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, wr = bufio.NewScanner(os.Stdin), bufio.NewWriter(os.Stdout)

func scanString() string { sc.Scan(); return sc.Text() }
func scanInt() int { a,_ := strconv.Atoi(scanString()); return a }
func scanInt64() int64 { a,_ := strconv.ParseInt(scanString(),10,64); return a }
func scanFloat64() float64 { a,_ := strconv.ParseFloat(scanString(),64); return a }

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

func abs(a int) int { if a<0 { return -a }; return a }
func min(a,b int) int { if a<b { return a }; return b }
func max(a,b int) int { if a>b { return a }; return b }

//•*¨*•.¸¸♪Main•*¨*•.¸¸♪(　-ω-)ノ　(　・ω・)

func main() {
	defer wr.Flush()
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 10000), 1001001)

	n := scanInt()
	p := scanInts(n)
	q := scanInts(n)

	var a,b int
	cnt := 0
	permutationSearch(n, func(perm []int) {
		f1,f2 := true, true
		for i := 0; i < n; i++ {
			if perm[i]+1 != p[i] {
				f1 = false
			}
			if perm[i]+1 != q[i] {
				f2 = false
			}
		}
		if f1 {
			a = cnt
		}
		if f2 {
			b = cnt
		}
		cnt++
	})

	fmt.Fprintln(wr, abs(a-b))
	// fmt.Fprintln(wr, a,b)
}

func permutationSearch(n int, fn func(a []int)) {
	a := make([]int, n)
	for i := 0; i < n; i++ { a[i] = i }
	swap := func(i,j int) { a[i],a[j] = a[j],a[i] }

	fn(a)
	for i := n-2; i >= 0; i-- {
		if a[i] < a[i+1] {
			for j := n-1; j >= 0; j-- {
				if a[i] < a[j] {
					swap(i,j)
					for k := i+1; k < (n+i+1)/2; k++ { swap(k,n-(k-i)) }
					fn(a)
					i = n-1
					break
				}
			}
		}
	}
}