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.Linq;
using System.Collections.Generic;
using System.IO;


class Program
{
    public static long Read()
    {
        return long.Parse(Console.ReadLine());
    }

    public static long[] Reads()
    {
        return Console.ReadLine().Split().Select(long.Parse).ToArray();
    }

   
    public static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);

        var s = Read();
        bool b = true;
        var l = new List<long>
        {
            s
        };
        while (b)
        {
            if (l[l.Count - 1] % 2 == 0)
                l.Add(l[l.Count - 1] / 2);
            else
                l.Add(3 * l[l.Count-1] + 1);
            for(int i=0;i<l.Count-1;i++)
            {
                if (l[i] == l[l.Count - 1])
                {
                    b = false;
                    break;
                }
            }
        }
            Console.WriteLine(l.Count);


        Console.Out.Flush();
    }
}