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 fact (n)
  (if (= n 0)
      0
      (loop with a = 1
            for i from 2 to n
            do (setf a (* a i))
            finally (return a))))

(defun nth-permutation (n p)
  (if p
      (let ((x (first p)))
        (+ (* (fact (1- n)) (1- x))
           (nth-permutation (1- n)
                            (mapcar (lambda (y)
                                      (if (< x y)
                                          (1- y)
                                          y))
                                    (rest p)))))
      0))

(defun solve (n p q)
  (abs (- (nth-permutation n p)
          (nth-permutation n q))))

#-swank
(let* ((n (read))
       (p (loop repeat n collect (read)))
       (q (loop repeat n collect (read))))
  (format t "~A~%" (solve n p q)))