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;
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define REPE(i, a, b) for (int i = (a); i <= int(b); ++i)
using LL = long long;
typedef long long LL;
//}}}
int main() {
  int n;
  vector<tuple<int, int>> a;
  scanf("%d", &n);
  REP(i, n) {
    int x;
    scanf("%d", &x);
    a.emplace_back(x, 0);
  }
  REP(i, n) {
    int x;
    scanf("%d", &x);
    a.emplace_back(x, 1);
  }
  sort(a.begin(), a.end());
  int c[2] = {};
  int ans = 1;
  const int mod = 1e9 + 7;
  for (auto &it : a) {
    int x = get<1>(it);
    if (c[x^1]) ans = 1LL * ans * (c[x^1]--) % mod;
    else c[x]++;
  }
  printf("%d\n", ans);
  return 0;
}

