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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(String args[]) {

        // 入力
        Scanner sc = new Scanner(System.in);
        Integer s = Integer.parseInt(sc.next());

        // 主処理
        List<Integer> list = new ArrayList<>();
        list.add(s);

        int result = 0;
        boolean doContinue = true;
        for (int i = 0; doContinue; i++) {
            if (s % 2 == 0) {
                if (list.contains(s / 2)) {
                    result = i + 2;
                    doContinue = false;
                } else {
                    s = s / 2;
                    list.add(s);
                }
            } else {
                if (list.contains(3 * s + 1)) {
                    result = i + 2;
                    doContinue = false;
                } else {
                    s = 3 * s + 1;
                    list.add(s);
                }
            }
        }

        // 出力
        System.out.println(result);
        sc.close();
    }
}