A sequence of $n$ numbers, $S = (s_1, s_2, \dots, s_n)$, is said to be non-decreasing if and only if $s_i \leq s_{i+1}$ holds for every $i$ $(1 \leq i \leq n - 1)$.

Given are non-decreasing sequences of $N$ integers each: $A = (a_1, a_2, \dots, a_N)$ and $B = (b_1, b_2, \dots, b_N)$.  
Consider a non-decreasing sequence of $N$ integers, $C = (c_1, c_2, \dots, c_N)$, that satisfies the following condition:

-   $a_i \leq c_i \leq b_i$ for every $i$ $(1 \leq i \leq N)$.

Find the number, modulo $998244353$, of sequences that can be $C$.

Input is given from Standard Input in the following format:

```
$N$
$a_1$ $a_2$ $\dots$ $a_N$
$b_1$ $b_2$ $\dots$ $b_N$
```

Print the number, modulo $998244353$, of sequences that can be $C$.

-   $1 \leq N \leq 3000$
-   $0 \leq a_i \leq b_i \leq 3000$ $(1 \leq i \leq N)$
-   The sequences $A$ and $B$ are non-decreasing.
-   All values in input are integers.

5

There are five sequences that can be C, as follows.

• (1,1)
• (1,2)
• (1,3)
• (2,2)
• (2,3)

Note that (2,1) does not satisfy the condition since it is not non-decreasing.

1

There is one sequence that can be C, as follows.

• (2,2,2)