Building Spanning Trees

Consider an undirected, complete, simple graph $G$ on $n$ vertices. The vertices of $G$ are labeled from $1$ to $n$. Specifically, each pair of distinct vertices is connected by a single undirected edge, so there are precisely n \cdot (n - 1) / 2 edges in this graph.

You are given a set $E$ that consists of n - 3 edges of this graph $G$. More precisely, you are given two arrays $x$ and $y$ with n - 3 elements each. For each valid $i$, (x_i, y_i) is one of the edges in $E$.

A spanning tree of $G$ is a subset of exactly n - 1 edges of $G$ such that the edges connect all $n$ vertices. You may note that the edges of a spanning tree do indeed form a tree that is a subgraph of $G$ and spans all its vertices.

We are interested in spanning trees that contain all of the edges in the provided set $E$. Find the number of such spanning trees modulo $987654323$. Two spanning trees are different if there is an edge of $G$ that is in one of them but not in the other.

Output

Print the number of spanning trees modulo $987654323$.