Problem:
Score : 500 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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

Solution in Ruby (2.3.3) (judge verdict: Accepted)

M = 1000000007
N = gets.to_i
xs = []
(0...N).each{
  x = gets.to_i
  xs << [x, 0]
}
(0...N).each{
  x = gets.to_i
  xs << [x, 1]
}
xs.sort!

ans = 1
box = 0
bt = nil
xs.each{ |x,t|
  #p [ans, box, bt, [x,t]]
  if !bt
    box = 1
    bt = t
    next
  end
  
  if t == bt
    box += 1
  else
    ans = (ans * box) % M
    box -= 1
    if box == 0
      bt = nil
    end
  end
}
p ans