Problem:
Score : 300 points

Problem Statement

We have two permutations P and Q of size N (that is, P and Q are both rearrangements of (1,~2,~...,~N)).

There are N! possible permutations of size N. Among them, let P and Q be the a-th and b-th lexicographically smallest permutations, respectively. Find |a - b|.

Notes

For two sequences X and Y, X is said to be lexicographically smaller than Y if and only if there exists an integer k such that X_i = Y_i~(1 \leq i < k) and X_k < Y_k.

Constraints

2 \leq N \leq 8

P and Q are permutations of size N.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 ... P_N
Q_1 Q_2 ... Q_N

Output

Print |a - b|.

Sample Input 1

3
1 3 2
3 1 2

Sample Output 1

3

There are 6 permutations of size 3: (1,~2,~3), (1,~3,~2), (2,~1,~3), (2,~3,~1), (3,~1,~2), and (3,~2,~1). Among them, (1,~3,~2) and (3,~1,~2) come 2-nd and 5-th in lexicographical order, so the answer is |2 - 5| = 3.

Sample Input 2

8
7 3 5 4 2 1 6 8
3 8 2 5 4 6 7 1

Sample Output 2

17517

Sample Input 3

3
1 2 3
1 2 3

Sample Output 3

0

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php

 list($n) = explode(" ", trim(fgets(STDIN)));
 $p = str_replace(" ", "", trim(fgets(STDIN)));
 $q = str_replace(" ", "", trim(fgets(STDIN)));

 $all = permutationAll(1, $n);
 sort($all);
   
 $p_c = array_search($p, $all);
 $q_c = array_search($q, $all);

 echo abs($p_c - $q_c);

 function permutationAll($start, $end)
  {
    if($end < $start){
      return [];
    }
    $n=[];
    for($i=$start;$i<=$end;$i++){
      $n[$i]=true;
    }

    $arr = appendCount($n, "");

    return $arr;
  }

  function appendCount($n, $str){
    if(count($n)===1){
      return [$str.key($n)];
    }
    $arr = [];
    foreach($n as $key => $value){
      unset($n[$key]);
      $childs = appendCount($n, $str.$key);
      foreach($childs as $child){
        $arr[] = $child;
      }
      $n[$key]=true;
    }
    return $arr;
  }