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.*

fun main(args: Array<String>) {
    val n = readLine()!!.toInt()
    val p = readLine()!!.split(" ").map { it.toInt() }.reversed()
    val q = readLine()!!.split(" ").map { it.toInt() }.reversed()
    val pn = calc(p)
    val qn = calc(q)
//    println(pn)
//    println(qn)
    println(Math.abs(pn - qn))

}

private fun calc(list: List<Int>): Long {
    var n = 0L
    val que = ArrayDeque(list)
    while (que.isNotEmpty()) {
        val i = que.removeLast()
        val size = que.filter { it < i }.size
        val f = size * factorial(que.size)
        // println("$i $que ($size * ${factorial(que.size)})=$f")
        n += f
    }
    return n + 1
}

private fun factorial(n: Int): Long {
    var sum = 1L
    for (i in (1..n)) {
        sum *= i
    }
    return sum
}