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 fi first
#define se second
#define mp make_pair
#define pb push_back
#define all(x) x.begin(),x.end()
#define dbg(x) cout<<#x<<":"<<x<<endl
typedef long long ll;
typedef pair<ll,ll> P;
typedef pair<ll,P> PP;

int main(){
  ll n,p=1e9+7;
  cin>>n;
  vector<P> v;
  for(int i=0;i<n;i++){
    ll a;
    cin>>a;
    v.pb(P(a,1));
  }
  for(int i=0;i<n;i++){
    ll b;
    cin>>b;
    v.pb(P(b,-1));
  }
  sort(all(v));
  
  vector<ll> lap;
  ll sum=0;
  for(int i=0;i<v.size();i++){
    ll tmp=sum;
    sum+=v[i].second;
    if(sum==0)continue;
    if(abs(tmp)<abs(sum))lap.pb(abs(sum));
  }
  
  ll ans=1;
  for(int i=0;i<lap.size();i++){
    ans*=lap[i];
    ans%=p;
  }
  cout<<ans<<endl;
  
  return 0;
}
