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 <cmath>
#include <algorithm>
typedef long long ll;
using namespace std;
typedef pair<ll,ll> P;
ll n;
vector<P> x;
const ll mod = 1e9 + 7;
int main() {
  cin >> n;
  for(int i = 0; i < n; i++) {
    ll a;
    cin >> a;
    x.push_back(P(a,1));
  }
  for(int i = 0; i < n; i++) {
    ll b;
    cin >> b;
    x.push_back(P(b,-1));
  }
  sort(x.begin(),x.end());
  ll c = 0;
  ll ans = 1;
  for(int i = 0; i < x.size(); i++) {
    if((c != 0) && (x[i].second > 0) != (c > 0)) ans = ans *  abs(c) % mod;
    c += x[i].second;
  }

  cout << ans << endl;
}
    
