Maximum Topological Sort

Chef has a tree $G$ with $N$ nodes (numbered $1$ through $N$) and $N-1$ undirected edges. For each node $u$ in the tree, he can assign directions to the edges in such a way that $u$ is reachable from all the other nodes. Let $C_u$ be the number of valid [topological orderings](https://en.wikipedia.org/wiki/Topological_sorting) in the resulting directed acyclic graph. This way, Chef obtains $N$