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
#include <iostream>
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>
#include <map>
#include <iomanip>
#include <stdlib.h>
#include <queue>

using namespace std;

const int nmax = 1e9 + 7;
typedef long long ll;

int main(){
  int N; cin >> N;
  vector <int> A(N), B(N);

  ll kaijou[N + 1]; kaijou[0] = 1;
  for (ll i = 1; i < N + 1; i++){
    kaijou[i] = kaijou[i - 1] * i;
    kaijou[i] %= nmax;
  }
  
  vector < pair<int, int> > AB(2 * N);

  for (int i = 0; i < 2 * N; i++){
    int K; cin >> K;
    if (i < N){
      AB[i] = make_pair(K, 1);
    }else{
      AB[i] = make_pair(K, 2);
    }
  }
  sort(AB.begin(), AB.end());

  ll cnt = 0, ans = 1;
  for (int i = 0; i < 2 * N; i++){
    if (AB[i].second == 1){
      if (cnt > 0){
        ans = ans * cnt;
      }
      cnt--;
    }else{
      if (cnt < 0){
        ans = ans * (-1 * cnt);
      }
      cnt++;
    }
    ans = ans % nmax;
  }
  
  cout << ans << endl;
  

  return 0;
}
