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 "bits/stdc++.h"
#define FOR(i, a, b) for (int i = a; i < b; i++)
#define mFOR(i, a, b) for (int i = a; i > b; i--)
#define MP make_pair
#define PB push_back
#define N 1000007
#define INF 1000000000
using namespace std;

typedef long long ll;

int main()
{
    int s, tmp;
    cin >> s;
    vector<int> v;
    v.push_back(s);
    tmp = s;
    FOR(i, 1, N)
    {
        if (tmp % 2 == 0)
            tmp = tmp / 2;
        else
            tmp = tmp * 3 + 1;
        if (binary_search(v.begin(), v.end(), tmp))
        {
            cout << i + 1 << "\n";
            break;
        }
        v.push_back(tmp);
        sort(v.begin(), v.end());
    }
    return 0;
}