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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 $n$?

Poveste şi cerinţă...

h2. Date de intrare

The first line of the file $occurences.in$ will contain $t$, the number of test cases.
 
Each of the next $t$ lines will contain a single number $n$, .

Fişierul de intrare $occurences.in$ ...

h2. Date de ieşire

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.

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

h2. Restricţii

* $1 ≤ n ≤ 10^18$
* $1 ≤ t ≤ 10^5$
* For tests worth $50$ points, $1 ≤ n ≤ 1000$.

* $... ≤ ... ≤ ...$

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

| 3
2
18
1
| 2
  4
  1

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

|
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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