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.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {
    public static PrintWriter out;

    public static void main(String[] args) {
        Main.run();
    }

    private static void run() {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        Scanner sc = new Scanner(System.in);
        int s = Integer.parseInt(sc.next());
        ArrayList<Integer> list = new ArrayList<>();
        list.add(s);
        for (int i = 1, answer = 0;; i++) {
            answer = Main.calcF(list.get(i - 1));
            if (list.contains(answer)) {
                out.println(i + 1);
                break;
            }
            list.add(answer);
        }
        out.close();
        sc.close();
    }

    private static int calcF(int pnum) {
        int n = pnum;
        if (n % 2 == 0) {
            return n / 2;
        } else {
            return 3 * n + 1;
        }
    }
}