A14131 | Pairs of Paths

You are given a tree consisting of $n$ vertices, and $m$ simple vertex paths. Your task is to find how many pairs of those paths intersect at exactly one vertex. More formally you have to find the number of pairs $(i, j)$ $(1 \leq i < j \leq m)$ such that $path_i$ and $path_j$ have exactly one vertex in common.

First line contains a single integer $n$ $(1 \leq n \leq 3 \cdot 10^5)$ .

Next $n - 1$ lines describe the tree. Each line contains two integers $u$ and $v$ $(1 \leq u, v \leq n)$ describing an edge between vertices $u$ and $v$ .

Next line contains a single integer $m$ $(1 \leq m \leq 3 \cdot 10^5)$ .

Next $m$ lines describe paths. Each line describes a path by it's two endpoints $u$ and $v$ $(1 \leq u, v \leq n)$ . The given path is all the vertices on the shortest path from $u$ to $v$ (including $u$ and $v$ ).

Output a single integer — the number of pairs of paths that intersect at exactly one vertex.