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 namespace std;
int main () {
    vector<pair<int, int>> l;
    int n;
    cin >> n;
    for (int i = 0; i < n; i++) {
        int a;
        cin >> a;
        l.push_back(make_pair(a, 1));
    }
    for (int i = 0; i < n; i++) {
        int a;
        cin >> a;
        l.push_back(make_pair(a, -1));
    }
    sort(l.begin(), l.end());
    long long ans = 1, mod = 1000000007, k = 0;
    for (int i = 0; i < n+n; i++) {
        if (k / l[i].second < 0) {
            ans *= abs(k);
            ans %= mod;
        }
        k += l[i].second;
    }
    cout << ans << endl;
}