Count Possibilities

You are given a *directed* tree with $N$ vertices. The edges are directed away from the root. For each $i = 1, 2, 3, \ldots, N$, count the number of vertices that can possibly appear at the $i$-th position of a [topological order](https://en.wikipedia.org/wiki/Topological_sorting) of this tree. That is, for each $i$, find the number of vertices $u$ such that there exists a topological order $T$