pass.

Feels like a throwaway, can't imagine this solution being recyclable in
any way for part 2.

.. and there it is. What a twist.

The annoying thing is now that the input is whitespace sensitive, I had
to account for my editor stripping trailing whitespaces on save, or `mix
format` doing the same thing. I don't want to turn those off, so alter
the get_example input instead.

This turned out to be easier than expected. Simply turn the input into
graphmemes, then transpose the matrix, then it's just a single pass,
using a state machine to hold the operation, numeric buffer, and
accumulated sum. Easy.