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: Wrong Answer)

<?php
	fscanf(STDIN, "%d", $N);
$S1 = fgets(STDIN);
$S2 = fgets(STDIN);
	$S1array = explode(' ', $S1);
	$S2array = explode(' ', $S2);
    echo getScore($N, $S1array);


function getScore ($num, $S) {
  $originArray = $S;
  $sortedArray = $S;
  rsort($sortedArray);
  $score = 0;
  foreach ($S as $currentNum) {
    $order = array_search($currentNum, $sortedArray);
    if ($order === 0) {continue;}

    $score += gmp_fact(count($sortedArray) - 1) * $order;
    $sortedArray = array_splice($sortedArray, $order - 1, 1);
    
  }
  return $score;
}

function gmp_fact ($i) {
  $number = 1;
  for ($j = $i; $j >= 1; $j--){
    $number *= $j;
  }
  return $number;
}