AT_arc227_f.Erase and Raise

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.

• 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.

Here, $|A|$ denotes the length of the sequence $A$ at that point.

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.

有一个长度为 $N$ 的整数序列 $A=(0,0,\ldots,0)$。只要还能执行，就重复以下操作：

• 选择一对满足 $1\le i\lt j\le |A|$ 且 $A_i=A_j$ 的整数 $(i,j)$；
• 从序列中删除 $A_i$ 和 $A_j$；
• 将删除前位于 $A_i$ 与 $A_j$ 之间的所有元素均加 $1$。

其中，$|A|$ 表示当前序列 $A$ 的长度。

求当无法再执行任何操作时，可能得到的不同最终序列的个数（对 $998244353$ 取模）。若两个最终序列完全相同，则无论操作过程是否不同，均视为同一种序列（即不区分操作路径）。空序列（长度为 $0$）也计为一种序列。

The input is given from Standard Input in the following format:

$N$

输入从标准输入中按以下格式给出：

$N$

Output the answer.

输出答案。

Sample 1 Explanation:
No operation can be performed, so there is one possible final sequence: $(0)$.

Sample 2 Explanation:
There are three possible final sequences: $(0)$, $(1)$, $(2)$.

Sample 3 Explanation:
Depending on the choices made during the operations, eight different sequences can be obtained.

Sample 4 Explanation:
Be sure to find the count modulo $998244353$.

Constraints

• $1 \le N \le 2 \times 10^5$
• All input values are integers.

样例 1 解释：
无法执行任何操作，因此只存在一种可能的最终序列：$(0)$。

样例 2 解释：
存在三种可能的最终序列：$(0)$、$(1)$、$(2)$。

样例 3 解释：
根据操作过程中所作的选择，可得到八种不同的序列。

样例 4 解释：
请务必对答案取模 $998244353$。

约束条件

• $1 \le N \le 2 \times 10^5$
• 所有输入值均为整数。