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: Wrong Answer)


#include <iostream>
#include <string>
#include <algorithm>
#include <set>
#include <cmath>
#include <vector>
#include <numeric>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <queue>

using ll = long long int;
using ul = unsigned long long int;
const ll LL_MAX (1LL<<60);
const ll MOD (1000000007);

#define rep(i,s,e) for(ll i=(s); i<(e); i++) 

using namespace std;

ll f(ll n)
{
    if (n%2==0) n/=2;
    else n=3*n+1;

    return n;
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    ll s;
    cin >> s;
    unordered_set<ll> ss;

    ll cnt(0);
    while (true)
    {
        s = f(s);

        cnt++;

        if (ss.find(s)==ss.end())
            ss.insert(s);
        else
            break;
    }

    cout << cnt+1 << endl;

    return 0;
}