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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

#define REP(i,a,b) for(int i=a;i<b;i++)
#define rep(i,n) REP(i,0,n)

typedef long long ll;

int main() {
    int MAX_M = 1000003;
    int s; cin>>s;
    int a[MAX_M];
    rep(i,MAX_M) a[i]=0;
    
    a[s]=1;
    
    int ans;
    
    rep(i,MAX_M){
        if(s % 2 == 1)s = 3*s +1;
        else s/=2;
        
        ++a[s];
        if(a[s]==2){
            ans = i+1;
            break;
        }
    }
    cout<<ans<<endl;
	return 0;
}