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 PHP (5.6.30) (judge verdict: Accepted)

<?php
    $n;
    $ar = array();
    $ans = 1;
    $r = 0;
    $s = -1;
    fscanf(STDIN, "%d", $n);
    for($i = 0; $i < $n; $i++){
        $a;
        fscanf(STDIN, "%d", $a);
        $ar[$a] = 0;
    }
    for($i = 0; $i < $n; $i++){
        $b;
        fscanf(STDIN, "%d", $b);
        $ar[$b] = 1;
    }
    ksort($ar);
    foreach($ar as $v){
        if($v == $s){
            $r++;
        }else if($r == 0){
            $r++;
            $s = $v;
        }else{
            $ans *= $r;
            $ans %= 1000000007;
            $r--;
        }
    }
    echo "$ans\n";
?>