Problem:
Score : 500 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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.

Sample Input 1

2
0
10
20
30

Sample Output 1

2

There are two optimal connections: 0-20, 10-30 and 0-30, 10-20.
In both connections the total length of the cables is 40.

Sample Input 2

3
3
10
8
7
12
5

Sample Output 2

1

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<algorithm>
#include<cstdlib>
using namespace std;
struct point{
    int ck, x;
    bool operator<(const point &p)const{
        return x<p.x;
    }
}w[201000];
int n, s;
long long res = 1;
int main(){
    int i, j;
    scanf("%d",&n);
    for(i=0;i<2*n;i++){
        scanf("%d",&w[i].x);
        w[i].ck = i/n;
    }
    sort(w,w+2*n);
    for(i=0;i<2*n;i++){
        int t1 = abs(s), t2;
        s += w[i].ck*2-1;
        t2 = abs(s);
        if(t2 < t1){
            res = res*t1%1000000007;
        }
    }
    printf("%lld\n",res);
}