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"
	"reflect"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)
var out = bufio.NewWriter(os.Stdout)

func main() {
	sc.Split(bufio.ScanWords)
	defer out.Flush() // !!!!caution!!!! you must use Fprint(out, ) not Print()
	/* --- code --- */

	n := nextInt()
	p, q := nextInts(n), nextInts(n)
	base := make([]int, n)
	for i := 0; i < n; i++ {
		base[i] = i
	}
	g := next_permutation(base)
	var a, b int
	count := 1
	for {
		indicies := g()
		if len(indicies) == 0 {
			break
		}
		arr := make([]int, n)
		for i := 0; i < n; i++ {
			arr[i] = base[indicies[i]] + 1
		}
		if reflect.DeepEqual(arr, p) {
			a = count
		}
		if reflect.DeepEqual(arr, q) {
			b = count
		}
		count += 1
	}
	fmt.Fprintln(out, abs(a, b))
}

func abs(a, b int) int {
	if a < 0 {
		a *= -1
	}
	if b < 0 {
		b *= -1
	}
	if a > b {
		a, b = b, a
	}
	return b - a
}

// -*-*-*-*-*-*-*-*-
// * I/O utilities *
// -*-*-*-*-*-*-*-*-

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

func nextInt() int {
	a, _ := strconv.Atoi(next())
	return a
}

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

func nextInts(n int) []int {
	ret := make([]int, n)
	for i := 0; i < n; i++ {
		ret[i] = nextInt()
	}
	return ret
}
func nextFloats(n int) []float64 {
	ret := make([]float64, n)
	for i := 0; i < n; i++ {
		ret[i] = nextFloat64()
	}
	return ret
}
func nextStrings(n int) []string {
	ret := make([]string, n)
	for i := 0; i < n; i++ {
		ret[i] = next()
	}
	return ret
}

func split(s string) []string {
	ret := make([]string, len([]rune(s)))
	for i, v := range []rune(s) {
		ret[i] = string(v)
	}
	return ret
}

func PrintOut(src interface{}, joinner string) {
	switch reflect.TypeOf(src).Kind() {
	case reflect.Slice:
		s := reflect.ValueOf(src)
		for idx := 0; idx < s.Len(); idx++ {
			fmt.Fprintf(out, "%v", s.Index(idx))
			if idx < s.Len()-1 {
				fmt.Fprintf(out, "%s", joinner)
			} else {
				fmt.Fprintln(out)
			}
		}
	default:
		fmt.Fprintln(out, "fuck")
	}
}

// -*-*-*-*-*-*-*-*-
// * tool snippets *
// -*-*-*-*-*-*-*-*-
func duplicate2Int(base [][]int) (ret [][]int) {
	ret = make([][]int, len(base))
	for i, v := range base {
		ret[i] = append([]int{}, v...)
	}
	return
}

// -*-*-*-*-*-*-*-*-*-*-*-*-*-
// * Algorithms Utility Zone *
// -*-*-*-*-*-*-*-*-*-*-*-*-*-

// -*-*-*-*-*-*-*-
// * 1. nibutan  *
// -*-*-*-*-*-*-*-
func lower_bound(arr []int, target int) int {
	l, r := 0, len(arr)
	for l < r {
		mid := (l + r) / 2
		if arr[mid] < target {
			l = mid + 1
		} else {
			r = mid
		}
	}
	return l
}

func upper_bound(arr []int, target int) int {
	l, r := 0, len(arr)
	for l < r {
		mid := (l + r) / 2
		if target < arr[mid] {
			r = mid
		} else {
			l = mid + 1
		}
	}
	return l
}

// *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
// * math flavor typical theories *
// *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
func gcd(a, b int) int {
	if a > b {
		return gcd(b, a)
	}
	for a != 0 {
		a, b = b%a, a
	}
	return b
}

func pow(a, b int) (ret int) {
	ret = a
	// 10^2 = 100ってことは10に10を1回掛けることだね
	// なので初期値を含めると上限b-1未満
	for i := 0; i < b-1; i++ {
		ret *= a
	}
	return
}

func powMod(n, m, mod int) (ret int) {
	ret = 1
	for m > 0 {
		if m&1 == 1 {
			ret *= n
			ret %= mod
		}
		n *= n
		n %= mod
		m >>= 1
	}
	return ret
}

func next_permutation(arr []int) func() []int {
	/*
		how to use it:
			this is a generator, so should be invoked such as below example.

			"""code"""
			np := next_permutation(arr)
			for{
				lis := np()
				if len(lis) == 0{
					break
				}
				fmt.Println(lis)
			}
			"""code end"""
	*/
	first := true
	ret := append([]int{}, arr...)
	_next_permutation := func() []int {
		if first {
			first = false
			return arr
		}
		n := len(ret)
		for i := n - 2; i >= 0; i-- {
			if ret[i] < ret[i+1] {
				j := n
				for {
					j -= 1
					if ret[i] < ret[j] {
						break
					}
				}
				ret[i], ret[j] = ret[j], ret[i]
				for k := n - 1; i < k; i, k = i+1, k-1 {
					ret[i+1], ret[k] = ret[k], ret[i+1]
				}
				return ret
			}
		}
		return []int{}
	}
	return _next_permutation
}

func factorial_n(n int) int {
	ret := n
	for i := n - 1; i > 0; i-- {
		ret *= i
	}
	return ret
}