CF1146F.Leaf Partition

You are given a rooted tree with $n$ nodes, labeled from $1$ to $n$. The tree is rooted at node $1$. The parent of the $i$-th node is $p_i$. A leaf is node with no children. For a given set of leaves $L$, let $f(L)$ denote the smallest connected subgraph that contains all leaves $L$.

You would like to partition the leaves such that for any two different sets $x, y$ of the partition, $f(x)$ and $f(y)$ are disjoint.

Count the number of ways to partition the leaves, modulo $998244353$. Two ways are different if there are two leaves such that they are in the same set in one way but in different sets in the other.

给你一棵有 $n$ 个节点的有根树，节点编号为 $1$ 到 $n$，根节点为节点 $1$。第 $i$ 个节点的父节点为 $p_i$。叶子节点是指没有子节点的节点。对于给定的叶子节点集合 $L$，记 $f(L)$ 为包含所有 $L$ 中叶子节点的最小连通子图。

你希望将所有叶子节点划分为若干个集合，使得该划分中任意两个不同的集合 $x$ 和 $y$ 满足：$f(x)$ 与 $f(y)$ 互不相交（即二者无公共节点）。

求满足条件的叶子节点划分方案数，对 $998244353$ 取模。若存在两个叶子节点，在一种方案中属于同一集合，而在另一种方案中属于不同集合，则认为这两种方案不同。

The first line contains an integer $n$ ($2 \leq n \leq 200\,000$) — the number of nodes in the tree.

The next line contains $n-1$ integers $p_2, p_3, \ldots, p_n$ ($1 \leq p_i \lt i$).

第一行包含一个整数 $n$（$2 \leq n \leq 200\,000$）——树中节点的数量。

接下来的一行包含 $n-1$ 个整数 $p_2, p_3, \ldots, p_n$（$1 \leq p_i \lt i$）。

Print a single integer, the number of ways to partition the leaves, modulo $998244353$.

输出一个整数，表示划分叶子节点的方案数，对 $998244353$ 取模。

In the first example, the leaf nodes are $2,3,4,5$. The ways to partition the leaves are in the following image

In the second example, the only leaf is node $10$ so there is only one partition. Note that node $1$ is not a leaf.

在第一个例子中，叶子节点为 $2,3,4,5$。叶子节点的划分方式如下图所示：

在第二个例子中，唯一的叶子节点是节点 $10$，因此只存在一种划分方式。注意，节点 $1$ 并非叶子节点。