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<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
using namespace std;


long long N;
pair<long long, long long> point[200000];
long long mod = 1000000007;

int main(){
    cin >> N;
    for(int i = 0; i < N; i++){
        long long a;
        cin >> a;
        point[i] = make_pair(a, -1);
    }
    for(int i = 0; i < N; i++){
        long long b;
        cin >> b;
        point[i+N] = make_pair(b, 1);
    }
    sort(point, point+2*N);

    long long ans = 1, in_hand = 0;
    for(int i = 0; i < 2*N; i++){
        long long  coord, kind;
        coord = point[i].first;
        kind = point[i].second;
        if(in_hand * kind < 0){
            ans *= abs(in_hand);
            ans %= mod;
        }
        in_hand += kind;
    }
    cout << ans << endl;
}