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,a,b) for(int i=int(a);i<int(b);++i)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
int INF = (1LL << 30) - 1;
int MOD = 1e9+7;
int main(){
    int N;
    cin >> N;
    vector<int>A(N),B(N);
    vector<P>V(N*2);
    rep(i,0,N){
        cin >> A[i];
        V[i] = P(A[i], 0);
    }
    rep(i,0,N){
        cin >> B[i];
        V[i + N] = P(B[i], 1);
    } 
    
    sort(V.begin(), V.end());
    ll ans = 1;
    int cnt = 0;
    rep(i,0,N*2){
        if(V[i].second)ans *= (cnt < 0 ? -cnt : 1);
        else ans *= (cnt > 0 ? cnt : 1);
        ans %= MOD; 
        cnt += V[i].second ? 1 : -1;
    }   
    cout << ans << endl;
}