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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

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

func nextInt() int {
	sc.Scan()
	i, _ := strconv.Atoi(sc.Text())
	return i
}

func nextFloat64() float64 {
	f, _ := strconv.ParseFloat(next(), 64)
	return f
}

func nextInts(n int) []int {
	slice := make([]int, n)
	for i := 0; i < n; i++ {
		slice[i] = nextInt()
	}
	return slice
}

func fact(n int) int {
	ret := 1
	for i := 1; i <= n; i++ {
		ret *= i
	}
	return ret
}

func rank(n int, x []int) int {
	t := make([]int, n)
	ret := 0
	// xのi番目の数字
	for i := 0; i < n-1; i++ {
		for j := 1; j <= n; j++ {
			if t[j-1] == 0 && j != x[i] {
				ret += fact(n - 1 - i)
			} else if j == x[i] {
				t[j-1] = 1
				break
			}
		}
	}
	return ret
}

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

func main() {
	sc.Split(bufio.ScanWords)
	n := nextInt()
	p := nextInts(n)
	q := nextInts(n)

	fmt.Println(abs(rank(n, p) - rank(n, q)))
}