CF1172B Nauuo and Circle

给定一圆，上有n个节点（不重合，从1到n编号）。它们按照输入连成一棵树。 求合法树的方案总数，对998244353取模。 一棵树是合法的，当且仅当这棵树中无交叉的边（两边共用一端点除外）。 注意：只要从 **最上面端点(不一定对于每个都是1，见样例1解释3&5)** 顺时针沿圆遍历所有节点得到的序列不同，那么两种方案就是不同的，即使它们本质相同。

The first line contains a single integer $ n $ ( $ 2\le n\le 2\cdot 10^5 $ ) — the number of nodes in the tree. Each of the next $ n-1 $ lines contains two integers $ u $ and $ v $ ( $ 1\le u,v\le n $ ), denoting there is an edge between $ u $ and $ v $ . It is guaranteed that the given edges form a tree.

The output contains a single integer — the number of permutations suitable to draw the given tree on a circle satisfying the rule, modulo $ 998244353 $ .

Example 1 All valid permutations and their spanning trees are as follows.  Here is an example of invalid permutation: the edges $ (1,3) $ and $ (2,4) $ are crossed.  Example 2 Every permutation leads to a valid tree, so the answer is $ 4! = 24 $ .