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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

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

class AtCoder {
  static private int[] f = new int[9];
  static void Main() {
    //var inputs = Console.ReadLine().Trim().Split(' ').Select(x => int.Parse(x)).ToList();
    var N = int.Parse(Console.ReadLine().Trim());
    var P = Console.ReadLine().Trim().Split(' ').Select(x => int.Parse(x)).ToList();
    var Q = Console.ReadLine().Trim().Split(' ').Select(x => int.Parse(x)).ToList();
    
    Console.WriteLine(Math.Abs(Order(P) - Order(Q)));
    //Console.WriteLine(Order(P));
  }
  static private int Factorial(int n) {    
    if(f[n] != 0) return f[n];
    var r = 1;
    for(var i = 2; i <= n; i++) {
      r *= i;
    }
    return r;
  }
  static private int Order(List<int> l) {
    //char[] cs = s.ToCharArray();
    var r = 0;
    for(int i = 0; i < l.Count(); i++) {
      if(l[i] > i + 1) {
        r += Factorial(l.Count() - (i + 1)) * (l[i] - (i + 1));
      }
    }
    return r;
  }
}