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>
using namespace std;
typedef long long ll;
typedef pair<int,int> iint;
typedef pair<ll,ll> llll;
const ll zero = 0;
const ll INF = 3000000000000000000; //10^18
const int inINF = 1000000000; //10^9
const ll MOD = 1000000007; //10^9+7
const ll MOD2 = 998244353;

int main(){
    int s;
    cin >> s;
    vector<int> a(1000005, 0);
    a[s] = 1;
    int m = 1;
    while(1){
        m++;
        if(s % 2 == 1){
            s = 3 * s + 1;
        }
        else{
            s = s / 2;
        }
        a[s]++;
        if(a[s] == 2){
            printf("%d\n", m);
            break;
        }

    }
    

    
}