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 sc = java.util.Scanner(System.`in`)
    val n = sc.nextInt()
    val p = sc.asSequence().take(n).map { it.toInt() }.joinToString("")
    val q = sc.asSequence().take(n).map { it.toInt() }.joinToString("")

    val s = (1..n).map { it.toString() }.joinToString("")
    val all = mutableListOf<String>()
    permutation(s, "", all)
    all.sort()
//    println(p)
//    println(q)
//    println(all)
    print(Math.abs(all.indexOf(q) - all.indexOf(p)))
}

fun permutation(q: String, ans: String, all: MutableList<String>) {
    // Base Case
    if (q.length <= 1) {
        all.add(ans + q)
    } else {
        for (i in 0 until q.length) {
            permutation(
                q.substring(0, i) + q.substring(i + 1),
                ans + q[i],
                all
            )
        }
    }// General Case
}