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.

Examples

Input

2
0
10
20
30


Output

2


Input

3
3
10
8
7
12
5


Output

1
/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author ei13333
 */

#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;

class TaskA
{
public:
  void solve(istream &cin, ostream &cout)
  {
    int N;
    cin >> N;
    vector < pair < int, int > > D(N + N);
    for(int i = 0; i < N; i++) {
      cin >> D[i].first;
      D[i].second = 0;
    }
    for(int i = 0; i < N; i++) {
      cin >> D[i + N].first;
      D[i + N].second = 1;
    }
    sort(begin(D), end(D));

    int inA = 0, inB = 0;
    int64 ret = 1;

    for(auto &p : D) {
      if(p.second == 0) {
        if(inB == 0) {
          ++inA;
        } else {
          (ret *= inB--) %= mod;
        }
      } else {
        if(inA == 0) {
          ++inB;
        } else {
          (ret *= inA--) %= mod;
        }
      }
    }

    cout << ret << endl;
  }
};


int main()
{
  TaskA solver;
  std::istream &in(std::cin);
  std::ostream &out(std::cout);
  solver.solve(in, out);
  return (0);
}
