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.HashSet;
import java.util.Scanner;
import java.util.Set;

/**
 * 
 * @author morisin
 * 
 */
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		int S = sc.nextInt();
		
		int nextNum = S;
		
		Set<Integer> list = new HashSet<>();
		
		list.add(S);

		int size_before=0;
		int size_after=0;
		
		for(int i=2;i<=1000000;i++) {
			size_before=list.size();
			if(nextNum%2 == 0) {
				nextNum=nextNum/2;
				list.add(nextNum);
			}else {
				nextNum=nextNum*3+1;
				list.add(nextNum);
			}
			size_after=list.size();
			
			if(size_before==size_after) {
				System.out.println(i);
				break;
			}
		}
	}
}