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 = nextInt()
    val P = listOfInt(-1).joinToString(separator = "")
    val Q = listOfInt(-1).joinToString(separator = "")
    val A = IntArray(N)
    val R = mutableListOf<String>()
    fun Permutation(n: Int) {
        if (n == N) {
            R.add(A.joinToString(separator = ""))
        } else {
            for (m in 0 until N) {
                if (A.slice(0 until n).all { it != m }) {
                    A[n] = m
                    Permutation(n + 1)
                }
            }
        }
    }
    Permutation(0)
    var p = 0
    var q = 0
    for (a in R) {
        if (a == P) break;
        p += 1
    }
    for (a in R) {
        if (a == Q) break;
        q += 1
    }
    println(Math.abs(p - q))
}
fun next() = readLine()!!
fun listOfString() = next().split(" ")
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun listOfInt(delta: Int = 0) = listOfString().map { Integer.parseInt(it) + delta }