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 <set>
#include <map>
#include <queue>
#include <deque>
#include <algorithm>
using namespace std;
using ll = long long;

const ll MOD = 1e9 + 7;

int main() {
  int N;
  cin >> N;
  vector<pair<ll,int>> ps;
  for (int t = 0; t < 2; t++) {
    for (int i = 0; i < N; i++) {
      ll a;
      cin >> a;
      ps.emplace_back(a, t);
    }
  }
  sort(ps.begin(), ps.end());
  vector<int> acc(2, 0);
  ll res = 1;
  for (auto p: ps) {
    int t = p.second;
    if (acc[t^1] > 0) {
      res = res * acc[t^1] % MOD;
      --acc[t^1];
    } else {
      ++acc[t];
    }
  }
  cout << res << endl;
  return 0;
}
