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 (GCC 5.4.1) (judge verdict: Accepted)

#include <limits.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
#include <math.h>

#define P 1000000007

int comp(const void *a, const void *b){return *(int*)a-*(int*)b;}

int main(void){
	int n, i, j;
	int p[8];
	char u[8];
	scanf("%d", &n);

	int k[8];
	k[0]=0; k[1]=1;
	for(i=2; i<n; i++) k[i]=k[i-1]*i;

	for(i=0; i<n; i++){
		scanf("%d", p+i);
		u[i]=0;
	}
	int a=0;
	for(i=0; i<n; i++){
		int s=0;
		for(j=0; j<p[i]-1; j++) if(u[j]==0) s++;
		a += s*k[n-i-1];
		u[p[i]-1]=1;
	}

	for(i=0; i<n; i++){
		scanf("%d", p+i);
		u[i]=0;
	}
	int b=0;
	for(i=0; i<n; i++){
		int s=0;
		for(j=0; j<p[i]-1; j++) if(u[j]==0) s++;
		b += s*k[n-i-1];
		u[p[i]-1]=1;
	}

	printf("%d\n", a>b?a-b:b-a);
}