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 <vector>
#include <algorithm>

using namespace std;

const int MOD = 1000000007;

int main(){
    int N;
    while(cin >> N){
        vector<pair<int,int>> p(2*N);
        for(int i=0;i<2*N;i++){
            cin >> p[i].first;
            p[i].second = (i < N ? 1 : -1);
        }
        sort(p.begin(), p.end());
        int sum = 0;
        long long res = 1;
        for(const auto& pr : p){
            if(sum * pr.second < 0){
                res *= abs(sum);
                res %= MOD;
            }
            sum += pr.second;
        }
        cout << res << endl;
    }
}