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 lli long long int
#define endl "\n"
 
using namespace std;
 
typedef long long int LLI;
typedef double DB;
 
void fastio()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
}
 
 
bool comparator(pair<lli,lli> a,pair<lli,lli> b)
{
    if(a.first>b.first)
        return true;
    else if (a.first==b.second)
    {
        if(a.second>=b.second)
            return false;
        return true;
    }
    return false;
}
 
int mods(int x)
{
    if(x>0)
        return x;
    return -x;
}
 
lli gcd(lli a,lli b)
{
    return __gcd(a,b);
}
 
lli lcm(lli x,lli y,lli z)
{
    lli j=gcd(x,y);
    lli k=gcd(y*x/j,z);
    return (((x*y)/j)*z)/k;
} 

int main()
{
    fastio();
    int n; cin>>n; set <int> s; s.insert(n);
    int prev=s.size();
    for(;;)
    {
        if(n%2) n=3*n+1;
        else n>>=1;
        s.insert(n);
        if(prev==s.size()) {cout<<s.size()+1; return 0;}
        prev=s.size();
    }
    return 0;
}