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"
	"strconv"
	"strings"
)

func main() {
	readInt()
	S, Result, Checker := readString(), 0, 0

	for _, c := range strings.Split(S, "") {
		switch c {
		case "A":
			Checker = 1

		case "B":
			if Checker == 1 {
				Checker = 2
			} else {
				Checker = 0
			}

		case "C":
			if Checker == 2 {
				Result++
			}
			Checker = 0
		}
	}

	fmt.Println(Result)
}

var scanner = bufio.NewScanner(os.Stdin)

func init() {
	scanner.Split(bufio.ScanWords)
	//scanner.Split(bufio.ScanLines)
}

func readInt() int {
	scanner.Scan()
	t, _ := strconv.Atoi(scanner.Text())
	return t
}

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