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
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  int n;
  cin >> n;
  vector<pair<int, int>> a;
  for (int i = 0; i < n + n; i++) {
    int x;
    cin >> x;
    a.emplace_back(x, i < n ? 1 : -1);
  }
  sort(a.begin(), a.end());
  long long ans = 1;
  const long long mod = 1e9 + 7;
  int c = 0;
  for (int i = 0; i < n + n; i++) {
    if (c * a[i].second < 0) {
      ans *= 1LL * abs(c);
      ans %= mod;
    }
    c += a[i].second;
  }
  cout << ans << endl;
  return 0;	
}