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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
#include<algorithm>
#include<stdio.h>
#include<string>
#include<cmath>
#include<cstdio>
#include<set>
#include<map>
#include<iomanip>

using namespace std;

#define rep(i, n) for(int i = 0; i < n; i++)
#define repn(i, n) for(int i = 1; i <= n; i++) 
#define lint long long
#define all(x) (x).begin(), (x).end()

int f(int x){
    if(x%2 == 0) return x/2;
    else return 3*x+1;
}

int main(){
    int s; cin>>s;
    map<int,bool> M; M[1]=true;
    int c = 1;
    while(1){
        c++;
        s = f(s);
        if(M.find(s) == M.end()) M[s]=true;
        else break;
    }
    cout<<c<<endl;
}