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>
int cmp(int a[],char bb[],int n)
{
	char aa[10];
	for(int i=0;i<n;i++){
		aa[i]=a[i]-'0';
	}
	aa[n]='\0';
	if(strcmp(aa,bb)==0){
		return 1;
	}
	return 0;
}
using namespace std;
int main()
{
	int n;
	cin>>n;
	int a[10],b[10],c[10],d[10];
	for(int i=1;i<=n;i++){
		a[i-1]=i;
		d[i-1]=i;
	}
	char bb[10],cc[10];
	for(int i=0;i<n;i++){
		scanf("%d",&b[i]);
		bb[i]=b[i]-'0';
	}
	for(int i=0;i<n;i++){
		scanf("%d",&c[i]);
		cc[i]=c[i]-'0';
	}
	bb[n]='\0';cc[n]='\0';
	int aaa=0,bbb=0;
	while(cmp(a,bb,n)!=1){
		aaa++;
		next_permutation(a,a+n);
	}
	while(cmp(d,cc,n)!=1){
		bbb++;
		next_permutation(d,d+n);
	}
	cout<<abs(aaa-bbb)<<endl;
	return 0;
}