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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <iomanip>
#include <random>
#include <cstdio>
#include <cmath>
#include <map>
using namespace std;
typedef long long ll;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)

int main() {
    int s; cin >> s;
    int size = 100000;
    vector<int> a(size);
    a[0] = s;
    for (int m = 1; m < size; m++)
    {
        int prev = a[m-1];
        if (prev % 2 == 0)
        {
            a[m] = prev/2;
        } else {
            a[m] = 3*prev + 1;
        }
        rep(i,m) {
            if (a[i] == a[m])
            {
                cout << ++m << endl;
                return 0;
            }
        }
    }
    return 0;
    
}