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 double db;
typedef pair<ll,ll> P;
#define ft first
#define sd second
#define mp make_pair
#define fr(i,n) for(int i=0;i<n;i++)
#define Fr(i,n) for(int i=0;i++<n;)
#define ifr(i,n) for(int i=n-1;i>=0;i--)
#define iFr(i,n) for(int i=n;i>0;i--)

const ll MOD=1e9+7;

ll ad(ll x,ll y=0){
  return (x+y)%MOD;
}

ll mlt(ll x,ll y=1){
  return (x*y)%MOD;
}

int main(){
  ll n,a,cnt=0,ans=1;
  P c[200010];
  bool f;
  cin>>n;
  fr(i,n){cin>>a;c[i]=mp(a,0);}
  fr(i,n){cin>>a;c[n+i]=mp(a,1);}
  sort(c,c+2*n);
  fr(i,2*n){
    if(cnt==0){f=c[i].sd;cnt++;}
    else if(c[i].sd^f){
      ans=mlt(ans,cnt);
      cnt--;
    }
    else cnt++;
  }
  cout<<ans<<endl;
}