Problem Statement

$(2N+1)$ people are forming two rows to take a group photograph. There are $N$ people in the front row; the $i$-th of them has a height of $A_i$. There are $(N+1)$ people in the back row; the $i$-th of them has a height of $B_i$. It is guaranteed that the heights of the $(2N+1)$ people are distinct. Within each row, we can freely rearrange the people.

Suppose that the heights of the people in the front row are $a_1,a_2,\dots,a_N$ from the left, and those in the back row are $b_1,b_2,\dots,b_{N+1}$ from the left. This arrangement is said to be good if all of the following conditions are satisfied:

• $a_i < b_i$ or $a_{i-1} < b_i$ for all $i\ (2 \leq i \leq N)$.
• $a_1 < b_1$.
• $a_N < b_{N+1}$.

Among the $N!$ ways to rearrange the front row, how many of them, modulo $998244353$, are such ways that we can rearrange the back row to make the arrangement good?

Constraints

• $1\leq N \leq 5000$
• $1 \leq A_i,B_i \leq 10^9$
• $A_i \neq A_j\ (1 \leq i < j \leq N)$
• $B_i \neq B_j\ (1 \leq i < j \leq N+1)$
• $A_i \neq B_j\ (1 \leq i \leq N, 1 \leq j \leq N+1)$
• All input values are integers.

Input

The 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+1}

Output

Print the answer as an integer.