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<climits>
#include<math.h>
#include<vector>
#include<algorithm>
#include<cstdio>
#include<stdio.h>
#include <string>
#include <complex>
#include <functional>
#include <map>
#include <queue>
using namespace std;
using ll = long long;
//typedef pair<string,string> P;
//double dat[100][100];
//int dp[6][1010];//動的計画法
//int prime[100001];
//char str[1010][1010];
//vector<pair<int,int> > pc[100001];
//int ABS(int a){return max(a,-a);}
int f(int n){
    if(n%2) return 3*n+1;
    else return n/2;
}
int main(){
    int s;
    cin>>s;
    if(s==1||s==2){
        cout<<4<<endl;
        return 0;
    }
    vector<int> a(1000000);
    a[1]=s;
    int ans;
    int i=2;
    while(1){       
        a[i]=f(a[i-1]);
        if(a[i]==4){
            ans=i+3;
            break;
        }
        i++;
    }
    cout<<ans<<endl;
    return 0;
}