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.Linq;

class K
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
		var M = 1000000007;

		var f = new long[n + 1];
		f[0] = 1;
		for (int i = 0; i < n; i++)
			f[i + 1] = f[i] * (i + 1) % M;

		var r = 0L;
		var st = new SegmentTree(n + 1);
		for (int i = 0; i < n; i++)
		{
			var c = st.Sum(0, a[i]);
			r = (r + (a[i] - c - 1) * f[n - i - 1]) % M;
			st.Add(a[i], 1);
		}
        var Pnum = r + 1;
      
        a = Console.ReadLine().Split().Select(int.Parse).ToArray();
       	f = new long[n + 1];
		f[0] = 1;
		for (int i = 0; i < n; i++)
			f[i + 1] = f[i] * (i + 1) % M;

		r = 0L;
		st = new SegmentTree(n + 1);
		for (int i = 0; i < n; i++)
		{
			var c = st.Sum(0, a[i]);
			r = (r + (a[i] - c - 1) * f[n - i - 1]) % M;
			st.Add(a[i], 1);
		}
        var Qnum = r + 1;
		Console.WriteLine(Math.Abs(Qnum-Pnum));
	}
}

class SegmentTree
{
	static int[] p2 = Enumerable.Range(0, 30).Select(i => (int)Math.Pow(2, i)).ToArray();
	static Dictionary<int, int> p2_ = Enumerable.Range(0, 30).ToDictionary(i => p2[i], i => i);

	static int LogFloor(int v)
	{
		for (int i = 1; ; i++) if (p2[i] > v) return i - 1;
	}

	int n2, logn;
	int[] a;
	public SegmentTree(int n)
	{
		logn = (int)Math.Ceiling(Math.Log(n, 2));
		n2 = p2[logn];
		a = new int[2 * n2];
	}

	public void Add(int i, int v)
	{
		for (i += n2; i > 0; i /= 2) a[i] += v;
	}

	// 簡易実装
	public int Sum(int start, int count)
	{
		if (p2_.ContainsKey(count))
		{
			return a[(start + n2) / count];
		}
		else
		{
			var c2 = p2[LogFloor(count)];
			return Sum(start, c2) + Sum(start + c2, count - c2);
		}
	}
}