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,n) for(int i=0;i<(int)(n);++i)
#define repone(i,n) for(int i=1;i<(int)(n);++i)
#define repo(i,o,n) for(int i=o;i<(int)(n);++i)
#define Rep(j,n) for(int j=0;j<(int)(n);++j)
#define Repo(j,o,n) for(int j=o;j<(int)(n);++j)
#define Repone(j,n) for(int j=1;j<(int)(n);++j)
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define int long long
#define pb(a) push_back(a)
#define eraser(v,i) (v).erase(v.begin()+(i))
#define pbpair(a,b) push_back(make_pair(a,b))
#define MOD 1000000007
#define INF 9223372036854775807
#define pairint pair<int,int>
int euclidean_gcd(int a, int b) {
  if(a < b) return euclidean_gcd(b, a);
  int r;
  while ((r=a%b)) {
    a = b;
    b = r;
  }
  return b;
}
signed main()
{
int x=0,y=0,z=0,w=0,n=1,m=0,a=0,b=0;
std::cin >> x;
while(1){
  if(x==4){
    std::cout << n+3 << '\n';
    return 0;
  }else{
    if(x%2==0){
      x/=2;
    }else{
      x=3*x+1;
    }
  }
  n++;
}

}