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;
typedef pair<int,int> P;
constexpr double EPS = 1e-12;
constexpr int INF = numeric_limits<int>::max()/2;
constexpr int MOD = 1e9+7;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n;cin>>n;
    vector<P> v;
    for(int i=0;i<n;i++){
      ll a;cin>>a;
      v.push_back(P(a,0));
    }
    for(int i=0;i<n;i++){
      ll b;cin>>b;
      v.push_back(P(b,1));
    }
    sort(v.begin(),v.end());
    ll acnt=0,bcnt=0;
    ll res=1;
    for(int i=0;i<2*n;i++){
      if(v[i].second==0){
        if(bcnt){
          res *= bcnt;
          res %= MOD;
          bcnt--;
          continue;
        }
        acnt++;
      }
      else{
        if(acnt){
          res *= acnt;
          res %= MOD;
          acnt--;
          continue;
        }
        bcnt++;
      }
    }
    cout<<res<<endl;
}
