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.io.InputStream;
import java.io.PrintStream;
import java.util.Scanner;

public class Main {
	InputStream in = System.in;
	PrintStream out = System.out;

	int f(int n) {
		if (n % 2 == 0) {
			return n / 2;
		} else {
			return 3 * n + 1;
		}
	}

	public void _main(String[] args) {
		Scanner sc = new Scanner(in);
		int s = sc.nextInt();

		int[] a = new int[1000000];

		a[s] = 1;
		int i, i_1 = s;
		int n = 1;
		for (;;) {
			i = f(i_1);
			n++;
			if (a[i] == 1) {
				out.println(n);
				break;
			}
			a[i] = 1;
			i_1 = i;
		}

		sc.close();

	}

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

}