擦除与提升AI (CI翻译)
Problem Statement
题目描述
AI (CI翻译)There is an integer sequence $A=(0,0,\ldots,0)$ of length $N$. The following operation is repeated as long as it can be performed.
有一个长度为 $N$ 的整数序列 $A=(0,0,\ldots,0)$。只要还能执行以下操作，就重复执行该操作。AI (CI翻译)
- Choose a pair of integers
$(i,j)$satisfying$1\le i\lt j\le |A|$and$A_i=A_j$. - Remove
$A_i$and$A_j$from the sequence. - Add
$1$to every element that was between$A_i$and$A_j$immediately before the removal.
- 选择一对满足
$1\le i\lt j\le |A|$且$A_i=A_j$的整数$(i,j)$。 - 从序列中移除
$A_i$和$A_j$。 - 将移除前位于
$A_i$和$A_j$之间的每个元素都加$1$。
Here, $|A|$ denotes the length of the sequence $A$ at that point.
这里，$|A|$ 表示此时序列 $A$ 的长度。AI (CI翻译)
Find the number, modulo $998244353$, of possible sequences when no more operations can be performed. If the final sequences are the same, they are not distinguished even if the process of operations differs. A sequence of length $0$ is also counted as one sequence.
请求出当无法再执行任何操作时，可能得到的不同序列数量，结果对 $998244353$ 取模。如果最终序列相同，则即使操作过程不同，也视为同一个序列。长度为 $0$ 的序列也计作一个序列。AI (CI翻译)
Constraints
约束条件
AI (CI翻译)$1 \le N \le 2 \times 10^5$- All input values are integers.
$1 \le N \le 2 \times 10^5$- 所有输入值均为整数。
Input
输入格式
AI (CI翻译)The input is given from Standard Input in the following format:
输入从标准输入中按以下格式给出：AI (CI翻译)
NNOutput
输出格式
AI (CI翻译)Output the answer.
输出答案。AI (CI翻译)
样例
1
1
5
3
7
8
200000
159211719
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（gpt-6.1-sol），如有出入请以原文为准。