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: Wrong Answer)

package main

import (
	"fmt"
	"math"
	"reflect"
)

func permutation(n int, k int) int {
	v := 1
	if 0 < k && k <= n {
		for i := 0; i < k; i++ {
			v *= (n - i)
		}
	} else if k > n {
		v = 0
	}
	return v
}

func factorial(n int) int {
	return permutation(n, n-1)
}

func main() {
	// Code for C - Count Order
	var N int
	fmt.Scanf("%d", &N)

	P := make([]int, N)
	Q := make([]int, N)
	for i := 0; i < N; i++ {
		fmt.Scanf("%d", &P[i])
	}

	for i := 0; i < N; i++ {
		fmt.Scanf("%d", &Q[i])
	}

	a := make([]int, 0)
	for i := 1; i <= N; i++ {
		a = append(a, i)
	}

	var n = len(a) - 1
	var i, j int
	var ans1, ans2 int
	for c := 1; c < factorial(len(a)); c++ { // 3! = 6:
		i = n - 1
		j = n
		for a[i] > a[i+1] {
			i--
		}
		for a[j] < a[i] {
			j--
		}
		a[i], a[j] = a[j], a[i]
		j = n
		i++
		for i < j {
			a[i], a[j] = a[j], a[i]
			i++
			j--
		}

		if reflect.DeepEqual(a, P) {
			ans1 = c + 1
		}
		if reflect.DeepEqual(a, Q) {
			ans2 = c + 1
		}
	}

	fmt.Println(int(math.Abs(float64(ans2 - ans1))))
}