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: Time Limit Exceeded)


#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <vector>
#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <numeric>
#include <cassert>
#include <memory>
#include <stack>
#include <set>
#include <map>

#define INF 1000000000
#define MOD 1000000007
typedef long long ll;
typedef unsigned long long ull;
using namespace std;

int fn(int n) {
  if(n % 2 == 0) {
    return n / 2;
  } else {
    return 3 * n + 1;
  }
}

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

  int s; cin>>s;
  int keep = s;
  int cnt = 0;
  for(int i = 1;;i++) {
    int a;
    if(i == 1) {
      a = s;
    } else {
      a = fn(keep);
    }

    if(a == 8) {
      cnt = i;
      break;
    }

    keep = a;
  }

  cout << cnt + 4 << endl;
}