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)

package main

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

var sc = bufio.NewScanner(os.Stdin)

func scanInt() int {
	num, _ := strconv.Atoi(scanString())
	return num
}

func scanString() string {
	sc.Scan()
	return sc.Text()
}

func init() {
	sc.Split(bufio.ScanWords)
}

func abs(n int) int {
	if n >= 0 {
		return n
	}
	return -n
}

func Perm(arr []int) [][]int {
	ret := make([][]int, 0)
	perm(arr, &ret, 0)
	return ret
}

func perm(arr []int, ret *[][]int, i int) {
	if i > len(arr) {
		*ret = append(*ret, append([]int{}, arr...))
		return
	}
	perm(arr, ret, i+1)
	for j := i + 1; j < len(arr); j++ {
		arr[i], arr[j] = arr[j], arr[i]
		perm(arr, ret, i+1)
		arr[i], arr[j] = arr[j], arr[i]
	}
}

func index(a []int, t [][]int) int {
	i := 0
	for _, arr := range t {
		for j, e := range a {
			if e == arr[j] {
				continue
			} else {
				if e > arr[j] {
					i++
				}
				break
			}
		}
	}
	return i
}

func main() {
	n := scanInt()
	arr := make([]int, n)
	for i := range arr {
		arr[i] = i + 1
	}

	p := make([]int, n)
	for i := range p {
		p[i] = scanInt()
	}

	q := make([]int, n)
	for i := range q {
		q[i] = scanInt()
	}

	permutations := Perm(arr)
	indexP := index(p, permutations) + 1
	indexQ := index(q, permutations) + 1

	fmt.Println(abs(indexP - indexQ))
}