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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;

class Program {
  static void Main (string[] args) {
    var t = 0;
    var f = 0;
    int s = int.Parse(Console.ReadLine());
    List<int> nums = new List<int>();
    nums.Add(s);
    while (f == t) {
      nums.Add(Calc(nums[nums.Count - 1]));
      int ind = nums.IndexOf(nums[nums.Count - 1]);
      if (ind != nums.Count - 1) f = nums.Count - 1;
    }
    Console.WriteLine(f);
  }
  
  static int Calc (int s) {
    return ((s % 2 == 0) ? s / 2 : (3 * s) + 1);
  }
}