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<vector>
#include<algorithm>
#include<queue>
#include<tuple>

using namespace std;
const long long MOD = (long long)1e9 + 7;

int main(){
    int n;
    cin >> n;
    vector<pair<int, int>> c(2 * n);
    for(int i = 0; i < n; i++){
        int x;
        cin >> x;
        c[i] = {x, 0};
    }
    for(int i = 0; i < n; i++){
        int x;
        cin >> x;
        c[i + n] = {x, 1};
    }
    sort(begin(c), end(c));
    long long ans = 1;
    queue<int> a, b;
    for(int i = 0; i < 2 * n; i++){
        int x, y;
        tie(x, y) = c[i];
        if(y == 0){
            if(b.empty()){
                a.push(x);
            }else{
                ans *= b.size();
                ans %= MOD;
                b.pop();
            }
        }else{
           if(a.empty()){
                b.push(x);
            }else{
                ans *= a.size();
                ans %= MOD;
                a.pop();
            }     
        }
    }
    cout << ans << endl;
    return 0;
}
