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)

fun <T> permutation(sortedList: List<T>): List<List<T>> {
    val queue = mutableListOf<List<T>>()
    queue += arrayListOf<T>()
    val permutations = mutableListOf<List<T>>()
    while (queue.isNotEmpty()) {
        val p = queue.removeAt(0)

        if (p.size == sortedList.size) {
            permutations += p
            continue
        }

        for (item in (sortedList - p)) {
            queue += (p + item)
        }
    }

    return permutations
}

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

    val per = permutation((1..n).toList()).map { it.joinToString("") }
    Math.abs(per.indexOf(p) - per.indexOf(q)).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)