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Poveste şi cerinţă...

You are given an integer $n$ and you have to do one operation at a time:
 
$1.$ If $n$ is odd, you must multiple it by $3$ and add $1$ to the result.
 
$2.$ If $n$ is even, you must divide it by $2$.
 
What is the number with maximum occurrences if you do $10^{100}$ operations on the given number $n$?

h2. Date de intrare

Fişierul de intrare $occurences.in$ ...

The first line of the file $occurences.in$ will contain $t$, the number of test cases ($1 \le t \le 10^5$).
 
Each of the next $t$ lines will contain a single number $n$, ($1 \le n \le 10^{18}$).
 
For tests worth $50$ points, ($1 \le n \le 1000$).

h2. Date de ieşire

În fişierul de ieşire $occurences.out$ ...

On each line of the output file $occurences.out$ we will print an integer, representing the answer to the problem. If there are multiple solutions, print the biggest one of them.

h2. Restricţii

h2. Exemplu
table(example). |_. occurences.in |_. occurences.out |

| This is some
  text written on
  multiple lines.
| This is another
  text written on
  multiple lines.

| 3
2
18
1
| 2
  4
  1

|
h3. Explicaţie

...

For the first sample test case, the numbers printed will be $2$, $1$, $4$, $2$, $1$, ..., and therefore $2$ and $1$ will show up one more time than the other numbers. Since we need to print the biggest integer, then we will print $2$.

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