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 (3.4.3) (judge verdict: Wrong Answer)

a=int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
C=[0,1,2,6,24,120,720,5040,40320]
d=0
e=0

for i in range(a,2,-1):
  d1=C[i-1]*(A[a-i]-1)
  e1=C[i-1]*(B[a-i]-1)
  d=d+d1
  e=e+e1
if A[a-2]==a-1 and A[a-1]==a:
  d+=0
elif A[a-2]<A[a-1]:
  d+=1
else:
  d+=2
if B[a-2]==a-1 and B[a-1]==a:
  d+=0
elif B[a-2]<B[a-1]:
  e+=1
else:
  e+=2




print(abs(d-e))