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;
#define ll long long

int main() {
	ll n;
	cin>>n;
	ll a[n+1];
	ll b[n+1];
	map< ll , ll > m;
	bool open[n+1];
	memset(open, true, sizeof(open));
	ll temp = 1;
	for(ll i = 1; i<=n; i++){
	    temp = temp * i;
	    m.insert(make_pair(i,temp));
	}
	
	for(ll i=1; i<=n; i++){
	    cin>>a[i];
	}
	for(ll i=1; i<=n; i++){
	    cin>>b[i];
	}
	
	ll a_rank = 0;
	for(ll i=1; i<=n; i++){
	    ll count = 0;
	    for(ll j=1; j<=a[i]; j++){
	        if(open[j])
	            count++;
	    }
	    a_rank += (count * m[n-i]);
	    open[a[i]] = false;
	}
	ll b_rank = 0;
	memset(open, true, sizeof(open));
	
	for(ll i=1; i<=n; i++){
	    ll count = 0;
	    for(ll j=1; j<=b[i]; j++){
	        if(open[j])
	            count++;
	    }
	    b_rank += (count * m[n-i]);
	    open[b[i]] = false;
	}
	cout<<abs(a_rank - b_rank);
}