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.