CF1032F.Vasya and Maximum Matching

Vasya has got a tree consisting of $n$ vertices. He wants to delete some (possibly zero) edges in this tree such that the maximum matching in the resulting graph is unique. He asks you to calculate the number of ways to choose a set of edges to remove.

A matching in the graph is a subset of its edges such that there is no vertex incident to two (or more) edges from the subset. A maximum matching is a matching such that the number of edges in the subset is maximum possible among all matchings in this graph.

Since the answer may be large, output it modulo $998244353$.

瓦西娅有一棵由 $n$ 个顶点构成的树。他希望删除该树中的一些（可能为零条）边，使得所得图的最大匹配是唯一的。请你计算选择待删除边集的方法数。

图中的一个匹配是指其边集的一个子集，满足其中任意顶点至多与该子集中的两条（或更多）边关联。一个最大匹配是指在该图所有匹配中，边数最多的匹配。

由于答案可能很大，请将结果对 $998244353$ 取模后输出。

The first line contains one integer $n$ ($1 \le n \le 3 \cdot 10^5$) — the number of vertices in the tree.

Each of the next $n − 1$ lines contains two integers $u$ and $v$ ($1 \le u, v \le n, u \neq v$) denoting an edge between vertex $u$ and vertex $v$. It is guaranteed that these edges form a tree.

第一行包含一个整数 $n$（$1 \le n \le 3 \cdot 10^5$）——树中顶点的数量。

接下来的 $n - 1$ 行，每行包含两个整数 $u$ 和 $v$（$1 \le u, v \le n,\ u \neq v$），表示顶点 $u$ 与顶点 $v$ 之间的一条边。保证这些边构成一棵树。

Print one integer — the number of ways to delete some (possibly empty) subset of edges so that the maximum matching in the resulting graph is unique. Print the answer modulo $998244353$.

输出一个整数——表示删除某个（可能为空的）边子集的方式数目，使得剩余图中的最大匹配是唯一的。答案对 $998244353$ 取模。

Possible ways to delete edges in the first example:

• delete $(1, 2)$ and $(1, 3)$.
• delete $(1, 2)$ and $(1, 4)$.
• delete $(1, 3)$ and $(1, 4)$.
• delete all edges.

Possible ways to delete edges in the second example:

• delete no edges.
• delete $(1, 2)$ and $(2, 3)$.
• delete $(1, 2)$ and $(3, 4)$.
• delete $(2, 3)$ and $(3, 4)$.
• delete $(2, 3)$.
• delete all edges.

第一个示例中删除边的可能方式：

• 删除边 $(1, 2)$ 和 $(1, 3)$。
• 删除边 $(1, 2)$ 和 $(1, 4)$。
• 删除边 $(1, 3)$ 和 $(1, 4)$。
• 删除所有边。

第二个示例中删除边的可能方式：

• 不删除任何边。
• 删除边 $(1, 2)$ 和 $(2, 3)$。
• 删除边 $(1, 2)$ 和 $(3, 4)$。
• 删除边 $(2, 3)$ 和 $(3, 4)$。
• 删除边 $(2, 3)$。
• 删除所有边。