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<iostream>
#include<cstdlib>
#include<cstring>
#include<climits>
#include<vector>
#include<list>
#include<functional>
#include<algorithm>
#include<string>
#include<cmath>
#include<complex>
#include<set>
#include<map>
#include<stack>
#include<queue>
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,n) for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;
typedef pair<int, int> P;


int s;
bool memo[10000000];

int res() {
	memo[s] = 1;
	for (int i = 2;i <= 1000000;i++) {
		if (s % 2 == 0) s /= 2;
		else s = 3 * s + 1;
		if (memo[s]) return i;
		else memo[s] = 1;
	}
}

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	cin >> s;
	cout << res() << "\n";
	
	return 0;
}