AT_arc226_a.Meeting Division

There are $N$ meetings numbered $1,2,\dots,N$. Meeting $i$ starts at time $S_i$ and ends at time $T_i$.

Takahashi and Aoki are going to assign exactly one of themselves to each meeting as the person in charge. The same person cannot be in charge of two meetings that overlap for a positive length of time. More formally, the same person can be in charge of meetings $i$ and $j$ only if $T_i \le S_j$ or $T_j \le S_i$.

Find the number, modulo $998244353$, of ways to assign the people in charge that satisfy the conditions.

有 $N$ 场会议，编号为 $1,2,\dots,N$。第 $i$ 场会议在时刻 $S_i$ 开始，在时刻 $T_i$ 结束。

高桥和青木将为每场会议恰好指定其中一人作为负责人。同一人不能同时负责两场在时间上存在正长度重叠的会议。更准确地说，同一人可以同时负责会议 $i$ 和会议 $j$，当且仅当 $T_i \le S_j$ 或 $T_j \le S_i$。

求满足上述条件的负责人分配方案数（对 $998244353$ 取模）。

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

$N$
$S_1$ $T_1$
$S_2$ $T_2$
$\vdots$
$S_N$ $T_N$

输入从标准输入中按以下格式给出：

$N$
$S_1$ $T_1$
$S_2$ $T_2$
$\vdots$
$S_N$ $T_N$

Output the number, modulo $998244353$, of ways to assign the people in charge that satisfy the conditions.

输出满足条件的负责人分配方案数对 $998244353$ 取模的结果。

Sample 1 Explanation:
The following four assignments satisfy the conditions:

• Takahashi is in charge of meetings $1,3$, and Aoki is in charge of meeting $2$.
• Takahashi is in charge of meeting $1$, and Aoki is in charge of meetings $2,3$.
• Takahashi is in charge of meetings $2,3$, and Aoki is in charge of meeting $1$.
• Takahashi is in charge of meeting $2$, and Aoki is in charge of meetings $1,3$.

Sample 2 Explanation:
Zero assignments satisfy the conditions.

Constraints

• $1 \le N \le 3 \times 10^5$
• $1 \le S_i < T_i \le 2N$
• $S_1,T_1,S_2,T_2,\dots,S_N,T_N$ are all different.
• All input values are integers.

样例 1 解释：
以下四种分配方案满足条件：

• 高桥负责会议 $1,3$，青木负责会议 $2$。
• 高桥负责会议 $1$，青木负责会议 $2,3$。
• 高桥负责会议 $2,3$，青木负责会议 $1$。
• 高桥负责会议 $2$，青木负责会议 $1,3$。

样例 2 解释：
不存在满足条件的分配方案。

约束条件

• $1 \le N \le 3 \times 10^5$
• $1 \le S_i < T_i \le 2N$
• $S_1,T_1,S_2,T_2,\dots,S_N,T_N$ 互不相同。
• 所有输入值均为整数。