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 readInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return i
}

var perms [][]int

func main() {
	sc.Split(bufio.ScanWords)
	n := readInt()

	rest := make([]int, n)
	p := make([]int, n)
	for i := 0; i < n; i++ {
		p[i] = readInt()
		rest[i] = i + 1
	}
	q := make([]int, n)
	for i := 0; i < n; i++ {
		q[i] = readInt()
	}

	perms = make([][]int, 0)
	perm([]int{}, rest)

	pi, pq := 0, 0
	for i := 0; i < len(perms); i++ {
		if equal(perms[i], p) {
			pi = i
		}
		if equal(perms[i], q) {
			pq = i
		}
	}
	fmt.Println(abs(pi - pq))
}

func abs(x int) int {
	if x < 0 {
		return x * -1
	}
	return x
}

func equal(x, y []int) bool {
	if len(x) != len(y) {
		return false
	}
	n := len(x)
	for i := 0; i < n; i++ {
		if x[i] != y[i] {
			return false
		}
	}
	return true
}

func perm(head, rest []int) []int {
	if len(rest) == 0 {
		perms = append(perms, head)
		return head
	}
	res := make([]int, 0)
	for i := 0; i < len(rest); i++ {
		restx := make([]int, len(rest))
		copy(restx, rest)

		headx := make([]int, len(head))
		copy(headx, head)

		headx = append(headx, restx[i])
		restx = append(restx[:i], restx[i+1:]...)
		res = perm(headx, restx)
	}
	return res
}