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. \InputFile The first line contains number $n~(4 \le n \le 1000)$. The second and the third lines contain arrays $x$ and $y~(1 \le x_i, y_i \le n)$ of length $n - 3$ each. \OutputFile Print the number of spanning trees modulo $987654323$. \includegraphics{https://static.eolymp.com/content/c6/c61c7a091d76c2fc464ad45159c675062a9d9f7d.gif}