Problem Statement

There is a box containing $N$ balls numbered $1$ through $N$. Each ball is painted with a color represented as an integer, and ball $i$ is painted with color $C_i$.

Takahashi performed $N$ operations. The $k$-th operation $(1\le k\le N)$ is as follows:

• Draw one ball uniformly at random from the box and discard it. If the drawn ball has color $G_k$, gain $1$ point.

Find the probability, modulo $998244353$, that the total score over $N$ operations is $0$ points.

Definition of probability modulo $998244353$ It can be proved that the sought probability is always a rational number. Furthermore, under the constraints of this problem, when the rational number is expressed as an irreducible fraction $\frac{P}{Q}$, it can be proved that $Q {{}\not\equiv{}} 0 \pmod{998244353}$. Thus, there exists a unique integer $R$ satisfying $R \times Q \equiv P \pmod{998244353}$ and $0 \leq R \lt 998244353$. Find this $R$.

Constraints

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

Input

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

N
C_1 C_2 \ldots C_N
G_1 G_2 \ldots G_N

Output

Output the sought probability modulo $998244353$.