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 <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
typedef long long ll;
using namespace std;
const ll MOD = 1e9 + 7;

int main(){
  int N;
  cin >> N;
  pair<int, char> a[2 * N];
  for(int i = 0; i < N; i++){
    int c; cin >> c;
    a[i] = pair<int, char>(c, 'a');
  }
  for(int i = N; i < 2 * N; i++){
    int c; cin >> c;
    a[i] = pair<int, char>(c, 'b');
  }

  sort(a, a + 2 * N);

  ll cnta = 0;
  ll cntb = 0;
  ll ans = 1;
  for(int i = 0; i < 2 * N; i++){
    if(a[i].second == 'a'){
      if(cntb == 0){
        cnta++;
      } else {
        ans *= cntb;
        cntb--;
      }
    }
    else{
      if(cnta == 0){
        cntb++;
      } else {
        ans *= cnta;
        cnta--;
      }
    }

    ans %= MOD;
  }

  cout << ans << endl;
  return 0;
}