F. Tree Coloringtime limit per test4.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard 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.InputThe 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.OutputPrint one integer — the number of beautiful colorings, taken modulo 998244353.ExamplesInput
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

5
1 2
3 2
4 2
2 5

42 
['combinatorics', 'divide and conquer', 'fft', '*2600']