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>
#define rep(i,n,m) for(int i=n;i<(int)(m);i++)
#define rrep(i,n,m) for(int i=((int)(n)-1);i>=m;i--)
#define all(x) (x).begin(),(x).end()
typedef long long ll;
const int INF = 1e9;
const int MOD = 1e9+7;
const ll LINF = 1e18;
using namespace std;
int main(){
    int n;
    cin>>n;
    vector<pair<int,char>> vec(2*n);
    rep(i,0,n){
        int a;
        cin>>a;
        vec[i]=make_pair(a,'a');
    }
    rep(i,0,n){
        int b;
        cin>>b;
        vec[n+i]=make_pair(b,'b');
    }
    sort(all(vec));
    
    ll cnt_a=0,cnt_b=0;
    ll ans=1;
    rep(i,0,2*n){
        if(vec[i].second=='a'){
            if(cnt_b>0){
                ans*=cnt_b;
                ans%=MOD;
                cnt_b--;
            }
            else cnt_a++;
        }
        if(vec[i].second=='b'){
            if(cnt_a>0){
                ans*=cnt_a;
                ans%=MOD;
                cnt_a--;
            }
            else cnt_b++;
        }
        //cout<<cnt_a<<" "<<cnt_b<<endl;
    }
    cout<<ans<<endl;
}
