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.Threading.Tasks;


public class ABC116b
{
    public static void Main()
    {

        int s = int.Parse(Console.ReadLine());
        int cnt = 1;
        while (s > 4)
        {
            cnt++;
            if (s % 2==1)
            {
                s *= 3;
                s++;
            }
            else
            {
                s /= 2;
            }
            
        }
        int[] L = new int[100];//Lが小さいとs==3でバグる
        while (true)
        {
            
            if (L[s] == 1)
            {
                System.Console.WriteLine(cnt);
                Environment.Exit(0);
            }
            else
            {
                L[s] = 1;
                if (s % 2==1)
                {
                    s *= 3;
                    s++;
                }
                else
                {
                    s /= 2;
                }
               
            }
            cnt++;
        }
    }
}