P13550 宇宙分解

[宇宙分解](https://music.163.com/song?id=492999800)。 > あなたのこと 僕は何も 知っちゃいないから > > 全部全部知ろうとして 宇宙を覗き込んでしまった

You are given a sequence $a$ and two operations: 1. Choose $a_i < a_{i+1}$ and delete $a_{i+1}$. 2. Choose $a_i < a_{i+1}$ and swap these two numbers. You must repeatedly perform these operations **until no more operations can be done**. How many **distinct** sequences can be obtained at the end?

The first line contains an integer $n$. The second line contains $n$ integers, where the $i$-th integer is $a_i$.

Output an integer representing the number of distinct sequences obtained at the end, modulo $998244353$.

### Sample Explanation For Sample #1, there are four possible outcomes: - $[4, 2, 1]$: Obtained by performing two deletions to remove $5$ and $3$. - $[5, 4, 2, 1]$: Obtained by deleting $3$ and moving $5$ to the front. - $[5, 4, 3, 2, 1]$: Obtained by performing two swaps to sort the sequence. - $[4, 3, 2, 1]$: Obtained by deleting $5$ and then sorting the sequence. For Sample #2, no operations can be performed initially. ### Constraints | Test | $n\le$ | $a_i\le$ | Special Properties | | :-: | :-: | :-: | :-: | | $1$ | $5$ | $5$ | None | | $2\sim 3$ | $10^3$ | $10^3$ | All $a_i$ are distinct | | $4\sim 5$ | $10^5$ | $10^9$ | All $a_i$ are distinct | | $6\sim 7$ | $10^5$ | $5$ | None | | $8\sim 10$ | $10^5$ | $10^9$ | None | For all test cases, $1 \le n \le 10^5$, $1 \le a_i \le 10^9$. Generated by Deepseek V3.