Problem Statement

You are given a rooted tree $T$ with $N$ vertices labeled from $1$ to $N$. The root is the vertex $1$, and the parent of vertex $i$ $(2 \leq i \leq N)$ is $p_i$ $(p_i \lt i)$.

Consider a directed graph $G$ with $N$ vertices labeled from $1$ to $N$. We call $G$ good if it satisfies all of the following conditions (here, let $u \to v$ denote an edge from vertex $u$ to vertex $v$):

• Every vertex in $G$ has outdegree $1$.
• $G$ has no cycle of even length.
• For every $i$ $(2 \leq i \leq N)$, $G$ does not contain the edge $i \to p_i$.

Find the sum, modulo $998244353$, of $2^{(\text{number of cycles in }G)}$ over all good graphs $G$.

Constraints

• $2 \leq N \leq 10^5$
• $1 \leq p_i \lt i$
• All values given in the input are integers.

Input

The input is given from Standard Input in the following format:

N
p_2 p_3 \dots p_N

Output

Print the sum, modulo $998244353$, of $2^{(\text{number of cycles in }G)}$ over all good graphs $G$.