Help me sub-divide a time signature This challenge is based on a video in which Andrew Huang discusses unusual time signatures...

https://www.youtube.com/watch?v=JQk-1IXRfew

In it, he advises that you can understand time signatures by dividing them into 3's and 2's. So you count to a small number a few times, instead of counting to a large number.

Here's the pattern he builds which repeats after 19 steps:


5 groups of 3
2 groups of 2


This is how it looks:

#..#..#..#..#..#.#.


Actually, as you'd play each beat alternatively, the accented beats move from left to right, because there's an odd number of steps. So now this pattern is:

R..L..R..L..R..L.L.
L..R..L..R..L..R.R.


If we reduce this to an algorithm, it can be described like this.

Step 1: where are the accents


From your number of steps, start by taking groups of 3 from the start until there's 4 or fewer steps remaining.


E.g. for a pattern 8 steps long.

8 steps - take three, 5 steps remaining

#..


5 steps - take 3, 2 steps remaining

#..#..


Once we're down to 4 steps or fewer, there's 3 possibilities.


4 steps - 2 groups of 2
3 steps - 1 group of 3
2 steps - 1 group of 2


So from our above example:

#..#..#. 


Step 2: Which hand are the accents on

Let's assume that each individual step will be played on alternate hands, starting with the right.

So for 8 steps, the (underlying) pattern will go

rlrlrlrl


The pattern we output will only tell use which hand the accents are on. With the above example:

R..L..R.


That's fine, it's repeatable.

but

If it's an odd number, you've got the same hand for both the first and last steps, and you can't keep alternating when you repeat the pattern. Instead, the second pattern will be on the other hand. Here's the pattern on an 11 step pattern.

R..L..R..L.
L..R..L..R.


To clarify, if the pattern length is odd, we need to see the repeated, alternated pattern. If the length is even, we only need to see it once.

Hopefully that's clear enough:



The Rules


It's code golf, go for the shortest code.
Your code will accept one pattern, a positive integer higher than 1.
It will output some text describing a pattern diagram, as described above.
Any language you like.
Please include a link to an online interpreter.


Test cases

2

R.


3

R..
L..


4

R.R.


7

R..L.L.
L..R.R.


9

R..L..R..
L..R..L..


10

R..L..R.R.


19

R..L..R..L..R..L.L.
L..R..L..R..L..R.R.


22

R..L..R..L..R..L..R.R.
Retina 0.8.2, 66 bytes

.+
$*
1
RL
^(.+)RL\1$
$1R¶L$1
^(.+)\1$
$1
(.)(..?)(?!.\b)
$1$.2$*.


Try it online! Link includes test cases. Explanation:

.+
$*


Convert the input to unary.

1
RL


Alternate between hands.

^(.+)RL\1$
$1R¶L$1


If there are an odd number of beats then divide the output in the middle.

^(.+)\1$
$1


But if there are an even number of beats then just use one copy.

(.)(..?)(?!.\b)
$1$.2$*.


Try to match groups of three beats, but without leaving a lone beat at the end, and replace the offbeats with .s.