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"
#include <math.h>
#include <time.h>
using namespace std;
const long long mod = 1000000007;
#define dump(x)                             \
    if (dbg) {                              \
        cout << #x << " = " << (x) << endl; \
    }
bool dbg = false;
long long gcd(long long a, long long b){
   if (a % b == 0)
   {
       return(b);
   }
   else
   {
       return(gcd(b, a % b));
   }
}
long long lcm(long long a, long long b){
   return (a / gcd(a, b))* b;
}
//---------------------------------------------------------------------------------------------------
/*ここからいじる*/
//---------------------------------------------------------------------------------------------------
int s;
int f(int n){
    if(n % 2 == 0){
        return n / 2;
    }
    else{
        return 3 * n + 1;
    }
}
int an(int n){
    if(n == 1){
        return s;
    }
    else{
        return f(an(n - 1));
    }
}
void solve(){
    set<int>st;
    int cnt = 0;
    while(true){
        cnt++;
        st.insert(an(cnt));
        if(st.size() != cnt){
            cout << cnt << endl;
            break;
        }
    }
}
int main(){
    cin >> s;
    solve();
    return 0;
}