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 <utility>
#include <vector>
#include <algorithm>
using namespace std;

using int64 = long long;

const int64 MOD = 1e9 + 7;

int main() {
    int N;
    cin >> N;

    vector<pair<int, int>> vec;
    for (int i = 0; i < N; i++) {
        int a;
        cin >> a;
        vec.emplace_back(a, -1);
    }
    for (int i = 0; i < N; i++) {
        int b;
        cin >> b;
        vec.emplace_back(b, 1);
    }
    sort(vec.begin(), vec.end());

    int64 ans = 1;
    int64 h = 0;
    for (int i = 0; i < 2 * N; i++) {
        int sec = vec[i].second;
        if (h * sec < 0) (ans *= abs(h)) %= MOD;
        h += sec;
    }
    cout << ans << endl;

    return 0;
}