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: Wrong Answer)

(defun parse-int-ex-ex (n)
  (cond ((char= n #\1) 1)
        ((char= n #\2) 2)
        ((char= n #\3) 3)
        ((char= n #\4) 4)
        ((char= n #\5) 5)
        ((char= n #\6) 6)
        ((char= n #\7) 7)
        ((char= n #\8) 8)
        ((char= n #\9) 9)
        ((char= n #\0) 0)))
(defun f (k)
  (remove-if-not (lambda (a) (ff a k)) (print (loop :for a :from 1 :upto (1- (expt (1+ k) k)) :collect (mapcar #'parse-int-ex-ex (concatenate 'list (format nil (format nil "~~~A,~A,'0R" (1+ k) k) a)))))))
(defun ff (j k)
  (loop :for a :from 1 :upto k :always(position a j :test #'=)))
(let* ((n (read))
       (a (loop :repeat n :collect (read)))
       (b (loop :repeat n :collect (read)))
       (ll (f n)))
  (princ (abs (- (position a ll :test #'equal) (position b ll :test #'equal)))))