For each of the following languages, construct a context$-$free grammar that generates exactly the given language.

$($a$)$ LA $=\{($b$^$y $)($a$^$x$)($a

$^2$x$+3$y$)$: x$,$y $>=0\}$For each of the following languages, construct a context$-$free grammar that generates exactly the given language.

$($a$)L_A=\{b^y{a}^x{a}^{2x+3y}$:$x,y0\},=\{a,b\}$

$($b$)L_B=(110|01{)}^{**}{000}^{**},=\{0,1\}$

$($c$)L_C=$ binary strings with at most two $0\text{'}$s where the number of $1\text{'}$s is equal to the number of $0\text{'}$s$,=\{0,1\},\backslash$Sigma $=\{$a$,$ b$\}$

$($b$)$ LB $=(110|01)000$

$,\backslash$Sigma $=\{0,1\}$

$($c$)$ LC $=$ binary strings with at most two $0$s where the number of $1$s is equal to the number of $0$s$,\backslash$Sigma $=\{0,1\}$