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.Collections.Generic;
using System;

public class Hello
{
    public static void Main()
    {
        var s = long.Parse(Console.ReadLine().Trim());
        var hs = new HashSet<long>();
        var pre = s;
        hs.Add(s);
        var w = 0L;
        for (int i = 2; i <= 1000000; i++)
        {
            if (pre % 2 == 0)
            {
                 w = pre / 2;
                if (!hs.Add(w)) { Console.WriteLine(i); break; }
            }
            else
            {
                 w = pre * 3 + 1;
                if (!hs.Add(w)) { Console.WriteLine(i); break; }
            }
            pre = w;
        }

    }
}