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 PyPy3 (2.4.0) (judge verdict: Accepted)

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

# P=tuple([7, 3, 5, 4, 2, 1, 6, 8])
# Q=tuple([3 ,8 ,2 ,5 ,4 ,6 ,7 ,1])
# P=tuple([1 ,3 ,2])
# Q=tuple([3 ,1 ,2])

import itertools
# N=3
s=[i for i in range(1,N+1)]
number_id=0
id_p=0
id_q=0
for v in itertools.permutations(s):
    number_id+=1
#     print(number_id)
#     print(v)
    if v==P:
        id_p=number_id
    if v==Q:
        id_q=number_id
        
print(abs(id_p-id_q))