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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp4
{
    class Program
    {
        /// <summary>
        ///  Let f(n) be the following function: f(n)=n/2 if n is even, and f(n)=3n+1 if n is odd.
        /// </summary>
        /// <param name="n"></param>
        /// <returns></returns>
        public static double f(double n)
        {
            if(n % 2 == 0)
            {
                return n / 2;
            }
            else
            {
                return (3 * n) + 1;
            }
        }

        /// <summary>
        /// main
        /// </summary>
        /// <param name="args"></param>
        static void Main(string[] args)
        {
            var s = Console.ReadLine();

            var a = new double[100];

            // ai=s when i=1, and ai=f(ai−1) when i>1.
            for (var i=0; i<100; i++)
            {
                if (i == 0)
                {
                    a[i] = double.Parse(s);
                }
                else
                {
                    a[i] = f(a[i - 1]);
                }
            }
            var min = 100;
            var found = false;
            for(var i=0; i<100; i++)
            {
                if (!found)
                {
                    for (var j = i + 1; j < 100; j++)
                    {
                        if (a[i] == a[j])
                        {
                            if (!found)
                            {
                                min = j;
                                found = true;
                            }
                        }
                    }
                }
            }

            Console.WriteLine(min+1);

            //Console.ReadLine();
        
        }
    }
}