Please, try EDU on Codeforces! New educational section with videos, subtitles, texts, and problems.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

F. Leaf Partition

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Input

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 $$$p_2, p_3, \ldots, p_n$$$ ($$$1 \leq p_i < i$$$).

Output

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

Examples

Input

5 1 1 1 1

Output

12

Input

10 1 2 3 4 5 6 7 8 9

Output

1

Note

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/06/2020 11:18:27 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|