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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std ;
int n ;
int a[10] , b[10] , c[10] ;
int main()
{
	scanf("%d" , &n) ;
	for(int i = 1 ; i <= n ; i ++)
	  scanf("%d" , &a[i]) ;
	for(int i = 1 ; i <= n ; i ++)
	  scanf("%d" , &b[i]) ;
	int ans_a = 0 , ans_b = 0 ;
	for(int i = 1 ; i <= n ; i ++)
	  c[i] = i ;
	bool flag ;
	do
	{
		flag = 1 ;
		for(int i = 1 ; i <= n ; i ++)
		 if(c[i] != a[i]) flag = 0 ;
		if(flag)  break ;
		ans_a ++ ; 
	}while(next_permutation(c + 1 , c + n + 1)) ;
	
	for(int i = 1 ; i <= n ; i ++)
	  c[i] = i ;
	do
	{
		flag = 1 ;
		for(int i = 1 ; i <= n ; i ++)
		 if(c[i] != b[i]) flag = 0 ;
		if(flag)  break ;
		ans_b ++ ; 
	}while(next_permutation(c + 1 , c + n + 1)) ;
	printf("%d\n" , abs(ans_a - ans_b)) ;
	return 0 ;
}