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 <vector>
#include <string>
#include <array>
#include <queue>
#include <deque>
#include <set>
#include <list>
#include <map>
#include <stack>
#include <utility>
#include <algorithm>
#include <numeric>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cctype>
#include <cstring>
#include <climits>
#include <bitset>
#include <random>
#include <functional>
#include <sstream>
#include <iomanip>

using namespace std;

#define _CRT_SECURE_NO_WARNINGS
#define rep(i, n) for(int i=0; i<(n); i++)
#define FOR(i, m, n) for(int i=(m);i<(n);i++)
#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(),(x).end()
#define SORT(x) sort((x).begin(),(x).end())
#define REVE(x) reverse((x).begin(),(x).end())
#define MP make_pair
#define PB push_back

typedef vector<int> VI;
typedef vector<string> VS;
typedef vector<vector<int>> VVI;
typedef pair<int, int> PII;
typedef long long LL;

int f(int n) {
	if (n % 2 == 0)return n / 2;
	else return n * 3 + 1;
}
int main() {
	int s, ans;
	cin >> s;
	set<int> a;
	a.insert(s);
	vector<int> v;
	v.PB(s);
	for (int i = 1; true; i++) {
		int p = f(v[i - 1]);
		v.PB(p);
		a.insert(p);
		if (SZ(a) != i + 1) {
			ans = i + 1;
			break;
		}
	}
	cout << ans << endl;
}