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 Python (3.4.3) (judge verdict: Wrong Answer)

import math
MOD = 10**9 + 7
n = int(input())
a_s = []; b_s = []
for i in range(n):
    a_s.append(int(input()))
for i in range(n):
    b_s.append(int(input()))
a_s.sort()
b_s.sort()
match = []
a_itr = 0; b_itr = 0
while True:
    cnt = 0
    if a_s[a_itr] < b_s[b_itr]:
        while a_itr < n and a_s[a_itr] <= b_s[b_itr]:
            a_itr += 1
            cnt += 1
        match.append(cnt)
        b_itr += cnt
    elif b_s[b_itr] < a_s[a_itr]:
        while b_itr < n and b_s[b_itr] <= a_s[a_itr]:
            b_itr += 1
            cnt += 1
        match.append(cnt)
        a_itr += cnt
    elif b_s[b_itr] == a_s[a_itr]:
        a_itr += 1
        b_itr += 1
    if a_itr >= n or b_itr >= n:
        break
    
ans = 1
cnt = 0
for item in match:
    ans *= math.factorial(item) % MOD
    ans %= MOD
print(ans)