If $A$ is any language,let $A_{\frac{1}{2}-\frac{1}{3}}$ be the set of all strings in $A$ with their ,middle thirds removed so that
$A_{\frac{1}{2}-\frac{1}{3}}=\{\text{xz|for some y,|x|=|y|=|z| and xyz$\in$A\}}.$ Show that if $A$ is regular,then $A_{\frac{1}{2}-\frac{1}{3}}$ is not necessarily regular.