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;
import java.util.*;
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int s = sc.nextInt();
        List<Integer> a = new ArrayList<>();
        a.add(s);
        int len = 1000000;
        for (int i = 1; i <= len; i++) {
            int f;
            if (a.get(i - 1) % 2 == 0) {
                f = a.get(i - 1) / 2;
            } else {
                f = 3 * a.get(i - 1) + 1;
            }
            a.add(f);
        }
        int ans = 0;
        for (int i = 0; i <= len; i++) {
            for (int j = i + 1; j <= len; j++) {
                if (a.get(i) == a.get(j)) {
                    // System.out.printf("i = %d,j = %d %n", i, j);
                    // System.out.printf("a = %d,a = %d %n", a.get(i), a.get(j));
                    ans = j + 1;
                    System.out.println(ans);
                    return;
                }
            }
        }
    }
}