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
fscanf(STDIN, '%d', $n);
$p = array_map('intval', explode(' ', trim(fgets(STDIN))));
$q = array_map('intval', explode(' ', trim(fgets(STDIN))));
$arr = junretsu($n);
sort($arr);
foreach ($arr as $i => $v) {
    if (implode('', $v) === implode('', $p)) $a = $i + 1;
    if (implode('', $v) === implode('', $q)) $b = $i + 1;
}
$ans = abs($a - $b);
echo $ans . PHP_EOL;

function junretsu($n)
{
    if ($n === 1) return [[1]];
    $arr = [];
    foreach (junretsu($n - 1) as $v) {
        for ($i = 0; $i < $n; $i++) {
            $arr2 = $v;
            array_splice($arr2, $i, 0, $n);
            $arr[] = $arr2;
        }
    };
    return $arr;
}