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 <assert.h>
#include <limits.h>
#include <algorithm>
#include <bitset>
#include <cctype>
#include <cmath>
#include <complex>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>

using ll = long long;
using P = std::pair<ll, ll>;

#define rep(i, a, b) for (ll(i) = (a); i < (b); i++)
#define all(i) i.begin(), i.end()
#define debug(i) std::cerr << "debug "<< i << std::endl

// const ll MOD = 998244353;
const ll MOD = 1e9 + 7;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);
  //問題文中の添え字が0-indexか1-indexか確認!

  ll n,ans=1;
  std::cin>>n;

  ll pool[2]={0,0};

  std::vector<P> a(2*n);

  rep(i,0,n){
    ll temp;
    std::cin>>temp;
    a[i]=P(temp,0);
  }
  rep(i, 0, n) {
    ll temp;
    std::cin >> temp;
    a[n+i] = P(temp, 1);
  }

  std::sort(all(a));

  rep(i,0,2*n){
    ll type=a[i].second;
    if(pool[type^1]==0){
      pool[type]++;
    }else{
      ans=(ans*pool[type^1])%MOD;
      pool[type^1]--;
    }
  }

  std::cout<<ans;

  return 0;
}
