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"
)

var scanner = bufio.NewScanner(os.Stdin)
var a int
var b string
var c string

func main() {

	scanner.Scan()
	a, _ = strconv.Atoi(scanner.Text())
	scanner.Scan()
	b = scanner.Text()
	scanner.Scan()
	c = scanner.Text()

	bs := strings.Split(b, " ")
	cs := strings.Split(c, " ")
	var bc int
	var cc int
	for i := 0; i < a-1; i++ {
		for j := i + 1; j < a; j++ {
			in, _ := strconv.Atoi(bs[i])
			jn, _ := strconv.Atoi(bs[j])
			if in > jn {
				bc = bc + (a - i)
			}
			cin, _ := strconv.Atoi(cs[i])
			cjn, _ := strconv.Atoi(cs[j])
			if cin > cjn {
				cc = cc + (a - i)
			}
		}
	}
	if bc < cc {
		fmt.Print(cc - bc - 1)
	} else if cc < bc {
		fmt.Print(bc - cc - 1)
	} else {
		fmt.Print(0)
	}
}