Problem Statement

You are given a rooted tree with $N$ vertices, numbered from $1$ to $N$.

Vertex $1$ is the root, and the parent of vertex $i(2\leq i \leq N)$ is $P_{i}(1\leq P_{i}<i)$.

Find the number, modulo $998244353$, of non-negative integer sequences $A = (A_{1}, A_{2}, \dots , A_{N})$ of length $N$ that satisfy the following condition.

• There exists a way to write $1$ non-negative integer on each of the $N$ vertices such that the following holds for every vertex $i(1\leq i\leq N)$.
  • The smallest non-negative integer not written on any vertex in the subtree of vertex $i$ (including $i$ itself) is $A_{i}$.

Constraints

• $2\leq N\leq 5000$
• $1\leq P_{i}<i(2\leq i \leq N)$
• All input values are integers.

Input

The input is given from standard input in the following format.

$N$
$P_{2}$ $P_{3}$ $\cdots$ $P_{N}$

Output

Output the answer.

Sample

2
1

5

4
1 1 1

28

10
1 1 3 1 2 3 1 6 7

9744