$($e$)$ Recall that Haskell ships with the following algebraic datatype which is conve$-$

nient to do error$-$handling

data Maybe a $=$ Just a $|$ Nothing

Write a function

groupByPairsIfEven :: $[$a$]->$ Maybe $[($a$,$a$)]$

which takes as input a list of elements $[$x$0,$ x$1,$ x$2,$ x$3,...,$ x$2$n$,$ x$2$n$+1]$ and outputs

the list of pairs $[($x$0,$ x$1),($x$2,$ x$3),...,($x$2$n$,$ x$2$n$+1)]$ wrapped by Just if the input

has an even length and Nothing otherwise.

$[4$ marks$]$