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 <map>
using namespace std;
using ll = long long;
const ll MOD = 1e9 + 7;

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

    map<int, int> coo;
    for (int i = 0; i < N; ++i) {
        int a;
        cin >> a;
        coo[a] = 1;
    }
    for (int i = 0; i < N; ++i) {
        int b;
        cin >> b;
        coo[b] = -1;
    }

    ll ans = 1;
    ll cnt = 0;
    for (auto p : coo) {
        ll k = p.second;
        if (cnt * k < 0) {
            ans *= abs(cnt);
            ans %= MOD;
        }
        cnt += k;
    }

    cout << ans << endl;
    return 0;
}
