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.util.*;
public class Main {
	//定義関数から参照できる変数定義はこの辺
	static int S;
	static int Ary[]=new int[1000001];
	static int ans=0;

	public static void main(String[] args) {
    	Scanner sc = new Scanner(System.in);
		S = sc.nextInt();
		Ary[1] = S;
		loop1:for(int i=1;i<=1000000;i++){
			if (Ary[i]%2==0) {
				Ary[i+1] = Ary[i]/2;
				for(int j=1;j<=i;j++){
					if (Ary[j]==Ary[i+1]) {
					 	ans=i+1;
					 	break loop1;
					} 
				}
			}
			else{
				Ary[i+1] = Ary[i]*3+1;
					for(int j=1;j<=i;j++){
					if (Ary[j]==Ary[i+1]) {
					 	ans=i+1;
					 	break loop1;
					} 
				}
			}
		}
		System.out.println(ans);
    }
}