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 Python (3.4.3) (judge verdict: Wrong Answer)

import itertools

if __name__ == '__main__':
    # P and Q are both rearrangements of (1, 2, ..., N)).
    # N! possible permutations of size N
    # among them, let P and Q be the a-th and the b-th
    n = int(input())
    p = input().split(' ')
    q = input().split(' ')

    for i in range(0, len(q)):
        p[i] = int(p[i])
        q[i] = int(q[i])

    realnums = p.copy()

    realnums.sort()

    perm = list(itertools.permutations(realnums))

    for per in perm:
        print(per)

    it = 0

    qplace = 0
    pplace = 0

    for i in perm:
        if list(i) == q:
            qplace = it
        if list(i) == p:
            pplace = it
        it += 1
    print(abs(qplace - pplace))