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>
#define FOR(i, a, b) for(int i=(int)(a); i!=(int)(b); i++)
#define RFOR(i, a, b) for(int i=(int)(a); i!=(int)(b); i--)
#define REP(i, n) FOR(i, 0, n)
using namespace std;
using ll = long long;

constexpr int mod = 1e9+7;

int main(){
  int n; cin >> n;
  int a[n], b[n];
  pair<int, int> c[2*n];
  REP(i, n){
    cin >> a[i];
    c[i] = {a[i], 0};
  }
  REP(i, n){
    cin >> b[i];
    c[i+n] = {b[i], 1};
  }

  sort(c, c+2*n);

  ll ans = 1, com = 0, ele = 0;
  REP(i, 2*n){
    if(c[i].second == 0){
      if(ele >= 1){
        (ans *= ele) %= mod;
        ele--;
      }
      else{
        com++;
      }
    }
    else{
      if(com >= 1){
        (ans *= com) %= mod;
        com--;
      }
      else{
        ele++;
      }
    }
  }
  cout << ans << endl;
  
  return 0;
}
