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 ≤ 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