P5450 [THUPC 2018] Taomi God’s Tree

Lovely Tommy has a tree. In this tree, only vertices $a$ and $b$ are black, and all other vertices are white. Each time, Tommy can recolor a black vertex $p$ to red, and then recolor all white vertices adjacent to $p$ into black. In the end, all vertices will be recolored to red. Let the $i$-th vertex be recolored to red as the $t_i$-th one; then $t_i$ is a permutation of $1$ to $n$. Tommy wants you to help him find how many different $t_i$ there are.

Each input file contains only one testdata. * The first line contains three positive integers $n,a,b$ separated by spaces, representing the number of vertices of the tree and the indices of the initial black vertices. * The next $n-1$ lines each contain two positive integers $x,y$, describing an edge $\left( x,y\right)$ in the tree. The vertices of the tree are numbered starting from $1$.

Output $1$ line: * One integer, representing the number of different permutations $t_i$ modulo $998,244,353$.

### Constraints It is guaranteed that $a,b\le n\le 234,567$. ### Copyright Information From the 2018 Tsinghua University Programming Contest and Collegiate Invitational (THUPC2018). Thanks to [Pony.ai](http://pony.ai/) for supporting this contest. Resources such as editorials can be found at . Translated by ChatGPT 5