Problem Statement

Given is a directed tree with N vertices numbered 1 through N.
Vertex 1 is the root of the tree.
For each integer i such that $2 \leq i \leq N,$ there is a directed edge from Vertex p_i to i.
Let a be the permutation of $(1, \ldots, N)$, and a_i be the i-th element of a.
Among the N! sequences that can be a, find the number of sequences that satisfy the following condition, modulo 998244353.

• Condition: For every integer i such that $1 \leq i \leq N, Vertex i$ is unreachable from Vertex a_i by traversing one or more edges.

Input

Input is given from Standard Input in the following format:
N
$p_{2} \cdots p_N$

Output

Print the number of sequences a among the permutations of $(1, \ldots, N)$ that satisfy the condition in Problem Statement, modulo 998244353.

Constraints

• All values in input are integers.
• $1 \leq N \leq 2000$
• $1 \leq p_i < i$

Sample Input 1

4
1 1 3

Sample Output 1

4

Sample Input 2

30
1 1 3 1 5 1 1 1 8 9 7 3 11 11 15 14 4 10 11 12 1 10 13 11 7 23 8 12 18

Sample Output 2

746746186

• Remember to print the count modulo 998244353.

见题面 Input 部分

见题面 Output 部分