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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;

namespace atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.ReadLine();
            var r1 = CalcRank(Console.ReadLine().Split(' ').Select(num => int.Parse(num)).ToArray());
            var r2 = CalcRank(Console.ReadLine().Split(' ').Select(num => int.Parse(num)).ToArray());
            Console.WriteLine(Math.Abs(r1 - r2));

            int CalcRank(int[] nums)
            {
                var head = nums[0];
                var sorted = nums.OrderBy(x => x).ToArray();
                var len = nums.Length;
                var r = 0;
                for (var i = 0; i < len; i++)
                {
                    if (sorted[i] == head) r = len > 2 ? i : i + 1;
                }

                if (len > 2)
                {
                    return Factorial(len - 1) * r + CalcRank(nums.Skip(1).ToArray());
                }
                else
                {
                    return r;
                }
            }

            int Factorial(int num)
            {
                var result = 1;
                for (var i = 2; i <= num; i++)
                {
                    result *= i;
                }
                return result;
            }
        }
    }
}