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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class Program {
    const int mod = 1000000007;

    static void Main() {
        var s = int.Parse(Console.ReadLine());
        int[] ary = new int[1000000];

        ary[1] = s;
        for (int i = 2; i < ary.Length; i++) {
            ary[i] = Calc(ary[i-1]);
            for (int j = 1; j <= i; j++) {
                if (ary[i] == ary[j] && i != j) {
                    Console.WriteLine(i);
                    return;
                }
            }
        }
    }

    static int Calc(int n) {
        if (n % 2 == 0) {
            return n / 2;
        } else {
            return 3 * n + 1;
        }
    }
}