human
What is a Python program to print one integer — the number of different monotonic renumerations of $a$, taken modulo $998244353$ given the following:
I found an interesting problem on https://codeforces.com/problemset/problem/1102/E:
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 $998244353$.

-----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 $998244353$.

-----Examples-----
Input
5
1 2 1 2 3

Output
2

Input
2
100 1

Output
2

Input
4
1 3 3 7

Output
4

I tried it in Python, but could not do it. Can you solve it?
assistant
#Here is Python program to print one integer — the number of different monotonic renumerations of $a$, taken modulo $998244353$.

class SegmentTree(object):
    __slots__ = ["elem_size", "tree", "default", "op"]

    def __init__(self, a: list, default: int, op):
        import math
        real_size = len(a)
        self.elem_size = elem_size = 1 << math.ceil(math.log(real_size, 2))
        self.tree = tree = [default] * (elem_size * 2)
        tree[elem_size:elem_size+real_size] = a
        self.default = default
        self.op = op

        for i in range(elem_size - 1, 0, -1):
            tree[i] = op(tree[i << 1], tree[(i << 1)+1])

    def get_value(self, x: int, y: int) -> int:
        l, r = x + self.elem_size, y + self.elem_size
        tree, result, op = self.tree, self.default, self.op
        while l < r:
            if l & 1:
                result = op(tree[l], result)
                l += 1
            if r & 1:
                r -= 1
                result = op(tree[r], result)
            l, r = l >> 1, r >> 1

        return result

    def set_value(self, i: int, value: int) -> None:
        k = self.elem_size + i
        self.tree[k] = value
        self.update(k)

    def update(self, i: int) -> None:
        op, tree = self.op, self.tree
        while i > 1:
            i >>= 1
            tree[i] = op(tree[i << 1], tree[(i << 1) + 1])

def __starting_point():
    from collections import defaultdict
    N = int(input())
    a = list(map(int, input().split()))
    index_dict = defaultdict(list)
    for i, n in enumerate(a):
        index_dict[n].append(i)

    last_num = 0
    ans = []
    append = ans.append
    segtree = SegmentTree([10**6]*(N+1), 10**6, min)
    getv, setv = segtree.get_value, segtree.set_value

    for i, n in enumerate(a):
        if not index_dict[n]:
            continue
        last_num = min(last_num+1, getv(i+1, N+1))
        for j in index_dict[n]:
            setv(j, last_num)
        append(last_num)
        index_dict[n] = []

    mod = 998244353

    ans = pow(2, len(set(ans))-1, mod)
    print(ans)
__starting_point()