Q$5[$Difficult$]$ Define a bitstring$-$to$-$bitstring function Fun via the following rules:

Fun$()-.$

Fun$(s0)-s00$ for any $sin\{0,1{\}}^{**}.$

Fun $(s1)-1s$ for any $sin\{0,1{\}}^{**}.$

Establish that if $L$ is any regular language, then $\{Fun(s)$:$sinL\}$ is also a regular language.