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.Reflection;
using System.Linq.Expressions;
using System.Linq;
using System.IO;
using System.Collections.Generic;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder {
    public class Program {
        static int[] getKeys(char delimiter) {
            var Keys = Console.ReadLine().Split(' ');
            int[] Ns = new int[Keys.Length];
            for (int i = 0; i < Keys.Length; i++) {
                Ns[i] = int.Parse(Keys[i]);
            }
            return Ns;
        }
        static void Show<T>(T[,] map) {
            int H = map.GetLength(0);
            int W = map.GetLength(1);
            Console.WriteLine("-------------------------");
            for (int i = 0; i < H; i++) {
                for (int j = 0; j < W; j++) {
                    Console.Write(map[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine("-------------------------");
        }
        static void Show<T>(T[,] map, string delimiter) {
            int H = map.GetLength(0);
            int W = map.GetLength(1);
            Console.WriteLine("-------------------------");
            for (int i = 0; i < H; i++) {
                for (int j = 0; j < W; j++) {
                    Console.Write(map[i, j] + delimiter);
                }
                Console.WriteLine();
            }
            Console.WriteLine("-------------------------");
        }
        static void Show<T>(IEnumerable<T> ts) {
            foreach (var item in ts) {
                Console.Write(item + " ");
            }
            Console.WriteLine();
        }
        static void Show<T>(IEnumerable<T> ts, string delimiter) {
            foreach (var item in ts) {
                Console.Write(item + delimiter);
            }
            Console.WriteLine();
        }
        static void Main() {
            int s = int.Parse(Console.ReadLine());
            List<int> As = new List<int>();
            int i = 1;
            while (!As.Contains(s)) {
                As.Add(s);
                if (s % 2 == 0) {
                    s /= 2;
                } else {
                    s = s * 3 + 1;
                }
                i++;
            }
            Console.WriteLine(i);
        }
    }
}