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;
typedef long long ll;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

int main() {
    int n; cin >> n;
    vector<int> p(n);
    vector<int> q(n);
    vector<int> t(n);

    rep(i, n) cin >> p.at(i);
    rep(i, n) {
        cin >> q.at(i);
        t.at(i) = i + 1;
    }
    int i = 0;
    int p_ans = -1;
    int q_ans = -1; 
    do {
        int j = 0;
        for (j = 0; j < n; j++) {
            if (p.at(j) != t.at(j))
                break;
        }
        if (j == n)
            p_ans = i;

        for (j = 0; j < n; j++) {
            if (q.at(j) != t.at(j))
                break;
        }
        if (j == n)
            q_ans = i;

        if (p_ans >= 0 && q_ans >= 0)
            break;
        i++;
    } while (next_permutation(t.begin(), t.end()));
    //cout << p_ans << " " << q_ans << endl;
    cout << abs(p_ans+1 - (q_ans+1)) << endl;
    return 0;
}