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 (
	"fmt"
)

var n int

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

	ps := make([]int, n)
	for i := range ps {
		fmt.Scan(&ps[i])
	}
	qs := make([]int, n)
	for i := range qs {
		fmt.Scan(&qs[i])
	}
	p := calc(ps)
	q := calc(qs)

	fmt.Println(abs(p - q))
}

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

func calc(s []int) int {
	l := len(s)
	m := 1
	for i := 1; i <= l; i++ {
		m *= i
	}

	var sum int
	ms := make([]int, n)
	for _, v := range s {
		m /= l
		var cnt int
		for j := 0; j < n; j++ {
			if ms[j] == 0 {
				cnt++
				if j == v-1 {
					break
				}
			}
		}
		sum += m * (cnt - 1)
		ms[v-1] = 1
		l--
	}
	return sum + 1
}