Problem:
Score : 200 points

Problem Statement

A sequence a=\{a_1,a_2,a_3,......\} is determined as follows:

The first term s is given as input.

Let f(n) be the following function: f(n) = n/2 if n is even, and f(n) = 3n+1 if n is odd.

a_i = s when i = 1, and a_i = f(a_{i-1}) when i > 1.

Find the minimum integer m that satisfies the following condition:

There exists an integer n such that a_m = a_n (m > n).

Constraints

1 \leq s \leq 100

All values in input are integers.

It is guaranteed that all elements in a and the minimum m that satisfies the condition are at most 1000000.

Input

Input is given from Standard Input in the following format:

s

Output

Print the minimum integer m that satisfies the condition.

Sample Input 1

8

Sample Output 1

5

a=\{8,4,2,1,4,2,1,4,2,1,......\}. As a_5=a_2, the answer is 5.

Sample Input 2

7

Sample Output 2

18

a=\{7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1,......\}.

Sample Input 3

54

Sample Output 3

114

Solution in Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
  val s = io.StdIn.readLine.toInt

  def f(n: Int) = n match {
    case n if n % 2 == 0 => n / 2
    case n => 3 * n + 1
  }

  def test: Int = {
    var previous = s
    var map = Set[Int](s)

    for (i <- 2 to 1000000) {
      val ai = f(previous)
      if (map.contains(ai)) return i
      map = map + ai
      previous = ai
    }
    ???
  }

  val out = test

  println(out)
}