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;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Diagnostics;
class Program
{
    public static Scanner input;
    static void Main()
    {

        input = new Scanner();
        int first = input.Int();
        var arr = new List<double>();
        arr.Add(first);
        bool flag = true;
        while(flag)
        {
            if (arr.Count==0)
            {
                arr.Add(first);
            }
            else
            {
                arr.Add(f(arr[arr.Count-1]));
            }
            for(int a = 0; a < arr.Count-1; a++)
            {
                if (arr[a] == arr[arr.Count - 1]) { WriteLine(arr.Count); flag = false; break; }
            }
        }

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

    }
}

class Scanner
{

    public Scanner()
    {
    }

    public void skip()
    {
        ReadLine();
        return;
    }
    public string String()
    {
        return ReadLine();
    }
    public string[] arrayString()
    {
        return ReadLine().Split();
    }
    public int Int()
    {
        return int.Parse(ReadLine());
    }
    public int[] arrayInt()
    {
        return ReadLine().Split().Select(i => int.Parse(i)).ToArray();
    }
    public long Long()
    {
        return long.Parse(ReadLine());
    }
    public long[] arrayLong()
    {
        return ReadLine().Split().Select(i => long.Parse(i)).ToArray();
    }
    public double Double()
    {
        return double.Parse(ReadLine());
    }
    public double[] arrayDouble()
    {
        return ReadLine().Split().Select(i => double.Parse(i)).ToArray();
    }
}