Problem Statement

You are going to create $N$ sequences of length $3$, satisfying the following conditions.

• For each of $k = 1,2,3$, the following holds:
• Among the $k$-th elements of the sequences, each integer from $1$ through $N$ appears exactly once.

For this sequence of sequences, define sequences $a=(a_1,a_2,\ldots,a_N)$ and $b=(b_1,b_2,\ldots,b_N)$ as follows.

• Let $s_i$ be the $i$-th sequence, and let $t_i$ be the reverse of the $i$-th sequence. When all of these are sorted in lexicographical order, $s_i$ comes $a_i$-th, and $t_i$ comes $b_i$-th.
• Here, if there are identical sequences among the $2N$ sequences, $a$ and $b$ are not defined.

Therefore, if $a$ and $b$ are defined, each integer from $1$ through $2N$ appears exactly once in the concatenation of $a$ and $b$.

You are given sequences $A$ and $B$ of length $N$, where each element of $A$ is an integer between $1$ and $2N$, and each element of $B$ is either an integer between $1$ and $2N$ or $-1$. Also, in the concatenation of $A$ and $B$, each integer other than $-1$ appears at most once.

How many pairs of sequences $a,b$ are there such that $a$ and $b$ are defined and the following holds for each integer $i$ from $1$ through $N$?

• $a_i = A_i$.
• $b_i = B_i$ if $B_i \neq -1$.

Find the count modulo $998244353$.

Constraints

• $2 \leq N \leq 3000$
• $1 \leq A_i \leq 2N$
• $1 \leq B_i \leq 2N$ or $B_i = -1$.
• In the concatenation of $A$ and $B$, each integer other than $-1$ appears at most once. That is,
• $A_i \neq A_j$ if $i \neq j$.
  • $B_i \neq B_j$ if $i \neq j$ and $B_i,B_j \neq -1$.
  • $A_i \neq B_j$.
• All input values are integers.

Input

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

N
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_N

Output

Print the count modulo $998244353$.