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 (
	"fmt"
	"math"
	"reflect"
	"sort"
)

// NextPermutation test
func NextPermutation(x sort.Interface) bool {
	n := x.Len() - 1
	if n < 1 {
		return false
	}
	j := n - 1
	for ; !x.Less(j, j+1); j-- {
		if j == 0 {
			return false
		}
	}
	l := n
	for !x.Less(j, l) {
		l--
	}
	x.Swap(j, l)
	for k, l := j+1, n; k < l; {
		x.Swap(k, l)
		k++
		l--
	}
	return true
}
func main() {
	var n int
	fmt.Scan(&n)

	listp := make([]int, n)
	listq := make([]int, n)
	for i := 0; i < n; i++ {
		fmt.Scan(&listp[i])
	}
	for i := 0; i < n; i++ {
		fmt.Scan(&listq[i])
	}

	permu := make([]int, n)
	copy(permu, listp)
	sort.Sort(sort.IntSlice(permu))

	numP := 1
	numQ := 1
	for i := 1; NextPermutation(sort.IntSlice(permu)); i++ {
		if reflect.DeepEqual(permu, listp) {
			numP = i + 1
		}
		if reflect.DeepEqual(permu, listq) {
			numQ = i + 1
		}
	}
	fmt.Println(math.Abs(float64(numP) - float64(numQ)))

}