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 <algorithm>

using namespace std;

typedef struct {
  int type;
  int x;
} S;

int64_t MOD = 1000000007;

int main() {
  int N;
  cin >> N;

  vector<S> v;

  for (int i = 0; i < N; i++) {
    int a;
    cin >> a;
    v.push_back({ 0, a });
  }

  for (int i = 0; i < N; i++) {
    int b;
    cin >> b;
    v.push_back({ 1, b });
  }

  sort(v.begin(), v.end(), [](S a, S b) { return a.x < b.x; });

  int cnt0 = 0;
  int cnt1 = 0;
  int64_t ans = 1;
  for (auto i: v) {
    if (i.type == 0) {
      if (cnt1 == 0) {
        cnt0 += 1;
      } else {
        ans = ans * cnt1 % MOD;
        cnt1 -= 1;
      }
    } else {
      if (cnt0 == 0) {
        cnt1 += 1;
      } else {
        ans = ans * cnt0 % MOD;
        cnt0 -= 1;
      }
    }
  }

  cout << ans << endl;
}