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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defun split (input stack-string output-list)
  (let ((chara (car input)))
    (case chara
          ((nil) (append output-list (list stack-string)))
          (#\space (split (cdr input)
                                  '()
                                  (append output-list (list stack-string))))
          (otherwise (split (cdr input)
                                    (concatenate 'string stack-string (list chara))
                                    output-list)))))

(defun input-to-list (input)
  (mapcar #'parse-integer (split (concatenate 'list input)
                                 '()
                                 '())))

(defun fact (n)
  (labels ((inner (mem n)
                  (if (zerop n)
                      mem
                      (inner (* mem n) (1- n)))
                  ))
          (inner 1 n)))

(defun dec (lst n)
  (+ (* (fact (1- n)) (1- (car lst))) (dec (cdr lst) (1- n)))
  
(defvar n (parse-integer (read-line)))
(defvar p (input-to-list (read-line)))
(defvar q (input-to-list (read-line)))

(princ (abs (- (dec p n) (dec q n))))