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: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
)

var facts []int

func main() {
	// fetch
	N := readint()
	facts = make([]int, N)
	_ = facts[N-1]
	P := make([]int, N)
	for i := 0; i < N; i++ {
		P[i] = readint()
	}
	Q := make([]int, N)
	for i := 0; i < N; i++ {
		Q[i] = readint()
	}
	// calc
	pp := 1
	qp := 1
	for i := 0; i < N; i++ {
		p := append([]int{}, P[i:]...)
		q := append([]int{}, Q[i:]...)
		sort.Sort(sort.IntSlice(p))
		sort.Sort(sort.IntSlice(q))
		pi := sort.SearchInts(p, P[i])
		qi := sort.SearchInts(q, Q[i])
		pp += pi * factorial(N-i-1)
		qp += qi * factorial(N-i-1)
		fmt.Println(pp, qp)
	}
	fmt.Println(absub(pp, qp))
}

func absub(a, b int) int {
	if a < b {
		return b - a
	}
	return a - b
}

func factorial(n int) (res int) {
	if facts[n] != 0 {
		res = facts[n]
		return res
	}

	if n > 0 {
		res = n * factorial(n-1)
		return res
	}

	return 1
}

const (
	iobufsize = 1 * 1024 * 1024 // 1 MB
)

var stdinsc = func() *bufio.Scanner {
	sc := bufio.NewScanner(os.Stdin)
	sc.Buffer(make([]byte, iobufsize), iobufsize)
	sc.Split(bufio.ScanWords)
	return sc
}()

func readint() int {
	stdinsc.Scan()
	v, err := strconv.Atoi(stdinsc.Text())
	if err != nil {
		panic(err)
	}
	return v
}

func readstr() string {
	stdinsc.Scan()
	return stdinsc.Text()
}

func pow(x, y int) int {
	if y < 1 {
		return 1
	}
	return x * pow(x, y-1)
}

func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}