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 <cmath>
#include <algorithm>
#include <vector>
#include <iostream>
using namespace std;
int main() {
    int n; cin >> n;
    vector<pair<int, int> > x;
    for (int i = 0; i < n; i++) { int a; cin >> a; x.push_back(make_pair(a, -1)); }
    for (int i = 0; i < n; i++) { int a; cin >> a; x.push_back(make_pair(a, 1)); }
    sort(x.begin(), x.end());
    int c = 0;
    long long ans = 1;
    const int M = (int)1e9 + 7;
    for (auto p : x) {
        if (c != 0 && ((p.second > 0) != (c > 0))) ans = ans * abs(c) % M;
        c += p.second;
    }
    cout << ans << endl;
}
