Problem Statement

We have a rooted tree with $N$ vertices numbered $1$ to $N$. Vertex $1$ is the root of the tree, and the parent of vertex $i\ (2\leq i)$ is vertex $p_i$.

Each vertex has a color: black or white. Initially, all vertices are white.

In this rooted tree, vertex $i$ is said to be good when all vertices on the simple path connecting vertices $1$ and $i$ (including vertices $1$ and $i$) are black, and bad otherwise.

Until all vertices are black, let us repeat the following operation: choose one vertex from the bad vertices uniformly at random, and repaint the chosen vertex black.

Find the expected value of the number of times we perform the operation, modulo $998244353$.

The definition of the expected value modulo $998244353$ It can be proved that the sought expected value is always a rational number. Additionally, when that value is represented as an irreducible fraction $\frac{P}{Q}$, it can also be proved that $Q \not \equiv 0 \pmod{998244353}$. Therefore, there is a unique integer $R$ such that $R \times Q \equiv P \pmod{998244353}$ and $0 \leq R < 998244353$. Find this $R$.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq p_i < i$
• All values 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 answer.