CF1613F.Tree Coloring

You are given a rooted tree consisting of $n$ vertices numbered from $1$ to $n$. The root of the tree is the vertex $1$.

You have to color all vertices of the tree into $n$ colors (also numbered from $1$ to $n$) so that there is exactly one vertex for each color. Let $c_i$ be the color of vertex $i$, and $p_i$ be the parent of vertex $i$ in the rooted tree. The coloring is considered beautiful if there is no vertex $k$ ($k \gt 1$) such that $c_k = c_{p_k} - 1$, i. e. no vertex such that its color is less than the color of its parent by exactly $1$.

Calculate the number of beautiful colorings, and print it modulo $998244353$.

你被给定一棵包含 $n$ 个顶点（编号从 $1$ 到 $n$）的有根树，树的根为顶点 $1$。

你需要将树的所有顶点染成 $n$ 种颜色（颜色也编号为 $1$ 到 $n$），使得每种颜色恰好使用一次。设 $c_i$ 表示顶点 $i$ 的颜色，$p_i$ 表示顶点 $i$ 在该有根树中的父节点。若不存在顶点 $k$（其中 $k > 1$）满足 $c_k = c_{p_k} - 1$，即不存在某个顶点，其颜色比其父节点的颜色恰好小 $1$，则称该染色方案是“优美的”。

请计算优美的染色方案总数，并对 $998244353$ 取模后输出。

The first line contains one integer $n$ ($2 \le n \le 250000$) — the number of vertices in the tree.

Then $n-1$ lines follow, the $i$-th line contains two integers $x_i$ and $y_i$ ($1 \le x_i, y_i \le n$; $x_i \ne y_i$) denoting an edge between the vertex $x_i$ and the vertex $y_i$. These edges form a tree.

第一行包含一个整数 $n$（$2 \le n \le 250000$）——树中顶点的数量。

接下来是 $n-1$ 行，其中第 $i$ 行包含两个整数 $x_i$ 和 $y_i$（$1 \le x_i, y_i \le n$；$x_i \ne y_i$），表示顶点 $x_i$ 与顶点 $y_i$ 之间的一条边。这些边构成一棵树。

Print one integer — the number of beautiful colorings, taken modulo $998244353$.

输出一个整数——美丽染色方案的数量，对 $998244353$ 取模。