#P1102E. Monotonic Renumeration
Monotonic Renumeration
Description
You are given an array $a$ consisting of $n$ integers. Let's denote monotonic renumeration of array $a$ as an array $b$ consisting of $n$ integers such that all of the following conditions are met:
- $b_1 = 0$;
- for every pair of indices $i$ and $j$ such that $1 \le i, j \le n$, if $a_i = a_j$, then $b_i = b_j$ (note that if $a_i \ne a_j$, it is still possible that $b_i = b_j$);
- for every index $i \in [1, n - 1]$ either $b_i = b_{i + 1}$ or $b_i + 1 = b_{i + 1}$.
For example, if $a = [1, 2, 1, 2, 3]$, then two possible monotonic renumerations of $a$ are $b = [0, 0, 0, 0, 0]$ and $b = [0, 0, 0, 0, 1]$.
Your task is to calculate the number of different monotonic renumerations of $a$. The answer may be large, so print it modulo $998244353$.
The first line contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the number of elements in $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).
Print one integer — the number of different monotonic renumerations of $a$, taken modulo $998244353$.
Input
The first line contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the number of elements in $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).
Output
Print one integer — the number of different monotonic renumerations of $a$, taken modulo $998244353$.
Samples
5
1 2 1 2 3
2
2
100 1
2
4
1 3 3 7
4