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 = map(int, input().split())
q = map(int, input().split())

def ranking(n, numbers):
  tmp = list(range(1, n+1))
  ranking = []
  for n in numbers:
    index = tmp.index(n)
    ranking.append(index+1)
    tmp.pop(index)
  return ranking

def ranking2output(n, ranking):
  ret = 1
  x = 1
  for i in range(1, n+1):
    ret += (ranking[n-i]-1)*(x)
    x *= i
  return ret

a = ranking2output(n, ranking(n, p))
b = ranking2output(n, ranking(n, q))

print(abs(a-b))