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 = bufio.NewScanner(os.Stdin)

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

func scanInt() int {
	sc.Scan()
	a, err := strconv.Atoi(sc.Text())
	if err != nil {
		fmt.Println(err)
	}
	return a
}

func scanInt64() int64 {
	sc.Scan()
	a, err := strconv.Atoi(sc.Text())
	if err != nil {
		fmt.Println(err)
	}
	return int64(a)
}

func scanFloat() float64 {
	sc.Scan()
	a, err := strconv.ParseFloat(sc.Text(), 64)
	if err != nil {
		fmt.Println(err)
	}
	return a
}

func scanTextSlice(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = scanText()
	}
	return a
}

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

func scanFloatSlice(n int) []float64 {
	a := make([]float64, n)
	for i := 0; i < n; i++ {
		a[i] = scanFloat()
	}
	return a
}

func scanInt64Slice(n int64) []int64 {
	a := make([]int64, n)
	for i := int64(0); i < n; i++ {
		a[i] = scanInt64()
	}
	return a
}

// var sc = bufio.NewScanner(os.Stdin)

func main() {
	sc.Split(bufio.ScanWords)

	n := scanInt()
	// arr := make([]float64, 0)
	p := scanSlice(n)
	q := scanSlice(n)

	memo := make([]int, 0)
	for i := 1; i <= n; i++ {
		memo = append(memo, i)
	}

	m := n - 1
	partial := factorial(m)

	pNum := int64(1)

	for i := 0; i < n-1; i++ {
		num := p[i]
		index := binarySearch(memo, num)
		memo = deleteNumOfArray(memo, index)
		pNum += partial * int64(index)
		partial /= int64(m)
		m--
		// fmt.Println("memo: ", memo)
		// fmt.Println("pNum: ", pNum)

	}

	// fmt.Println("------------------------")

	memo = make([]int, 0)
	for i := 1; i <= n; i++ {
		memo = append(memo, i)
	}
	// fmt.Println(memo)

	m = n - 1
	partial = factorial(m)

	qNum := int64(1)

	for i := 0; i < n-1; i++ {
		num := q[i]
		index := binarySearch(memo, num)
		memo = deleteNumOfArray(memo, index)
		qNum += partial * int64(index)
		partial /= int64(m)
		m--
	}
	ans := pNum - qNum
	if ans < 0 {
		ans *= -1
	}
	fmt.Println(ans)

}

func binarySearch(arr []int, number int) int {
	// fmt.Println("number: %s", number)

	l := -1
	r := len(arr)
	index := 0
	for {
		mid := l + (r-l)/2
		tmp := arr[mid]
		// fmt.Println("number: %s", number)
		// fmt.Println("tmp: %s", tmp)
		// fmt.Println("mid: %s , left : %s , right : %s", mid, l, r)

		if r-l <= 1 || tmp == number {
			index = mid
			break
		} else if tmp < number {
			l = mid
		} else {
			r = mid
		}
	}
	return index
}

func factorial(n int) int64 {
	sum := int64(1)
	for i := 2; i <= n; i++ {
		sum *= int64(i)
	}
	return sum
}

func deleteNumOfArray(arr []int, position int) []int {
	left := arr[:position]
	r := arr[position+1:]
	appendArr := append(left, r...)
	return appendArr
}