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 lint = long long;
template<class T = int> using V  = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T, class H> void rsz(V<T> &v, H h) { v.resize(h); }
template<class T, class H, class... R> void rsz(V<T> &v, H h, R... r) { v.resize(h); for (auto&& i : v) rsz(i, r...); }
using P = pair<int, int>;
const lint mod = 1e9 + 7;
lint emod(lint a) { return (a % mod + mod) % mod; }

int main() {
  cin.tie(NULL); ios::sync_with_stdio(false);
  int n; cin >> n;
  V<P> a(2 * n);
  for (int i = 0; i < 2 * n; i++) {
    int x; cin >> x;
    a[i] = P(x, i / n);
  }
  sort(a.begin(), a.end());
  lint res = 1;
  int t = 0;
  for (int i = 0; i < 2 * n; i++) {
    if (a[i].second == 1) {
      if (t < 0) res = res * -t % mod;
      t++;
    } else {
      if (t > 0) res = res * t % mod;
      t--;
    }
  }
  cout << emod(res) << '\n';
}