write a go solution for Description:
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 Format:
The first line contains one integer n (2<=n<=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<=x_i,y_i<=n; x_iney_i) denoting an edge between the vertex x_i and the vertex y_i. These edges form a tree.

Output Format:
Print one integer — the number of beautiful colorings, taken modulo 998244353.

Note:
None. Output only the code with no comments, explanation, or additional text.