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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define int long long
#define uint unsigned int
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REPR(i, n) for (int i = (n); i >= 0; --i)
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define FORR(i, a, b) for (int i = (a); i >= (b); --i)
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define SZ(a) ((int)(a).size())
#define PB(a) push_back(a)
#define EB(...) emplace_back(__VA_ARGS__)
#define MP(a, b) make_pair(a, b)
#define MT(...) make_tuple(__VA_ARGS__)
#define Bit(n) (1LL << (n))
using namespace std;
using pii = pair<int, int>;
template <class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
template <class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
const int MOD = 1000000007;
const int INF = 1LL << 30;
const double EPS = 1e-10;

int N;

signed main() {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  
  cin >> N;
  vector<pii> v;
  REP(i, N) {
    int a;
    cin >> a;
    v.EB(a, 0);
  }
  REP(i, N) {
    int b;
    cin >> b;
    v.EB(b, 1);
  }
  sort(ALL(v));

  int s = 0;
  int ans = 1;
  for (auto p : v) {
    if (p.second == 0) {
      if (s < 0) (ans *= -s) %= MOD;
      s++;
    } else {
      if (s > 0) (ans *= s) %= MOD;
      s--;
    }
  }
  cout << ans << endl;

  return 0;
}