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.*;
import java.lang.*;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
 
		int N = sc.nextInt();
		int[] numP = new int[N+1];
		int[] numQ = new int[N+1];
		int ans1 = 0,ans2 = 0;
		int[] ff = new int[]{0,1,2,6,24,120,720,5040};
		for( int i=N; i>=1; i-- ){
			numP[i] = sc.nextInt();
		}
		for( int i=N; i>=1; i-- ){
			numQ[i] = sc.nextInt();
		}
		for( int i=N; i>=1; i-- ){
			int count1 = 0,count2 = 0;
			for( int j=N; j>=i; j-- ){
				if( numP[i] > numP[j] ){
					count1++;
				}
				if( numQ[i] > numQ[j] ){
					count2++;
				}
			}
			ans1 += (numP[i]-1-count1)*ff[i-1];
			ans2 += (numQ[i]-1-count2)*ff[i-1];
		}
		System.out.println(Math.abs(ans1-ans2));
	}
}