The largest closed set content in $A^c$

Question

Let $A=\{ (a,m)\in \mathbb R\times\mathbb Z\mid a^2-m^2<0 \}~ \bigcup ~\{ (a,m)\in \mathbb R\times\mathbb Z\mid a^2-m^2=0 ,\ a.m\not=0\} $.

and $A^c$ its complementary , I want to determine the largest closed set content in $A^c$.

Thanks a lot.