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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main implements Runnable {

    private static int MOD = 1_000_000_007;

    public static void main(String[] args) {
        // Run with 32MB stack
        Thread thread = new Thread(null, new Main(), "", 32 * 1024 * 1024);
        thread.start();
    }

    @Override
    public void run() {
        final Scanner scanner = new Scanner(System.in);
        solve(scanner);
    }

    static void solve(Scanner scanner) {
        N = Integer.parseInt(scanner.next());
        P = new int[N];
        for (int i = 0; i < N; i++) {
            P[i] = Integer.parseInt(scanner.next());
        }
        Q = new int[N];
        for (int i = 0; i < N; i++) {
            Q[i] = Integer.parseInt(scanner.next());
        }

        permuteAndProcess(new LinkedHashSet<>());
        assert (A > 0);
        assert (B > 0);
        System.out.println(Math.abs(A - B));
    }

    static int[] P, Q;
    static int N, A = -1, B = -1;
    static int curr = 0;
    static void permuteAndProcess(LinkedHashSet<Integer> visited) {
        if (visited.size() == N) {
            curr++;
            List<Integer> order = new ArrayList<>(visited);
            boolean f = true;
            for (int i = 0; i < N; i++) {
                if (order.get(i) + 1 != P[i]) {
                    f = false;
                }
            }
            if (f) {
                A = curr;
            }

            for (int i = 0; i < N; i++) {
                if (order.get(i) + 1 != Q[i]) {
                    return;
                }
            }
            B = curr;
        }

        for (int i = 0; i < N; i++) {
            if (!visited.contains(i)) {
                visited.add(i);
                permuteAndProcess(visited);
                visited.remove(i);
            }
        }
    }
}