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)

def main():
    N = int(input())
    P = tuple(map(int,input().split(' ')))
    Q = tuple(map(int,input().split(' ')))
    Pnum = dictNum(P,N)
    Qnum = dictNum(Q,N)
    ans = (abs(Pnum-Qnum))
    print(ans)

def dictNum(A, N):
    ans = 0
    restNum = [1]*N
    for i in range(N):
        restNum[A[i]-1]=0
        ans += count(sum(restNum[:A[i]]),N-i)
    return ans + 1
def count(a,N):
    ans = factorial(N-1)*a
    if N == 1:
        ans = 0
    return ans
def factorial(num):
    if num == 0:
        return 1
    else:
        return num*factorial(num-1)
main()