Run Length Encoding in Prolog

Run Length Enconding $($RLE$)$ is a compression technique used in areas such as image compression $($e$.$g$.$ GIFs$).$ It compresses runs of identical pieces of information $($in this case single$-$character atoms$)$ and records how many times they appear in a list in a consecutive run. For example, the list:

$[\text{'}$a$\text{'},\text{'}$a$\text{'},\text{'}$a$\text{'},\text{'}$b$\text{'},\text{'}$b$\text{'},\text{'}$c$\text{'},\text{'}$a$\text{'},\text{'}$a$\text{'}]$

will get encoded to:

$[(\text{'}$a$\text{'},3),(\text{'}$b$\text{'},2),(\text{'}$c$\text{'},1),(\text{'}$a$\text{'},2)]$

Write a predicate myencode$/2$ that takes the uncompressed list as a first parameter and returns the compressed list as shown as the second parameter. For example:

myencode$([],$X$)$ should yield X $=[].$

myencode$([\text{'}$a$\text{'},\text{'}$b$\text{'},\text{'}$b$\text{'},\text{'}$c$\text{'},\text{'}$c$\text{'},\text{'}$c$\text{'},\text{'}$d$\text{'},\text{'}$d$\text{'}],$X$)$ should yield X $=[($a$,1),($b$,2),($c$,3),($d$,2)].$

myencode$([\text{'}$a$\text{'},\text{'}$p$\text{'},\text{'}$p$\text{'},\text{'}$l$\text{'},\text{'}$e$\text{'}],$X$)$ should yield X $=[($a$,1),($p$,2),($l$,1),($e$,1)].$

Hint:

You may find it useful to write a tempencode$/2$ function that translates a list like

$[\text{'}$a$\text{'},\text{'}$a$\text{'},\text{'}$a$\text{'},\text{'}$b$\text{'},\text{'}$b$\text{'},\text{'}$c$\text{'},\text{'}$a$\text{'},\text{'}$a$\text{'}]$

into

$[(\text{'}$a$\text{'},1),(\text{'}$a$\text{'},1),(\text{'}$a$\text{'},1),(\text{'}$b$\text{'},1),(\text{'}$b$\text{'},1),(\text{'}$c$\text{'},1),(\text{'}$a$\text{'},1),(\text{'}$a$\text{'},1)]$