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.IO;
using System.Linq;

class Solve{
    static void Main(string[] args){
        var N = int.Parse(Console.ReadLine());
        var P = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var Q = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int a = 1, b = 1;
        var set = new HashSet<int>();
        for (int i = 0; i < N; i++){
            var pi = P[i];
            int count = 0;
            if(set.Any())
                foreach (var s in set){
                    if (s < pi) count++;}
            var x = pi - count;
            a += (x - 1) * Factorial(N - 1 - i);
            set.Add(pi);}
        set.Clear();
        for (int i = 0; i < N; i++){
            var qi = Q[i];
            int count = 0;
            if (set.Any())
                foreach (var s in set){
                    if (s < qi) count++;}
            var x = qi - count;
            b += (x - 1) * Factorial(N - 1 - i);
            set.Add(qi);}
        var answer = Math.Abs(a - b);
        var writer = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(writer);
        Console.WriteLine(answer);
        Console.Out.Flush();}

    public static int Factorial(int n){
        int result = 1;
        for (int i = n; i > 1; i--){
            result *= i;}
        return result;}}