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)

import numpy as np
N=int(input())
P=list(map(int,input().split()))
Q=list(map(int,input().split()))
A=[]
B=[]
import math
for i in range(1,N+1):
  A.append(i)
  B.append(i)
a=1
b=1
for i in range(1,N+1):
  if P[i-1]<len(A):
    a+=math.factorial(N-i)*(P[i-1]-1)
  else:
    a+=math.factorial(N-i)*(len(A)-1)
  A.remove(P[i-1])
for i in range(1,N+1):
  if Q[i-1]<len(B):
    b+=math.factorial(N-i)*(Q[i-1]-1)
  else:
    b+=math.factorial(N-i)*(len(B)-1)
  B.remove(Q[i-1])
print(abs(a-b))