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: Accepted)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static void Main(){
		Sc sc=new Sc();
		var s=sc.Ia;
		var a=sc.Ia;
		var b=sc.Ia;
		var h=new Pe<int>(1,s[0]);
		int c=0,d=0;
		for(int i=0;i<h.cnt;i++){
			var bo=false;
			for(int j = 0;j<s[0];j++) {
				if(a[j]!=h.li[i][j]){
					bo=true;
					break;
				}
			}
			if(!bo){
				c=i+1;
				continue;
			}
			bo=false;
			for(int j = 0;j<s[0];j++) {
				if(b[j]!=h.li[i][j]){
					bo=true;
					break;
				}
			}
			if(!bo){
				d=i+1;
				continue;
			}
		}
		if(c==0||d==0){
			Console.WriteLine(0);
			return;
		}
		Console.WriteLine("{0}",Abs(d-c));
	}
}
public class Pe<T>{
	public int o,n,cnt=0;
	private T[] arr,h;
	private bool[] b;
	public List<T[]> li;
	public Pe(int u,int v){o=v-u+1;n=o;Fu1(u);}
	public Pe(int u,int v,int x){o=v-u+1;n=x;Fu1(u);}
	public Pe(T[] a){n=a.Length;Fu2(a);}
	public Pe(T[] a,int x){n=x;Fu2(a);}
	public void Fu1(int u){
		h=new T[o];
		for(int i=0;i<o;i++){h[i]=(T)(object)(i+u);}
		Fu();
	}
	public void Fu2(T[] a){
		o=a.Length;
		h=new T[o];
		Array.Copy(a,h,o);
		Fu();
	}
	public void Fu(){
		b=new bool[o];
		arr=new T[n];
		li=new List<T[]>();
		Rc(0);
	}
	private void Rc(int a){
		for(int i=0;i<o;i++){
			if(!b[i]){
				arr[a]=h[i];
				if(a==n-1){
					li.Add(new T[n]);
					Array.Copy(arr,li[li.Count-1],n);
					cnt++;
				}
				else{b[i]=true;Rc(a+1);b[i]=false;}
			}
		}
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}