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 Go (1.6) (judge verdict: Accepted)

/**
 * func bitExhaustiveSearch(n int, fn func(a []bool))
 *
 * Verified
 *	ALDS1_5_A: Exhaustive Search
 *	http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_5_A&lang=ja
 *
 * These codes are licensed under CC0.
 * https://creativecommons.org/publicdomain/zero/1.0/
 */

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc, wr = bufio.NewScanner(os.Stdin), bufio.NewWriter(os.Stdout)

func scanString() string   { sc.Scan(); return sc.Text() }
func scanRunes() []rune    { return []rune(scanString()) }
func scanInt() int         { a, _ := strconv.Atoi(scanString()); return a }
func scanInt64() int64     { a, _ := strconv.ParseInt(scanString(), 10, 64); return a }
func scanFloat64() float64 { a, _ := strconv.ParseFloat(scanString(), 64); return a }

func scanInts(n int) []int {
	res := make([]int, n)
	for i := 0; i < n; i++ {
		res[i] = scanInt()
	}
	return res
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

// Main

func main() {
	defer wr.Flush()
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 10000), 1001001)

	n := scanInt()
	p := scanInts(n)
	q := scanInts(n)

	var a, b int
	cnt := 0

	permutationSearch(n, func(arr []int) {
		f := true
		for i := 0; i < n; i++ {
			if p[i] != arr[i]+1 {
				f = false
			}
		}

		if f {
			a = cnt
		}

		f = true
		for i := 0; i < n; i++ {
			if q[i] != arr[i]+1 {
				f = false
			}
		}

		if f {
			b = cnt
		}

		cnt++
	})

	fmt.Fprintln(wr, abs(a-b))

}

func permutationSearch(n int, fn func(a []int)) {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = i
	}
	swap := func(i, j int) { a[i], a[j] = a[j], a[i] }

	fn(a)
	for i := n - 2; i >= 0; i-- {
		if a[i] > a[i+1] {
			continue
		}
		for j := n - 1; j >= 0; j-- {
			if a[i] > a[j] {
				continue
			}
			swap(i, j)
			for k := i + 1; k < (n+i+1)/2; k++ {
				swap(k, n-(k-i))
			}
			fn(a)
			i = n - 1
			break
		}
	}
}