You are given a tree that contains $n$ vertices. Count the number of decompositions of the tree into paths modulo $998244353$.
A tree decompositions in paths is valid if each vertex belongs to exactly one path (a path can be only a single vertex).
Two decompositions are different if there are two vertices $v$ and $u$ that belong to the same path in one of the decompositions but two distinct paths in the other.

Input format

• The first line contains only $n$ denoting the number of vertices of the tree.
• Each of the following $n-1$ lines contains space-separated $v_i, u_i$ describing the $i^{th}$ edge of vertex ($v_i, u_i$).
  • $1 \leq n \leq 2 \times 10^5$
  • $1 \leq v_i, u_i \leq n$
  • It is guaranteed that the edges form a tree.

Output format

Print an integer that denotes the number of decompositions of the tree into paths modular $998244353$.