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 Ruby (2.3.3) (judge verdict: Accepted)

N = gets.to_i

# 1! ～ (N-1)! までを計算する
$kai = [1]
(N-2).times do |i|
  $kai.unshift($kai[0] * (i+2))
end
#p $kai

A = gets.split(' ').map(&:to_i)
B = gets.split(' ').map(&:to_i)

def n_banme(x)
  indexes = []
  N.times do |i|
    indexes << i+1
  end
  #print 'indexes = '
  #p indexes
  #p x
  ans = 0
  
  (N-1).times do |i|
    # puts 'i = '+ i.to_s
    # 順番未確定の数値のなかで何番目に大きいか
    idx = indexes.index(x[i])
    # puts 'idx = ' + idx.to_s
    ans += idx * $kai[i]
    # puts 'ans = '+ ans.to_s
    indexes.delete_at(idx)
  end
  ans += 1
  # puts 'final_ans = '+ans.to_s
  return ans
end

a = n_banme(A)
b = n_banme(B)
# puts a,b
puts (a-b).abs