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 (1.14.1) (judge verdict: Accepted)

package main

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

var sc = bufio.NewScanner(os.Stdin)

func main() {
	scanInit()

	n := nextInt()
	pl := make([]int, n)
	ql := make([]int, n)

	for i := 0; i < n; i++ {
		pl[i] = nextInt()
	}
	for i := 0; i < n; i++ {
		ql[i] = nextInt()
	}
	// p,qの数値化
	p, q := 0, 0
	for j := 0; j < n; j++ {
		p += pl[j] * pow(10, n-j-1)
	}
	for j := 0; j < n; j++ {
		q += ql[j] * pow(10, n-j-1)
	}

	// 順列作成
	var tl []int = []int{1, 2, 3, 4, 5, 6, 7, 8}
	pall := permutations(tl[:n])

	// 数値リスト化
	pallnum := make([]int, len(pall))
	for i := 0; i < len(pall); i++ {
		tmp := 0
		for j := 0; j < n; j++ {
			tmp += pall[i][j] * pow(10, n-j-1)
		}
		pallnum[i] = tmp
	}

	// 順列並びかえ
	sort.Ints(pallnum)

	pidx := -1
	qidx := -1
	for i := 0; i < len(pall); i++ {
		// pidxとqidxが求まっているならば終わり
		if pidx != -1 && qidx != -1 {
			break
		}

		// p比較
		if p == pallnum[i] {
			pidx = i
		}

		// q比較
		if q == pallnum[i] {
			qidx = i
		}
	}

	fmt.Println(abs(pidx - qidx))

}

func permutations(arr []int) [][]int {
	var helper func([]int, int)
	res := [][]int{}

	helper = func(arr []int, n int) {
		if n == 1 {
			tmp := make([]int, len(arr))
			copy(tmp, arr)
			res = append(res, tmp)
		} else {
			for i := 0; i < n; i++ {
				helper(arr, n-1)
				if n%2 == 1 {
					tmp := arr[i]
					arr[i] = arr[n-1]
					arr[n-1] = tmp
				} else {
					tmp := arr[0]
					arr[0] = arr[n-1]
					arr[n-1] = tmp
				}
			}
		}
	}
	helper(arr, len(arr))
	return res
}
func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}
func pow(a, b int) int {
	var ret int = 1
	for b > 0 {
		if (b & 1) == 1 {
			ret *= a
		}
		a *= a
		b >>= 1
	}
	return ret
}

// ---- readfunc
func scanInit() {
	const cap = 64 * 1024
	var buf = make([]byte, cap)
	sc.Buffer(buf, cap)
	sc.Split(bufio.ScanWords)
	return
}
func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}
func nextStr() string {
	sc.Scan()
	return sc.Text()
}