Score : $700$ points

Problem Statement

You are given a permutation $P=(P_1,P_2,\cdots,P_N)$ of $(1,2,\cdots,N)$.

You may perform the following operation zero or more times.

• Choose an integer $i$ ($1 \leq i \leq N-1$). Let $v=\max(P_i,P_{i+1})$ and replace the values of $P_i$ and $P_{i+1}$ with $v$.

How many sequences are there that $P$ can be after your operations? Find the count modulo $998244353$.

Constraints

• $2 \leq N \leq 5000$
• $(P_1,P_2,\cdots,P_N)$ is a permutation of $(1,2,\cdots,N)$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$P_1$ $P_2$ $\cdots$ $P_N$

Output

Print the answer.

3
1 3 2

4

The four sequences that $P$ can become are $(1,3,2)$, $(3,3,2)$, $(1,3,3)$, and $(3,3,3)$.

4
2 1 3 4

11

10
4 9 6 3 8 10 1 2 7 5

855