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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

using static System.Console;

namespace Atcoder01_10 {
    class Class1 {
        static void Main() {
            int n = int.Parse(ReadLine());
            int num1 = 0;
            int num2 = 0;
            int i;

            string[] P = ReadLine().Split();
            string[] Q = ReadLine().Split();

            int[] p = new int[n];
            int[] q = new int[n];

            for(i = 0; i < n; i++) {
                p[i] = int.Parse(P[i]);
                q[i] = int.Parse(Q[i]);
            }
            for (i = 0; i < n; i++) {
                num1 += beki((n - i) - 1) * (p[i] - 1);
                num2 += beki((n - i) - 1) * (q[i] - 1);
                WriteLine(num1 + "," + num2);
            }

            WriteLine(Math.Abs(num1 - num2));
        }

        static public int beki(int a) {
            int ans = 1;

            for(int i = 1; i <= a; i++) {
                ans *= i;
            }


            return ans;
        }
    }
}