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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;
typedef pair<int, int> P;
int main(void){
    int n;
    cin >> n;
    vector<P> v;
    for(int i=0;i<n*2;i++){
        int a;
        cin >> a;
        v.push_back(P(a, i));
    }
    sort(v.begin(), v.end());
    int lft = 0;
    long long ans = 1, mod = 1e9+7;
    for(int i=0;i<n*2;i++){
        int s = v[i].second;
        if(s < n){
            if(lft <= 0) lft--;
            else ans *= lft--;
        }else{
            if(lft >= 0) lft++;
            else ans *= -lft++;
        }
        ans %= mod;
    }
    cout << ans << endl;
}
