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.HashMap;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);

		int s = Integer.parseInt(scanner.nextLine());

		HashMap<Integer, Boolean> map = new HashMap<Integer, Boolean>();

		int preVal = 0;

		for (int i = 0; i < 1000000; i++) {
			if (i == 0) {
				map.put(s, true);
				preVal = s;

				continue;
			}

			int val = f(preVal);
			if (map.get(val) != null) {
				System.out.println(i + 1);
				return;
			} else {
				map.put(val, true);
				preVal = val;
			}
		}

	}

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

}