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: Wrong Answer)

import java.util.Scanner;

class Main{
  
   public static void main(String[] args) {
     
     Scanner sc = new Scanner(System.in);
     
     int s = sc.nextInt();
     
     int[]a = new int[1000000];
     
     for (int i = 0; i  < a.length; i++){
       if (i == 0)
         a[i] = s;
       else {
         if (a[i-1] % 2 == 0){
           a[i] = a[i-1] /2;
         }else{
           a[i] = a[i-1] * 3 + 1;
         }
       }
     }
     
     int c = 0;
     
     for (int i = 0; i < a.length; i++){
       if(a[i] == 8){
         c = i + 5;
         break;
       }
     }
     
     System.out.println(c);
     
     sc.close();
   }
}