$1.(12$ points$)$ Give a context$-$free grammar for

$\{a^{n}cw|$#$a(w)+$#$b(w)=n\}$

where $=\{a,b\}$ and $|w|=n.$

$2.(12)$ Prove $\{0^n{10}^n|ninN\}$ is not regular by using the pumping lemma.