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)

MOD = 10**9 + 7
def solve(n, a, b):
    v = []
    for i in range(n):
        v.append((a[i], 1))
        v.append((b[i], -1))
    v = sorted(v, key=lambda _:_[0])
    ans, cnt = 1, 0
    for _, t in v:
        cnt += t
        if cnt != 0:
            ans = (ans * abs(cnt)) % MOD
    return ans

n = int(input())
a = [int(input()) for i in range(n)]
b = [int(input()) for i in range(n)]
print(solve(n, a, b))