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.ArrayList;
import java.util.List;
import java.util.Scanner;

class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int s = sc.nextInt();
    sc.close();
    List<Integer> ls = new ArrayList<>();
    ls.add(s);
    int c = s;
    for (int i = 1; i < 1000000; i++) {
      if (c % 2 == 0) {
        int f1 = c/2;
        if (ls.contains(f1)) {
          System.out.println(ls.size()+1);
          return;
        }
        ls.add(f1);
        c = f1;
      } else {
        int f2 = 3 * c + 1;
        if (ls.contains(f2)) {
          System.out.println(ls.size()+1);
          return;
        }
        ls.add(f2);
        c = f2;
      }
    }
  }
}