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)

#
# 150C Count Order
#
import itertools
import sys

n = input()
p = input()
q = input()

if p==q:
    print(0)
    sys.exit()

p = p.replace(' ', ', ')
p = "(" + p + ")"

q = q.replace(' ', ', ')
q = "(" + q + ")"

a = [int(i)+1 for i in range(int(n))]
b = list(itertools.permutations(a))

pcount = 0
qcount = 0
pf = False
qf = False

for i in range(len(b)):
    if str(b[i])==p:
        pcount = i+1
        pf = True
    if str(b[i])==q:
        qcount = i+1
        qf = True
    if pf and qf:
        break

print(abs(pcount-qcount))