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>
#include <chrono>
#define watch(x) cout << (#x) << " is " << (x) << endl
#define eps 1e-9

typedef long long ll;

using namespace std;

const int mod = 1e9+7;
const int N = 1e6+5;
int a[N];

int main()

{
    ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);

    int n;

    cin >> n;

	a[n]++;

    for (int i = 2;; i++) {

        if (n%2) n = n*3+1;
        else n/=2;

        if (a[n]) {

            cout << i;
            break;
        }
        else a[n]++;
    }

    return 0;
}