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 (2.13.1) (judge verdict: Wrong Answer)

import scala.io.StdIn._

object Main extends App {

  val s = readInt()

  def solve() = {
    var set = Set.empty[Int]
    var isSearching = true
    var i = 0
    var prev = s
    while(isSearching) {
      if(i != 0) {
        val cur = if(prev % 2 == 0) prev/2 else 3*prev+1
        if(set(cur)) isSearching = false
        else {
          prev = cur
          set += cur
        }
      }
      i += 1
    }
    i
  }

  println(solve())

}