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;

class Program
{
    static void Main(string[] args)
    {
        //List<int> values = new List<int>(Console.ReadLine().Split(' ').Select(s => int.Parse(s)));
        //List<int> values = new List<int>();

        string input = Console.ReadLine();
        //int n = int.Parse(input.Split(' ')[0]);
        //int m = int.Parse(input.Split(' ')[1]);
        //int k = int.Parse(input.Split(' ')[2]);
        int n = int.Parse(input);

        List<int>  values = new List<int>();
        values.Add(n);

        int a = 1;

        if (n == 1)
        {
            Console.WriteLine(4);return;
        }
        if (n == 2)
        {
            Console.WriteLine(4); return;
        }

        while (n!=4)
        {
            if(n%2==0)
            {
                n /= 2;
            }
            else
            {
                n = n * 3 + 1;
            }
            a++;
        }



        Console.WriteLine(a+3);
        
    }
}