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"
	"math"
	"os"
	"strconv"
)

const (
	initialBufSize = 1024
	maxBufSize     = 1e6
)

var (
	scanner = bufio.NewScanner(os.Stdin)
)

func main() {
	scanner.Split(bufio.ScanWords)
	n := scanInt()
	p, q := scanInts(n), scanInts(n)
	fmt.Println(cal(n, p, q))
}

func cal(n int, p, q []int) int {

	pn := 1
	qn := 1
	for i := 0; i < n; i++ {
		f := fact(n - 1 - i)
		for j := (i + 1); j < n; j++ {
			if p[i] > p[j] {
				pn += f
			}
			if q[i] > q[j] {
				qn += f
			}
		}
	}

	return abs(pn - qn)
}

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

func scanInt() int {
	i, _ := strconv.Atoi(scanText())
	return i
}

func scanInts(size int) []int {
	ints := make([]int, size)
	for i := 0; i < size; i++ {
		ints[i] = scanInt()
	}
	return ints
}

func scanFloat64() float64 {
	f, _ := strconv.ParseFloat(scanText(), 64)
	return f
}

func scanFloat64s(size int) []float64 {
	f := make([]float64, size)
	for i := 0; i < size; i++ {
		f[i] = scanFloat64()
	}
	return f
}

func scanText() string {
	scanner.Scan()
	return scanner.Text()
}

func scanTexts(size int) []string {
	s := make([]string, size)
	for i := 0; i < size; i++ {
		s[i] = scanText()
	}
	return s
}

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

func pow(x, y int) int {
	return int(math.Pow(float64(x), float64(y)))
}

// greatest common divisor(最大公約数)
func gcd(a, b int) int {
	for {
		mod := a % b
		if mod == 0 {
			return b
		}
		a, b = b, mod
	}
}

// latest common multiple(最小公倍数)
func lcm(a, b int) int {
	return (a / gcd(a, b)) * b
}