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 fs first
#define sc second
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ALL(A) A.begin(),A.end()
#define RALL(A) A.rbegin(),A.rend()
typedef long long LL;
typedef pair<LL,LL> P;
const LL mod=1000000007;
const LL LINF=1LL<<60;
const int INF=1<<30;
int dx[]={1,0,-1,0};
int dy[]={0,1,0,-1};
 

int main(){
    int n;cin >> n;
    vector<P> a;
    for (int i = 0; i < n; i++) {
        LL k;cin >> k;
        a.pb(mp(k,0LL));
    }
    for (int i = 0; i < n; i++) {
        LL k;cin >> k;
        a.pb(mp(k,1LL));
    }
    sort(ALL(a));
    LL sa=0,sb=0,ans=1;
    for (int i = 0; i < 2*n; i++) {
        if(a[i].sc==0){
            if(sb>0){
                ans = ans * sb % mod;
                sb--;
            }
            else sa++;
        }
        else{
            if(sa>0){
                ans = ans * sa % mod;
                sa--;
            }
            else sb++;
        }
    }
    cout << ans%mod << endl;
    return 0;
}
