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 <cstdio>
#include <cstdint>
#include <vector>
#include <algorithm>
#include <utility>

int main() {
  size_t N;
  scanf("%zu", &N);

  std::vector<std::pair<int, int>> a(2*N);
  for (size_t i=0; i<N; ++i) {
    scanf("%d", &a[i].first);
    a[i].second = -1;
  }

  for (size_t i=0; i<N; ++i) {
    scanf("%d", &a[N+i].first);
    a[N+i].second = 1;
  }

  std::sort(a.begin(), a.end());

  constexpr intmax_t mod=1e9+7;
  intmax_t res=1, cur=0;
  for (size_t i=0; i<2*N; ++i) {
    if (cur != 0 && ((cur < 0) != (a[i].second < 0))) {
      res = res*std::abs(cur) % mod;
    }
    cur += a[i].second;
  }
  printf("%jd\n", res);
}
