Problem Statement

There are $N cards numbered 1,\ldots,N. Card i has P_i$ written on the front and Q_i written on the back.
Here, $P=(P_1,\ldots,P_N)$ and $Q=(Q_1,\ldots,Q_N)$ are permutations of $(1, 2, \dots, N)$.
How many ways are there to choose some of the N cards such that the following condition is satisfied? Find the count modulo 998244353.
Condition: every number $1,2,\ldots,N$ is written on at least one of the chosen cards.

Input

Input is given from Standard Input in the following format:
N
$P_1 P_2 \ldots P_N$
$Q_1 Q_2 \ldots Q_N$

Output

Print the answer.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq P_i,Q_i \leq N$
• P and Q are permutations of $(1, 2, \dots, N)$.
• All values in input are integers.

Sample Input 1

3
1 2 3
2 1 3

Sample Output 1

3

For example, if you choose Cards 1 and 3, then 1 is written on the front of Card 1, 2 on the back of Card 1, and 3 on the front of Card 3, so this combination satisfies the condition.
There are 3 ways to choose cards satisfying the condition: {1,3},{2,3},{1,2,3}.

Sample Input 2

5
2 3 5 4 1
4 2 1 3 5

Sample Output 2

12

Sample Input 3

8
1 2 3 4 5 6 7 8
1 2 3 4 5 6 7 8

Sample Output 3

1

见题面 Input 部分

见题面 Output 部分