Expected Value

You are given a connected plane graph on $n$ vertices. At first, you stand at vertex 1. Each second you move to an adjacent vertex, chosen uniformly at random among all vertices adjacent to your current one. Compute the expected value of the first time you arrive at vertex $n$.

The first line contains one integer $n$, the number of vertices ($2 \le n \le 3000$). The next $n$ lines each contain the coordinates $x_i$ and $y_i$ of a vertex ($0 \le x_i, y_i \le 5000$). All points are distinct.

The next line contains one integer $m$, the number of edges ($n - 1 \le m \le n(n-1)/2$). The next $m$ lines each contain two integers $a_i$ and $b_i$ ($1 \le a_i, b_i \le n$, $a_i \ne b_i$), meaning there is an edge between vertices $a_i$ and $b_i$, drawn as the straight segment between their points. No two segments intersect except at shared endpoints, there are no multiple edges, and the graph is connected.

It is guaranteed that in the given tests the expected value can be written as an irreducible fraction $P/Q$ with $P, Q > 0$. Print $P \times Q^{-1}$ modulo 998244353.