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.*;
import java.io.*;

public class Main {

    static int[] p;
    static int[] q;
    static boolean[] used;
    static int a, b, n, count = 0;

    static final Reader sc = new Reader();
    static final PrintWriter out = new PrintWriter(System.out,false);
    static public void main(String args[]) {
        n = sc.nextInt();
        p = new int[n];
        q = new int[n];
        used = new boolean[n];
        for (int i = 0; i < n; i++) {
            p[i] = sc.nextInt();
        }
        for (int i = 0; i < n; i++) {
            q[i] = sc.nextInt();
        }
        dfs(0, new boolean[n], new int[n]);
        out.println(Math.abs(a - b));
        out.flush();
        sc.close();
        out.close();
    }

    static void dfs(int index, boolean[] used, int[] perm) {
        if (index == n - 1) { 
            count++;
            for (int i = 0; i < n; i++) {
                if (!used[i]) {
                    perm[index] = i + 1;
                    boolean flag = false;
                    for (int j = 0; j < n; j++) {
                        if (perm[j] != p[j]) {
                            flag = true;
                            break;
                        }
                    }
                    if (!flag) {
                        a = count;
                    }
                    flag = false;
                    for (int j = 0; j < n; j++) {
                        if (perm[j] != q[j]) {
                            flag = true;
                            break;
                        }
                    }
                    if (!flag) {
                        b = count;
                    }
                }
            }
        } else {
            for (int i = 0; i < n; i++) {
                if (!used[i]) {
                    used[i] = true;
                    perm[index] = i + 1;
                    dfs(index + 1, used, perm);
                    used[i] = false;
                }
            }
        }
    }
}

class Reader {
 
    private final InputStream in;
    private final byte[] buf = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
 
    public Reader() { this(System.in);}
    public Reader(InputStream source) { this.in = source;}
 
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try{
            buflen = in.read(buf);
        }catch (IOException e) {e.printStackTrace();}
        if (buflen <= 0) return false;
        return true;
    }
 
    private int readByte() { if (hasNextByte()) return buf[ptr++]; else return -1;}
 
    private boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
 
    private void skip() { while(hasNextByte() && !isPrintableChar(buf[ptr])) ptr++;}
 
    public boolean hasNext() {skip(); return hasNextByte();}
 
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
 
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        boolean minus = false;
        long num = readByte();
 
        if(num == '-'){
            num = 0;
            minus = true;
        }else if (num < '0' || '9' < num){
            throw new NumberFormatException();
        }else{
            num -= '0';
        }
 
        while(true){
            int b = readByte();
            if('0' <= b && b <= '9')
                num = num * 10 + (b - '0');
            else if(b == -1 || !isPrintableChar(b))
                return minus ? -num : num;
            else
                throw new NoSuchElementException();
        }
    }
 
    public int nextInt() {
        long num = nextLong();
        if (num < Integer.MIN_VALUE || Integer.MAX_VALUE < num)
            throw new NumberFormatException();
        return (int)num;
    }
 
    public double nextDouble() {
        return Double.parseDouble(next());
    }
 
    public char nextChar() {
        if (!hasNext()) throw new NoSuchElementException();
        return (char)readByte();
    }
 
    public String nextLine() {
        while (hasNextByte() && (buf[ptr] == '\n' || buf[ptr] == '\r')) ptr++;
        if (!hasNextByte()) throw new NoSuchElementException();
 
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (b != '\n' && b != '\r') {
            sb.appendCodePoint(b);
            b = readByte();
        }
 
        return sb.toString();
    }
 
    public int[] nextIntArray(int n) {
        int[] res = new int[n];
        for (int i=0; i<n; i++) res[i] = nextInt();
        return res;
    }
 
    public char[] nextCharArray(int n) {
        char[] res = new char[n];
        for (int i=0; i<n; i++) res[i] = nextChar();
        return res;
    }
 
    public void close() {try{ in.close();}catch(IOException e){ e.printStackTrace();}};
}