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.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int s = sc.nextInt();
        ArrayList<Integer> data = new ArrayList<Integer>();
        data.add(s);
        boolean judge = false;
        
        int i=1;
        while(judge == false){
            if(data.get(i-1)%2 == 0){
                int tmp1 = data.get(i-1)/2;
                if(data.contains(tmp1)){
                    System.out.println(i+1);
                    judge = true;
                }
                data.add(tmp1);
            }else{
                int tmp2 = 3*data.get(i-1)+1;
                if(data.contains(tmp2)){
                    System.out.println(i+1);
                    judge = true;
                }
                data.add(tmp2);
            }
            
            i++;
            
        }
    }
}