CF1528B.Kavi on Pairing Duty

Kavi has $2n$ points lying on the $OX$ axis, $i$-th of which is located at $x = i$.

Kavi considers all ways to split these $2n$ points into $n$ pairs. Among those, he is interested in good pairings, which are defined as follows:

Consider $n$ segments with ends at the points in correspondent pairs. The pairing is called good, if for every $2$ different segments $A$ and $B$ among those, at least one of the following holds:

• One of the segments $A$ and $B$ lies completely inside the other.
• $A$ and $B$ have the same length.

Consider the following example:

$A$ is a good pairing since the red segment lies completely inside the blue segment.

$B$ is a good pairing since the red and the blue segment have the same length.

$C$ is not a good pairing since none of the red or blue segments lies inside the other, neither do they have the same size.

Kavi is interested in the number of good pairings, so he wants you to find it for him. As the result can be large, find this number modulo $998244353$.

Two pairings are called different, if some two points are in one pair in some pairing and in different pairs in another.

卡维在 $OX$ 轴上有 $2n$ 个点，其中第 $i$ 个点位于 $x = i$ 处。

卡维考虑将这 $2n$ 个点划分为 $n$ 个无序点对的所有方式。在这些划分中，他特别关注“好”的配对（good pairings），其定义如下：

考虑以每一对点为端点所构成的 $n$ 条线段。若对其中任意两条不同的线段 $A$ 和 $B$，以下条件至少有一条成立，则该配对称为“好”的：

• 线段 $A$ 和 $B$ 中，有一条完全位于另一条内部；
• 线段 $A$ 和 $B$ 的长度相等。

考虑如下示例：

配对 $A$ 是“好”的，因为红色线段完全位于蓝色线段内部。

配对 $B$ 是“好”的，因为红色线段与蓝色线段长度相等。

配对 $C$ 不是“好”的，因为红色线段与蓝色线段既不互相包含，长度也不相等。

卡维希望知道“好”配对的总数，因此请你帮他计算该数目。由于结果可能很大，请对 $998244353$ 取模后输出。

若两个配对中存在某两点，在一个配对中属于同一对，而在另一个配对中不属于同一对，则称这两个配对不同。

The single line of the input contains a single integer $n$ $(1\le n \le 10^6)$.

输入仅包含一行，其中有一个整数 $n$ $(1\le n \le 10^6)$。

Print the number of good pairings modulo $998244353$.

输出好配对的数量对 $998244353$ 取模的结果。

The good pairings for the second example are:

In the third example, the good pairings are:

第二个例子中的好配对为：

第三个例子中，好配对为：