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 long long MOD = 1000000007;

int main() {
    int n;
    cin >> n;
    vector<pair<int, int>> v(n * 2);
    for (int i = 0; i < n; i++) {
        int a;
        cin >> a;
        v.at(i) = make_pair(a, 0);
    }
    for (int i = n; i < n * 2; i++) {
        int b;
        cin >> b;
        v.at(i) = make_pair(b, 1);
    }
    sort(v.begin(), v.end());

    vector<int> cnt(2);
    long long ans = 1;
    for (int i = 0; i < n * 2; i++) {
        int kind = v.at(i).second;
        if (cnt.at(kind ^ 1) > 0) {
            ans *= cnt.at(kind ^ 1);
            ans %= MOD;
            cnt.at(kind ^ 1)--;
        }
        else cnt.at(kind)++;
    }
    cout << ans << endl;
}