F. Leaf Partitiontime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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). OutputPrint a single integer, the number of ways to partition the leaves, modulo 998244353.ExamplesInput
5
1 1 1 1
Output
12
Input
10
1 2 3 4 5 6 7 8 9
Output
1
NoteIn 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.
5
1 1 1 1

12 
['dp', 'trees', '*2500']