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"
	"io"
	"log"
	"os"
	"sort"
	"strconv"
	"strings"
)

func solution(n int, p, q []int) int {
	i := dictionaryOrder(p)
	j := dictionaryOrder(q)
	log.Printf("i: %d, j: %d", i, j)
	return abs(i, j)
}

func abs(x, y int) int {
	z := x - y
	if z < 0 {
		return z * -1
	}
	return z
}

func dictionaryOrder(nums []int) int {
	var ans int
	l := len(nums)
	for i := 0; i < l; i++ {
		n := nums[i]
		arr := make([]int, len(nums)-i)
		copy(arr, nums[i:])
		a := ascNumber(arr, n) - 1
		if a == 0 {
			ans += 0
		} else {
			ans += a * factorical(l-i-1)
		}
	}
	ans++
	return ans
}

func ascNumber(nums []int, n int) int {
	sort.Ints(nums)
	var i int = 1
	for _, v := range nums {
		if v == n {
			break
		}
		i++
	}
	return i
}

func factorical(n int) int {
	if n == 0 || n == 1 {
		return 1
	}
	return n * factorical(n-1)
}

func main() {
	reader := bufio.NewReaderSize(os.Stdin, 10240*10240)

	n, err := strconv.Atoi(readLine(reader))
	checkError(err)
	p := make([]int, n)
	ss := strings.Split(readLine(reader), " ")
	for i := range ss {
		p[i], err = strconv.Atoi(ss[i])
		checkError(err)
	}
	q := make([]int, n)
	ss = strings.Split(readLine(reader), " ")
	for i := range ss {
		q[i], err = strconv.Atoi(ss[i])
		checkError(err)
	}
	fmt.Println(solution(n, p, q))
}

func readLine(reader *bufio.Reader) string {
	str, _, err := reader.ReadLine()
	if err == io.EOF {
		return ""
	}

	return strings.TrimRight(string(str), "\r\n")
}

func checkError(err error) {
	if err != nil {
		panic(err)
	}
}