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: Wrong Answer)

n = gets.to_i
a = n.times.map{gets.to_i}.sort
b = n.times.map{gets.to_i}.sort

$mod = 10**9+7
$fact = Array.new(100010,1)

for i in 2..100000
  $fact[i] = $fact[i-1]*i%$mod
end

def clac(a,b,n)
  ret = 1
  p = 0
  for i in 0..n-1
    if a[i] > b[p]
      ret *= $fact[i-p]
      ret %= $mod
      p = i
    end
  end
  ret *= $fact[n-p]
  ret %= $mod
  return ret
end

p (clac(a,b,n)*clac(b,a,n))%$mod