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"
	"strconv"
)

func main() {
	n := readI()
	P, Q := make([]int, n), make([]int, n)
	for i := 0; i < n; i++ {
		P[i] = readI()
	}
	for i := 0; i < n; i++ {
		Q[i] = readI()
	}

	if isLager(P, Q) {
		P, Q = Q, P
	}

	i := 0
	for ; !isSame(P, Q); i++ {
		nextPermutation(P)
	}

	fmt.Println(i)
}

func isLager(a, b []int) bool {
	for i := 0; i < len(a); i++ {
		if a[i] != b[i] {
			if a[i] > b[i] {
				return true
			}
			return false
		}
	}
	return false
}

func isSame(a, b []int) bool {
	for i := 0; i < len(a); i++ {
		if a[i] != b[i] {
			return false
		}
	}
	return true
}

func nextPermutation(p []int) bool {
	swap := func(a []int, b, c int) {
		a[b], a[c] = a[c], a[b]
	}
	rev := func(s []int) {
		for i := 0; i < len(s)/2; i++ {
			swap(s, i, len(s)-1-i)
		}
	}

	l, r := len(p)-2, len(p)-1

	for p[l] >= p[l+1] {
		if l == 0 {
			rev(p)
			return false
		}
		l--
	}
	for p[l] >= p[r] {
		r--
	}

	swap(p, l, r)
	rev(p[l+1:])
	return true
}

/*-----------Input utils-----------*/

var sc = bufio.NewScanner(os.Stdin)

func init() {
	if len(os.Args) >= 2 {
		if os.Args[1] == "debug" {
			debug()
		}
	}
	const buf = 200100
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, buf), buf)
}

func debug() {
	testFile, err := os.Open("./test/sample-2.in")
	if err != nil {
		fmt.Fprintln(os.Stderr, "There is no testfile.")
		os.Exit(1)
	}
	sc = bufio.NewScanner(testFile)
}

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

func readR() []rune {
	return []rune(readS())
}

func readI() int {
	i, _ := strconv.Atoi(readS())
	return i
}

func readF() float64 {
	f, _ := strconv.ParseFloat(readS(), 64)
	return f
}