Closure of regular languages to $A(L)=\{zyx|x,y,z \in \{0,1\}^*, xyz \in L\}$

Question

Given: $A(L)=\{zyx|x,y,z \in \{0,1\}^*, xyz \in L\}$

Given $L \subseteq\{0,1\}^*$, Prove/Disprove:

• If $L$ is regular $\implies$ $A(L)$ is regular
• If $L$ is context free$\implies$ $A(L)$ is context free

I'd like a proof not using a construction of DFA/NFA.