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>
#include<unordered_set>
#include<unordered_map>
using namespace std;
#define int long long
#define REP(i,m,n) for(int i=(m);i<(n);i++)
#define rep(i,n) REP(i,0,n)
#define pb push_back
#define all(a) a.begin(),a.end()
#define rall(c) (c).rbegin(),(c).rend()
#define mp make_pair
#define endl '\n'
typedef long long ll;
typedef pair<ll,ll> pll;
typedef long double ld;
const ll inf=1e9+7;
const ll mod=1e9+7;
signed main(){
    ll n;cin>>n;
    vector<pll>d(2*n);
    rep(i,n){
        ll a;cin>>a;
        d[i]=mp(a,0);
    }
    rep(i,n){
        ll b;cin>>b;
        d[i+n]=mp(b,1);
    }
    ll ans=1;
    ll cnta=0,cntb=0;
    sort(all(d));
    rep(i,2*n){
        if(d[i].second){
            if(cnta){
                ans=ans*cnta%inf;
                cnta--;
            }else{
                cntb++;
            }
        }else{
            if(cntb){
                ans=ans*cntb%inf;
                cntb--;
            }else{
                cnta++;
            }
        }
    }
    cout<<ans<<endl;
}