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 pair<int, bool> P;
#define MOD 1000000007

int main() {
    int N;
    cin >> N;
    vector<P> a(2 * N);
    for(int i=0; i<2*N; ++i) {
        cin >> a[i].first;
        a[i].second = (i < N ? true : false);
    }
    sort(begin(a), end(a));

    long long res = 1;
    int P = 0, C = 0;
    for(int i=0; i<2*N; ++i) {
        if(a[i].second) {
            if(C == 0) ++P;
            else {
                res *= C;
                res %= MOD;
                --C;
            }
        } else {
            if(P == 0) ++C;
            else {
                res *= P;
                res %= MOD;
                --P;
            }
        }
    }
    cout << res << endl;
}