Problem Statement

There are $N customers named 1,\ldots,N visiting a shop. Customer i arrives at time A_i$ and leaves at time B_i. The queue order is first in-first out, so A_i are increasing, and B_i are increasing. Additionally, all A_i and B_i are pairwise distinct.
At the entrance there's a list of visitors to put their names in. Each customer will write down their name next in the list exactly once, either when they arrive or when they leave. How many different orders of names can there be in the end?
Find the count modulo 998\,244\,353.

Input

Input is given from Standard Input in the following format:
N
A_1 B_1
$\vdots$
A_N B_N

Output

Print the answer.

Constraints

• $1 \leq N \leq 5 \cdot 10^5$
• $1 \leq A_i < B_i \leq 2N$
• $A_i < A_{i + 1} (1 \leq i \leq N - 1)$
• $B_i < B_{i + 1} (1 \leq i \leq N - 1)$
• $A_i \neq B_j (i \neq j)$
• All values in the input are integers.

Sample Input 1

3
1 3
2 5
4 6

Sample Output 1

3

The possible orders are (1, 2, 3), (2, 1, 3), (1, 3, 2).

Sample Input 2

4
1 2
3 4
5 6
7 8

Sample Output 2

1

The only possible order is (1, 2, 3, 4).

见题面 Input 部分

见题面 Output 部分