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;

class Test{
  public static void Main(){
    int K = int.Parse(Console.ReadLine());
    var str1 = Console.ReadLine().Split(' ');
    var str2 = Console.ReadLine().Split(' ');
    int calK =1;
    int Z = 0;
    int num1=0;
    int num2=0;
    for(int i = K;i>0;i--){
      calK *=i;
    }
    for(int i =1;i<=K;i++){
      Z+=i*(K-(i-1));
    }     
    for(int i=0;i<K;i++){
      num1 += int.Parse(str1[i])*((int)Math.Pow(2,K-i-1));
      num2 += int.Parse(str2[i])*((int)Math.Pow(2,K-i-1));
    }
    int rank1 =num1-Z;
    int rank2 =num2-Z;
    if(rank1<calK/2){
      rank1++; 
    }
    if(rank2<calK/2){
      rank2++;
    }
    if(rank1>=rank2){
      Console.Write(rank1-rank2);
    }else{
      Console.Write(rank2-rank1);
    }
  }
}