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 <iostream>
#include <string>
#include <stdio.h>
#include <cmath>
#include <cfloat>
#include <algorithm>
#include <functional>
#include <numeric>
#include <vector>
using namespace std;

const double PI=acos(-1);

int main(){
    int n;
    cin >> n;

    vector<int> p(n), q(n);
    for(int i = 0; i < n; i++){
        cin >> p[i];
    }
    for(int i = 0; i < n; i++){
        cin >> q[i];
    }
    int pp = 0, qq = 0;
    for(int i = 0; i < n; i++){
        if(i!=0){
            for(int j = i; j < n; j++){
                if(p[j] > p[i-1]) p[j]--;
                if(q[j] > q[i-1]) q[j]--;
            }
        }
        if(n-1 == i) break;
        int a = 1;
        for(int j = 1, k = 1; j <= n-i-1; j++, k++){
            a *= k;
        }
        pp += (p[i] - 1)*a;
        qq += (q[i] - 1)*a;
    }
    cout << abs(pp - qq) << endl;
    return 0;
}