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.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int s = sc.nextInt();
		sc.close();
		int[] a = new int[1000001];
		int[] b = new int[1000001];
		a[0] = s;
		b[s]++;
		for(int i = 1; i < a.length; i++) {
			int t = a[i - 1];
			if(t % 2 == 0) {
				a[i] = t / 2;
				//System.out.println(a[i]);
				b[a[i]]++;
				if(b[a[i]] == 2) {
					System.out.println(i + 1);
					System.exit(0);
				}
			}else {
				a[i] = 3 * t + 1;
				b[a[i]]++;
				if(b[a[i]] == 2) {
					System.out.println(i + 1);
					System.exit(0);
				}
			}

		}
	}
}