A12300 | Monotonic Renumeration

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 $998244353$ .