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 a1 = sc.nextInt();
        int an = a1;
        int n = 1;
        int anArray[] = new int[1000000];
        anArray[0] = an;

        for (int i = 0; ; i++) {
            //System.out.println(an);

            if (an == 4 || an == 2 || an == 1) {
                System.out.println(n + 3);
                System.exit(0);
            }
            
            n += 1;
            if (an % 2 == 0) {
                an = an / 2;
            } else {
                an = 3 * an + 1;
            }

            //for (int j = 0; j < i; j++) {
            //    if (an == anArray[j]) {
            //        System.out.println(n);
            //        System.exit(0);
            //    }
            //}

            anArray[n - 1] = an;

            
        }
    }
}