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;
#define inf 1e9
#define ll long long
#define ull unsigned long long
#define M 1000000007
#define P pair<int,int>
#define PLL pair<ll,ll>
#define FOR(i,m,n) for(int i=m;i<n;i++)
#define RFOR(i,m,n) for(int i=m;i>=n;i--)
#define rep(i,n) FOR(i,0,n)
#define rrep(i,n) RFOR(i,n,0)
#define all(a) a.begin(),a.end()
const int vx[4] = {0,1,0,-1};
const int vy[4] = {1,0,-1,0};
#define PI 3.14159265


int n;
P a[1000000];
ll va,vb;
ll ans=1;

int main(){
  cin>>n;
  rep(i,n){
    int b;
    cin>>b;
    a[i] = P(b,0);
  }
  rep(i,n){
    int b;
    cin>>b;
    a[n+i] = P(b,1);
  }

  sort(a,a+2*n);



  rep(i,2*n){
    if(a[i].second==0){
      if(!vb) va++;
      else{
        ans *= vb;
        ans %= M;
        vb--;
      }
    }
    else{
      if(!va) vb++;
      else{
        ans *= va;
        ans %= M;
        va--;
      }
    }

  }

  cout<<ans<<endl;

  return 0;
}
