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: Accepted)

(defun splitat (c line)
  (labels ((rec (line acc)
				(let ((pos (position-if (lambda(cc) (char= c cc)) line)))
				  (if pos
					  (rec (subseq line (1+ pos)) (cons (subseq line 0 pos) acc))
					(nreverse (cons line acc))))))
	(rec line nil)))
(defun lessp(a b)
  (labels ((rec(a b)
             (if (null a)
               nil
               (if (< (car a) (car b))
                 t
                 (if (= (car a) (car b))
                   (rec (cdr a) (cdr b))
                   nil)))))
    (rec a b)))
(defun flatten1(lst)
  (nreverse (reduce (lambda (acc a)
					  (reduce (lambda (acc a)
								(cons a acc))
							  a :initial-value acc))
					lst :initial-value nil)))
(defun permutations(lst)
  (labels ((skip(i n lst acc)
			 (cond ((null lst) acc)
				   ((= i n) (skip (1+ i) n (cdr lst) acc))
				   (t (skip (1+ i) n (cdr lst) (cons (car lst) acc)))))
		   (rec (lst acc acc0)
				(if (null lst)
				  (cons acc acc0)
				  (flatten1 (mapcar (lambda(i) (rec (nreverse (skip 0 i lst nil)) (cons (nth i lst) acc) acc0)) (loop for i from 0 to (1- (length lst)) collect i)))
				  ))
				)
	(rec lst nil nil)))
(defun equallst(a b)
  (labels ((rec(a b)
             (if (null a)
               t
               (if (= (car a) (car b))
                 (rec (cdr a) (cdr b))
                 nil))))
    (rec a b)))
(defun searcher (hystack needle)
  (labels ((rec(hystack i)
             (if (null hystack)
               -1
               (if (equallst (car hystack) needle)
                 i
                 (rec (cdr hystack) (1+ i))))))
    (rec hystack 0)))
(defun f(n p q)
  (let* ((pq (sort (permutations (loop for i from 1 to n collect i)) #'lessp))
         (pn (searcher pq p))
         (qn (searcher pq q)))
    (abs (- pn qn))))

(compile 'lessp)
(compile 'equallst)
(compile 'searcher)
(compile 'f)
(let* ((n (parse-integer (read-line nil nil)))
       (p (mapcar #'parse-integer (splitat #\space (read-line nil nil))))
       (q (mapcar #'parse-integer (splitat #\space (read-line nil nil)))))
  (format t "~A~%" (f n p q)))