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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;

using System.Collections;

class Program
{
    static void Main()
    {
        var s = int.Parse(Console.ReadLine());

        int[] a = new int[1000000];
        a[0] = s;

        var set = new HashSet<int>();
        set.Add(s);

        for(int i = 1; i < a.Length; i++)
        {
            var next = f(a[i - 1]);

            if(set.Contains(next))
            {
                Console.WriteLine(i + 1);
                return;
            }
            set.Add(next);
            a[i] = next;
        }
    }

    static int f(int n)
    {
        if (n % 2 == 0)
        {
            return n / 2;
        }
        else
        {
            return 3 * n + 1;
        }
    }
    
}