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 PHP (5.6.30) (judge verdict: Accepted)

<?php
function pat($a, $s = '')
{
  $r = array();
  if (count($a) && is_array($a)) {
    //第1引数に文字の配列を渡されたらループして処理
    foreach ($a as $k => $v) {
      //文字の配列から1文字もらってこちらにくっつけて
      $_s = $s . $v;
      //もらった1文字を除いた文字の配列を作って
      $_a = $a;
      unset($_a[$k]);
      //再帰呼び出し
      $_r = pat($_a, $_s);
      //返り値にする変数に結果を追加
      $r = array_merge($r, $_r);
    }
  } else {
    //第1引数が空っぽの配列だったら、再帰呼び出しはここでストップ
    //返り値はこれだけ
    $r[] = $s;
  }
  return $r;
}

$a = array('1', '2', '3', '4', '5', '6', '7', '8');
fscanf(STDIN, "%d", $N);
$P = explode(" ", trim(fgets(STDIN)));
$Q = explode(" ", trim(fgets(STDIN)));

if ($P == $Q){
    echo 0;
    die();
}
$input = array_slice($a, 0, $N);
foreach(pat($input) as $key => $value){
    if ($value == implode($P)){
        $minimum = $key;
    } elseif ($value == implode($Q)){
        $maximum = $key;
    }
}
echo abs($minimum - $maximum);