In what concerns the continuous evaluation solving exercises grade during the semester, you should submit until 23:59 of March 24th
(this exercise will still be available for submission after that deadline, but without couting towards your grade)
[to understand the context of this problem, you should read the class #03 exercise sheet]

[PII018] Collatz Sequence

The Collatz sequence, also known as the 3n + 1 sequence, is a mathematical sequence defined for positive integers. The sequence starts with any positive integer n and follows these rules:

• If n is even, the next term is n/2
• If n is odd, the next term is 3n + 1
• The sequence ends when it reaches 1

Despite its simplicity, the Collatz conjecture, which says that this sequence will always eventually reach 1 for any positive integer n, remains unproven. This intriguing problem invites exploration of the patterns and behaviors of numbers as they traverse through the sequence.

The Problem

Write a program that, given several integers, generates the Collatz sequence that starts from each of them.

Input

The first line of input contains an integer T, representing the number of test cases that follow.

Each of the following T lines contains one integer N, representing the number that we want to start the Collatz sequence from.

Output

The output should have exactly T output lines, one per input test case.

Each of these lines should contain the respective sequence, starting from N. Numbers in the sequence should be separated by a comma and a space (see the format depicted in the example output).

Constraints

The following limits are guaranteed in all the test cases that will be given to your program:

4
1
3
42
17

1
3, 10, 5, 16, 8, 4, 2, 1
42, 21, 64, 32, 16, 8, 4, 2, 1
17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1