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: Accepted)

import scala.io.StdIn._
import scala.util.control.Breaks._

object Main extends App {
  val s = readInt()

  require(1 <= s && s <= 100)

  var i    = 1
  var j    = 0
  var a    = s
  var list = Seq(a)
  breakable {
    while (i <= 1000000) {
      i = i + 1
      val b = if (a % 2 == 0) a / 2 else 3 * a + 1
      if (list.contains(b)) {
        println(i)
        break()
      }
      list = list.appended(b)
      a = b
    }
  }
}