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;

namespace _20190315_08 {
    class Program {
        static void Main(string[] args) {
            var line = Console.ReadLine().Split(' ').Select(d => int.Parse(d)).ToArray();
            var s = line[0];
            var a = new List<int>() { s };
            for (int i = 0; i < int.MaxValue; i++) {
                var a_i = f(a[i]);
                if (a.Any(x => x == a_i)) {
                    Console.WriteLine(i + 2);
                    return;
                }
                a.Add(a_i);
            }
        }

        static int f(int n) {
            if ((n & 1) == 0) {
                return n >> 1;
            }
            return 3 * n + 1;
        }
    }
}