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)


// </> : towhid1zaman

#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef pair< int, int > pii;
typedef pair< pii, int > ppi;
#define fill(a,b) memset(a,b,sizeof(a))
#define all(v) (v).begin(),(v).end()
#define sp(k) cout<<setprecision(k)<<fixed;
#define rep(i,a) for(int i=0;i<a;i++)
#define rep1(i,a,b) for(int i=(a);i<=(b);++i)
#define irep(i,b,a) for(int i=(b);i>=(a);--i)
#define minv(v) *min_element(all(v))
#define maxv(v) *max_element(all(v))
#define unq(v) sort(all(v)),(v).erase(unique(all(v)),(v).end())
#define _ ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define endl "\n"
#define sqr(a) ((a)*(a))
#define sz(a) int(a.size())
#define ff first
#define ss second
#define pb push_back

const double pi = acos(-1.0);
const int mod = 1000000007; // (int)1e9+7
const int inf = 0x3f3f3f3f;// (int)3e18;
const int maxn = 2000100;



int main(){
        _
        int s; cin >> s;
        set<int>dis;
        while(true){
            if(dis.count(s))break;
            dis.insert(s);
            if(s%2==1)s = 3*s + 1;
            else s/=2;
        }
        cout<<dis.size()+1<<endl;

return 0;
}