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combinatorics

divide and conquer

fft

*2600

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F. Tree Coloring

time limit per test

4.5 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou 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

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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