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;
typedef long long ll;
#define mp make_pair
#define pb push_back
#define rep(i,n) for(int i=0;i<n;i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)

ll mod = ((ll) (1e9+7));
int main(){
  ios::sync_with_stdio(false);
  cin.tie(0);
  ll N;
  cin >> N;
  ll a[N],b[N];
  rep(i,N) cin >> a[i];
  rep(i,N) cin >> b[i];
  pair<ll, ll> h[2*N];//(座標), PC:0 cable:1
  rep(i,N){
    h[i] = mp(a[i], 0);
  }
  rep(i,N){
    h[i+N] = mp(b[i], 1);
  }
  sort(h, h+2*N);
  ll count=0; //pc+ cable-
  //  ll sum=0;
  ll ans=1LL;
  rep(i,2*N){
    if(h[i].second==0){
      count++;
      if(count <=0){
	ans = (ans* abs(count-1))%mod;
      }
    }else{
      count--;
      if(count>=0){
	ans = (ans* abs(count+1))%mod;
      }
    }
  }
  cout << ans << endl;
  return 0;
    

}
