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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int N = Integer.parseInt(sc.next());
    int[] facts = {1,2,6,24,120,720,5040,40320};
    int[] P = new int[N];
    int[] Q = new int[N];
    int[] PH = new int[N];
    int[] QH = new int[N];
    int i;
    int a = 0;
    int b = 0;
    for(i=0;i<N;i++){
      P[i] = Integer.parseInt(sc.next());
    }
    for(i=0;i<N;i++){
      Q[i] = Integer.parseInt(sc.next());
    }
    
    for(i=0;i<N;i++){
      for(int j=i+1;j<N;j++){
        if(P[i]>P[j]){
          PH[i]++;
        }
        if(Q[i]>Q[j]){
          QH[i]++;
        }
      }
    }
    
    for(i=0;i<N-1;i++){
      a+=facts[N-2-i]*PH[i];
      b+=facts[N-2-i]*QH[i];
    }
    if(a>b){
      System.out.print(a-b);
    }else{
      System.out.print(b-a);
    }
    System.out.flush();
    
  }
}