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)

import scala.io.{StdIn => in}
import scala.collection.{mutable => mu}

object Main extends App {
  val s = in.readInt
  val fEvn = (n:Int) => n / 2
  val fOdd = (n:Int) => 3 * n + 1

  def solve(s:Int):Int = {
    val set = mu.HashSet.empty[Int]
    def rec(acc:Int, i:Int):Int = {
      if(set.contains(acc)) i-1
      else {
        set += acc
        val n = if(acc % 2 == 0) fEvn(acc) else fOdd(acc)
        // println(n)
        rec(n, i+1)
      }
    }
    rec(s, 2)
  }

  val ans = solve(s)
  println(ans)
}