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.split(' ').join
q = gets.chomp.split(' ').join
arr = []
n.times { |i| arr << (i + 1) }
def rec(arr1, arr2)
  return [arr2.join('')] if arr1.length == 0
  res = []
  arr1.each do |i|
    copied_arr1 = arr1.dup
    copied_arr1.delete(i)
    copied_arr2 = arr2.dup
    copied_arr2 << i
    res += rec(copied_arr1, copied_arr2)
  end
  return res
end
list = rec(arr, [])
a, b = 0, 0
list.each_with_index do |x, i|
  a = i + 1 if x == p
  b = i + 1 if x == q
end
puts (a - b).abs