Number of topological sortings of neural network DAG

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How many topological sortings are there of a DAG G such that G is a fully connected neural network with layers of width 3, 2, and 1?

I would think the answer would be 3! * 2! * 1!, since any sorting without elements of the layer together would violate the definition of a topological sort--there would be a directed edge u → v, but v would be before u.

However, I have been told that this is too small...

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