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 (3.8.2) (judge verdict: Accepted)

N = int(input())
P = list(map(int,input().split()))
Q = list(map(int,input().split()))

def kaijou(n):
    ans = 1
    while n > 0:
        ans *= n
        n -= 1
    return ans

def calc(misiyou, num, cnt, x):
    if cnt == len(num):
        return x
    else:
        siyou = num[cnt]
        ind = misiyou.index(siyou)
        misiyou.remove(siyou)
        misiyou2 = misiyou.copy()
        x2 = x + (kaijou(len(misiyou2)-1))*(ind-1)
        return calc(misiyou2, num, cnt+1, x2)

lis1 = [i for i in range(N+1)]
a = calc(lis1, P, 0, 1)
lis2 = [i for i in range(N+1)]
b = calc(lis2, Q, 0, 1)
print(abs(a-b))