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>
using i64 = long long;

int main() {
    constexpr i64 mod = 1000000007;
    int n;
    std::cin >> n;
    std::vector<std::pair<int, int>> v;
    for (int i = 0; i < 2 * n; i++) {
        int a;
        std::cin >> a;
        v.emplace_back(a, i / n);
    }
    std::sort(v.begin(), v.end());

    int t[] { 0, 0 };
    i64 ret = 1;
    for (auto e : v) {
        auto &c = t[!e.second];
        if (c) ret = ret * c-- % mod;
        else t[e.second]++;
    }

    std::cout << ret << std::endl;

    return 0;
}
