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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)n; i++)
using namespace std;
typedef vector<int> vi;

int f(int x){
    if(x % 2) return 3*x + 1;
    else return x / 2;
}

int main(){
    int s;
    cin >> s;
    vi a(1000001);

    a[1] = s;
    for(int i = 2; i <= 1000001; i++){
        a[i] = f(a[i-1]);
    }

    for(int i = 1; i <= 1000001; i++){
        if(a[i] == 8){
            cout << i+4 << endl;
            return 0;
        }
    }

    return 0;
}