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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mod = 1000000007
local mfl = math.floor
local function bmul(x, y)
  local x0, y0 = x % 31623, y % 31623
  local x1, y1 = mfl(x / 31623), mfl(y / 31623)
  return (x1 * y1 * 14122 + (x1 * y0 + x0 * y1) * 31623 + x0 * y0) % mod
end
local n = io.read("*n")
local t = {}
for i = 1, n do t[i] = {io.read("*n"), 1} end
for i = 1, n do t[i + n] = {io.read("*n"), 2} end
table.sort(t, function(x, y) return x[1] < y[1] end)
local ret = 1
local state = 0
for i = 1, 2 * n do
  local cur = t[i]
  if cur[2] == 1 then
    if 0 <= state then
      state = state + 1
    else
      ret = bmul(ret, -state)
      state = state + 1
    end
  else
    if state <= 0 then
      state = state - 1
    else
      ret = bmul(ret, state)
      state = state - 1
    end
  end
end
print(ret)