Problem Statement

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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

• $1 ≤ N ≤ 10^5$
• $0 ≤ a_i, b_i ≤ 10^9$
• 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 $10^9+7$.

Sample Input 1

2
0
10
20
30

Sample Output 1

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 $40$.

Sample Input 2

3
3
10
8
7
12
5

Sample Output 2

1