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;
typedef long long ll;

int N;
const int MAX_N = 2.0e5 + 100;
pair<int, char> ab[MAX_N];
const int MOD = 1.0e9 + 7;

int main() {
    cin >> N;
    for (int i = 0; i < 2*N; i++) {
        int ab_in;
        cin >> ab_in;
        if (i < N) ab[i] = make_pair(ab_in, 'a');
        else ab[i] = make_pair(ab_in, 'b');
    }

    sort(ab, ab+2*N);

  
    ll ans = 1;
    ll a = 0, b = 0;
    for (int i = 0; i < 2*N; i++) {
        if (ab[i].second == 'a') a++;
        else b++;

        if (a > 0 && b > 0) {
            ans = ((ans*a) % MOD * b) % MOD;
            a--;
            b--;
        }
    }

    cout << ans << endl;

    return 0;
}
