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<algorithm>
using namespace std;
using lli = long long int;
int main(){
  int n;
  std::cin >> n;
  vector<int> a(n), b(n);
  for (int i = 0; i < n; i++) std::cin >> a[i];
  for (int i = 0; i < n; i++) std::cin >> b[i];
  sort(a.begin(), a.end());
  sort(b.begin(), b.end());

  lli ans = 1, mod = 1e9 + 7;
  for (int i = 0; i < n; i++) {
    int pos, prev;
    if(a[i] < b[i]){
      pos  = *lower_bound(b.begin() + i, b.end(), a[i]);
      prev = lower_bound(a.begin(), a.end(), pos) - a.begin() - i;
    }else{
      pos  = *lower_bound(a.begin() + i, a.end(), b[i]);
      prev = lower_bound(b.begin(), b.end(), pos) - b.begin() - i;
    }
    ans *= prev;
    ans %= mod;
  }
  std::cout << ans << std::endl;
  return 0;
}
