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 = readInt()
  val P = readInts()
  val Q = readInts()

  val origin = (1..N).toMutableList()
  var pIndex = 0
  var qIndex = 0
  for (i in 0 until Int.MAX_VALUE) {
    if (origin == P) pIndex = i
    if (origin == Q) qIndex = i
    if (!nextPermutation(origin)) break
  }
  println(Math.abs(pIndex - qIndex))
}

fun readString() = readLine()!!
fun readInt() = readLine()!!.toInt()
fun readInts() = readLine()!!.split(" ").map { it.toInt() }

/** 順列の列挙 c++ のやつと一緒 */
fun nextPermutation(list: MutableList<Int>): Boolean {
  for (i in list.size - 2 downTo 0) {
    if (list[i] < list[i + 1]) {
      for (j in list.size - 1 downTo 0) {
        if (list[i] < list[j]) {
          val tmp = list[i]
          list[i] = list[j]
          list[j] = tmp
          list.subList(i + 1, list.size).reverse()
          return true
        }
      }
    }
  }
  list.reverse()
  return false
}