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;
using ll = long long;
using ull = unsigned long long;
const ll MOD = 1e9+7;
pair<int,int> p[200010];

int main(){
  ios::sync_with_stdio(false);
  cin.tie(0);

  ll ans = 1;
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> p[i].first;
    p[i].second = 1;
  }
  for (int i = 0; i < n; i++) {
    cin >> p[i + n].first;
  }
  sort(p,p+2*n);
  ll ct1 = 0, ct0 = 0;
  for (int i = 0; i < 2 * n; i++) {
    if (p[i].second == 0) {
      if (ct1 == 0) {
        ct0++;
      } else {
        ans *= ct1--;
        ans %= MOD;
      }
    } else {
      if (ct0 == 0) {
        ct1++;
      } else {
        ans *= ct0--;
        ans %= MOD;
      }
    }
  }
  cout << ans << endl;
  return 0;
}
