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 main(args: Array<String>) {
    val n = readInteger()
    val pList = readIntegerList().joinToString()
    val qList = readIntegerList().joinToString()

    val permutationList = permutationListFrom(Array(n) { it + 1 }).map {
        it.joinToString()
    }

    println(Math.abs(permutationList.indexOf(pList) - permutationList.indexOf(qList)))

}

fun <T : Comparable<T>> permutationListFrom(array: Array<T>): List<Array<T>> {
    val current = array.copyOf()
    val permutationList = mutableListOf<Array<T>>()
    do {
        permutationList += current.copyOf()
    } while (nextPermutation(current))

    return permutationList
}

fun <T : Comparable<T>> nextPermutation(currentPermutation: Array<T>): Boolean {
    fun <T> Array<T>.reverse(start: Int, end: Int) {
        val midPoint = ((start + end) / 2) - 1
        if (midPoint < 0) return
        var reverseIndex = end - 1
        for (index in start..midPoint) {
            val tmp = this[index]
            this[index] = this[reverseIndex]
            this[reverseIndex] = tmp
            reverseIndex--
        }
    }

    val n = currentPermutation.size

    var i = n - 2
    while (i >= 0) {
        if (currentPermutation[i] < currentPermutation[i + 1]) break
        i--
    }

    if (i < 0) return false

    var j = n
    do {
        j--
    } while (currentPermutation[i] > currentPermutation[j])

    if (currentPermutation[i] < currentPermutation[j]) {
        val tmp = currentPermutation[i]
        currentPermutation[i] = currentPermutation[j]
        currentPermutation[j] = tmp
        currentPermutation.reverse(i + 1, n)
        return true
    }

    return false
}

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