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.

Input

Input is given from Standard Input in the following format:
N
$P_1 P_2 \cdots P_N$

Output

Print the answer.

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.

Sample Input 1

3
1 3 2

Sample Output 1

4

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

Sample Input 2

4
2 1 3 4

Sample Output 2

11

Sample Input 3

10
4 9 6 3 8 10 1 2 7 5

Sample Output 3

855

见题面 Input 部分

见题面 Output 部分