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: Wrong Answer)

import java.util.*;
public class Main{
	public static void main(String args[]){
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] P = new int[N];
		int[] Q = new int[N];
		boolean flg = true;
		int[] numbers = new int[N];
		int a = 0;
		int b = 0;
		int buf = 0;
		int ans = -1;
		for(int i = 0;i < N;i++){
			P[i] = sc.nextInt();
			numbers[i] = 1 + i;
		}
		for(int i = 0;i < N;i++){
			Q[i] = sc.nextInt();
		}
		while(flg){
			flg = false;
			for(int i = N - 1;i > 0;i--){
				buf++;
				if(Arrays.equals(P,numbers)){
					a = buf;
				}else if(Arrays.equals(Q,numbers)){
					b = buf;
				}
				if(numbers[i] > numbers[i - 1]){
					swap(numbers,i,i - 1);
					flg = true;
				}
			}
		}
		ans = Math.abs(a - b);
		System.out.println(ans);
	}
	public static void swap(int[] a,int i,int j){
		int buf = a[i];
		a[i] = a[j];
		a[j] = a[i];
	}
}