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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt();
        int answer=1;
        List<Integer> list = new ArrayList<>();
        boolean returnFlag=false;
        
        list.add(a);
        answer+=1;
        if(a%2!=0){
            a=3*a+1;
        }else{
            a=a/2;
        }

        if(list.contains(a)){
            System.out.println(answer);
            return;
        }
        
        while(!returnFlag){
            list.add(a);
            answer+=1;
            if(a%2!=0){
                //奇数の時
                a=3*a+1;
                
            }else{
                a=a/2;
            }

            if(list.contains(a)){
                System.out.println(answer);
                return;
            }
        }    
    }
}