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 = explode(' ', trim(fgets(STDIN)));
$Q = explode(' ', trim(fgets(STDIN)));
$a = range(1, $N);
$s[] = implode('', $a);
while(true) {
    $a = next_permutation($a);
    if ($a === false) break;
    $s[] = implode('', $a);
}
$p = array_search(implode('', $P), $s);
$q = array_search(implode('', $Q), $s);
printf('%d', abs($p - $q));

function next_permutation($a) {
    $cnt = count($a);
    $r = null;
    for ($i = $cnt - 1; $i > 0; $i--) {
        if ($a[$i] > $a[$i - 1]) {
            $r = $a[$i - 1];
            break;
        }
    }
    if (is_null($r)) {
        return false;
    }
    $part_a = array_slice($a, 0, $i - 1);
    $part_b = array_slice($a, $i - 1);
    sort($part_b);
    $pos = array_search($r, $part_b);
    $num = $part_b[$pos + 1];
    unset($part_b[$pos + 1]);
    $part_a[] = $num;
    $part_c = array_merge($part_a, array_values($part_b));

    return $part_c;
}