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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.*;
import java.util.*;
import java.util.ArrayList;
import java.util.Iterator;
import java.util.List;
import java.util.Collections;
import java.util.Arrays;

public class Main {
	public static void main(final String[] args){
    
    final Scanner sc = new Scanner(System.in);
    final List<Integer> list = new ArrayList<>();
    //final List<Integer> list2 = new ArrayList<>();
    //final List<Long> list3 = new ArrayList<>();

    int s = sc.nextInt();
    int count = 1;
    int n = s;
    int check = 0;
    list.add(s);
    for(int i = 1 ; i < 50000 ; i++){
        if(n % 2 == 0){
            n = n / 2;
            list.add(n);
        }else{
            n = n*3 + 1;
            list.add(n);
        }
        count++;
        Collections.sort(list);
        for(int j = 0 ; j < list.size() - 1; j++){
            if(list.get(j).equals(list.get(j+1))){
                check = 1;
                break;
            }

        }
        if(check == 1){
            break;
        }
    }

    //System.out.println(list);
    System.out.println(count);
    

    

    




    







}
}