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 (
	"fmt"
	"strings"
)

func main() {
	var n int
	fmt.Scan(&n)

	var p, q, t int
	for i := 0; i < n; i++ {
		fmt.Scan(&t)
		p = p*10 + t
	}
	for i := 0; i < n; i++ {
		fmt.Scan(&t)
		q = q*10 + t
	}

	ps := make([]int, 0)
	var dfs func(s int)
	dfs = func(s int) {
		a := fmt.Sprint(s)
		if len(a) == n {
			ps = append(ps, s)
			return
		}
		for i := 1; i <= n; i++ {
			if !strings.Contains(a, fmt.Sprint(i)) {
				dfs(s*10 + i)
			}
		}
	}
	dfs(0)

	pi, qi := 0, 0
	for i := 0; i < len(ps); i++ {
		if ps[i] == p {
			pi = i + 1
		}
		if ps[i] == q {
			qi = i + 1
		}
	}

	ans := abs(pi - qi)
	fmt.Println(ans)
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}