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;


void solve(long long N, std::vector<long long> P, std::vector<long long> Q){
    vector<long long int> v(N);
    for (int i = 0; i < N; i++) {
        v[i] = i+1;
    }
    int idx_p = 0;
    int idx_q = 0;

    int i = 0;
    do {
        i++;
        if (P == v) {
            idx_p = i;
        }
        if (Q == v) {
            idx_q = i;
        }
    } while (next_permutation(v.begin(), v.end()));
    cout << abs(idx_p - idx_q) << endl;
}

// Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
int main(){
    long long N;
    scanf("%lld",&N);
    std::vector<long long> P(N);
    for(int i = 0 ; i < N ; i++){
        scanf("%lld",&P[i]);
    }
    std::vector<long long> Q(N);
    for(int i = 0 ; i < N ; i++){
        scanf("%lld",&Q[i]);
    }
    solve(N, std::move(P), std::move(Q));
    return 0;
}