CFG Design

For $=\{0,1\},$ let L $=$ xy $(|$x$|=|$y$|)$ x$=$ yR $.$

$$ That is$,$ for each string in L$,$ the first half of the string does not match the second half reversed.

Design a CFG for L$.$

$$ Hint: Think about $(1)$ how you match the length of each half and $(2)$ what to do when you detect$/$generate

a mismatch in each half.