$1.$ Fix an alphabet $.$ For any string w with $|$w$|2,$ let skip$($w$)$ be the string obtained by removing the first two symbols of w$.$ Define two operators on languages:

$$

f$1($L$)=\{$w in $$ : skip$($w$)$ in L$\},$ and

f$2($L$)=\{$skip$($w$)$ in $$ : w in L$\}$

$($a$)(5$ Points$)$ Consider L$=$ L$($bba$)$ over the alphabet $=\{$a$,$ b$\}.$ Write a regular expression representing f$1($L$).$ Write another regular expression representing f$2($L$).$