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 <utility>
#include <vector>
#include <algorithm>
#define llint long long
#define mod 1000000007

using namespace std;

llint n;
vector<pair<llint, llint> > vec;

int main(void)
{
  cin >> n;
  llint x;
  for(int i = 1; i <= n; i++){
    cin >> x;
    vec.push_back(make_pair(x, 1));
  }
   for(int i = 1; i <= n; i++){
    cin >> x;
    vec.push_back(make_pair(x, 2));
  }
  sort(vec.begin(), vec.end());
  
  llint cnt = 0, cnt2 = 0, ans = 1;
  for(int i = 0; i < vec.size(); i++){
    if(vec[i].second == 1){
      if(cnt2 == 0) cnt++;
      else ans *= cnt2, ans %= mod, cnt2--;
    }
    else{
      if(cnt == 0) cnt2++;
      else ans *= cnt, ans %= mod, cnt--;
    }
  }
  cout << ans << endl;
  return 0;
}
