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;
const int MOD = 1e9 + 7;

int main() {
    int n; cin >> n;
    vector<int> a(n, 0), b(n, 0);

    for(int i = 0; i < n; ++i)
        cin >> a[i];

    for(int i = 0; i < n; ++i)
        cin >> b[i];

    sort(a.begin(), a.end());
    sort(b.begin(), b.end());

    int ans = 1;
    
    set<int> s;
    for(int i = 0; i < n; ++i)
        s.insert(b[i]);
    
    auto many = [&] (int x, int y) -> int {
        auto lf = lower_bound(a.begin(), a.end(), x);
        if(lf == a.end())
            return 0;
        auto rt = upper_bound(a.begin(), a.end(), y);
        rt--;
        return (rt - lf + 1);
    };

    for(int i = 0; i < n; ++i) {
        int x = *(s.begin());
        s.erase(s.begin());
        ans = 1LL * ans * (many(min(x, a[i]), max(x, a[i]))) % MOD;
    }

    cout << ans << "\n";
}