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.HashSet;
import java.util.Scanner;
import java.util.Set;

	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];
			
			for(int i=0;i<n;i++) {
				p[i]=sc.nextInt();
			}
			
			for(int i=0;i<n;i++) {
				q[i]=sc.nextInt();
			}
			
			System.out.println(Math.abs((calc(n,p))-(calc(n,q))));
			
		}
		
		
		
		public static int calc(int n,int[] x) {
			int ret =0;
			Set<Integer> memo = new HashSet<>();
			for(int i=0;i<n;i++) {
				
				
				memo.add(x[i]);
				int count = 0;
				for(int j=1;j<=x[i];j++) {
					if(!(memo.contains(j))) {
						count++;
					}
				}
				ret+=(count)*factorial(n-i-1);
			}
			
			return ret;
		}
		
		
		static int  factorial(int n){
			  if(n == 0){
			    return 1;
			  }
			  return n * factorial(n-1);
			}

	}