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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

tailrec fun <T> calcPermutationList(
    sortedList: Array<T>,
    queue: ArrayDeque<List<T>>,
    permutationList: MutableList<List<T>> = mutableListOf()
): List<List<T>> {
    if (queue.isEmpty()) {
        return permutationList
    }

    val p = queue.removeFirst()
    if (p.size == sortedList.size) {
        permutationList += p
    } else {
        queue += sortedList.filterNot { p.contains(it) }.map { p + it }
    }

    return calcPermutationList(sortedList, queue, permutationList)
}

fun main(args: Array<String>) {
    val n = readInteger()
    val p = readIntegerList()
    val q = readIntegerList()

    calcPermutationList((1..n).toList().toTypedArray(), ArrayDeque<List<Int>>().apply { addFirst(listOf()) })
        .let { it.indexOf(p) - it.indexOf(q) }
        .let(Math::abs)
        .let(::println)
}

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)