F. Tree Coloring
time limit per test
4.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 $$$k$$$ ($$$k > 1$$$) 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 $$$998244353$$$.

Input

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.

Output

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

Examples
Input
5
1 2
3 2
4 2
2 5
Output
42
Input
5
1 2
2 3
3 4
4 5
Output
53
Input
20
20 19
20 4
12 4
5 8
1 2
20 7
3 10
7 18
11 8
9 10
17 10
1 15
11 16
14 11
18 10
10 1
14 2
13 17
20 6
Output
955085064