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
p = gets.chomp
q = gets.chomp
#puts p
#puts q
a = 0
b = 0

#def fact(n)
#  1.upto(n).inject(1) {|sum, n| sum * n}
#end

#f = fact(n)


patterns = 1.upto(n).map {|v| v }.permutation(n).map {|v| v.join(' ') }
#p patterns
patterns.each_with_index do |v, i|
  #puts "v = #{v}, i = #{i}, p = #{p}, q = #{q}\n"
  if v == p
    a = i + 1
  end

  if v == q
    b = i + 1
  end
end

#puts "a = #{a}, b = #{b}\n"

print (a - b).abs