Typical "don't even try brute-forcing it" part 2. I kept track of the timeline count as I worked my way vertically down the graph, and then added up the beams' shared timelines at the end. I also considered that dynamic programming with a recursive solution would probably have worked fine as well, but went for the approach that most matched the way I was already doing it.
I'll probably follow up with the dynamic programming approach, just for fun.
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