Score : $500$ points

Problem Statement

There are $N$ computers and $N$ sockets in a one-dimensional world. The coordinate of the $i$-th computer is $a_i$, and the coordinate of the $i$-th socket is $b_i$. It is guaranteed that these $2N$ coordinates are pairwise distinct.

Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.

In how many ways can he minimize the total length of the cables? Compute the answer modulo $10^9+7$.

Constraints

• $1 \leq N \leq 10^5$
• $0 \leq a_i, b_i \leq 10^9$
• The coordinates are integers.
• The coordinates are pairwise distinct.

Input

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

$N$

$a_1$

:

$a_N$

$b_1$

:

$b_N$

Output

Print the number of ways to minimize the total length of the cables, modulo $10^9+7$.

2
0
10
20
30

2

There are two optimal connections: $0-20, 10-30$ and $0-30, 10-20$. In both connections the total length of the cables is $40$.

3
3
10
8
7
12
5

1