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 (2.7.1) (judge verdict: Accepted)

def main(str)
  lines = str.split("\n").map { |x| x.split(" ").map(&:to_i) }
  n = lines[0][0]
  ps = lines[1]
  qs = lines[2]
  perm = []
  sub(perm, n, [], n.times.map { |i| i + 1 })
  ((perm.find_index { |x| x == qs } - perm.find_index { |x| x == ps })).abs
end

def sub(ret, n, cur, src)
  if cur.count == n
    ret << cur
    return
  end
  src.each do |i|
    dst = src.clone
    dst.delete(i)
    sub(ret, n, cur + [i], dst)
  end
end

unless ENV["TEST"]
  puts(main($stdin.read.chomp))
  exit(0)
end

require 'minitest/autorun'

class TestA < Minitest::Test
  def test_main
    assert_equal(3, main("3
1 3 2
3 1 2"))
    assert_equal(17517, main("8
7 3 5 4 2 1 6 8
3 8 2 5 4 6 7 1"))
    assert_equal(0, main("3
1 2 3
1 2 3"))
  end
end