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 <bits/stdc++.h>
using namespace std;
long long MOD = 1000000007;
int main(){
  int N;
  cin >> N;
  vector<int> a(N);
  for (int i = 0; i < N; i++){
    cin >> a[i];
  }
  vector<int> b(N);
  for (int i = 0; i < N; i++){
    cin >> b[i];
  }
  vector<pair<int, char>> P(N * 2);
  for (int i = 0; i < N; i++){
    P[i] = make_pair(a[i], 'a');
  }
  for (int i = N; i < N * 2; i++){
    P[i] = make_pair(b[i - N], 'b');
  }
  sort(P.begin(), P.end());
  long long ans = 1;
  int cnt = 0;
  for (int i = 0; i < N * 2; i++){
    if (P[i].second == 'a'){
      if (cnt < 0){
        ans *= -cnt;
        ans %= MOD;
      }
      cnt++;
    } else {
      if (cnt > 0){
        ans *= cnt;
        ans %= MOD;
      }
      cnt--;
    }
  }
  cout << ans << endl;
}