$(2\mathrm{.}48)$ Let $=\{0,1\}.$ Let $C_1$ be the language of all strings that contain a $1$ in their middle third. Let $C_2$ be the language of all strings that contain two $1s$ in their middle third. In particular,

$C_1=\{xyz|x,$zin${}^{**}$ and yin${}^{**}1{}^{**}$ where $|x|=|z||y|\}$

$C_2=\{xyz|x,$zin${}^{**}$ and yin${}^{**}1{}^{**}1{}^{**}$ where $|x|=|z||y|\}.$

$($a$)$ Show that $C_1$ is a CFL$.$

$($b$)$ Show that $C_2$ is not a CFL$.$