Design context$-$free grammars $($CFGs$)$ for the following languages:

$1.$ L$=\{$balanced parentheses$\}$:

This is the set of all strings with balanced parentheses, also known as the Dyck language. For example:

$\{\backslash$epsi $,(),(()),()(),(()(())),...\}$

$2.$ L$=\{0^$m $1^$n $2^$p $|$ m$,$ n$,$ p $>=0,$ m $+$ n $=$ p$\}$:

This language consists of strings where the number of $2$s is equal to the sum of the number of $0$s and $1$s$.$

$3.$ L$=\{$w $|$ w in $\{0,1\}*,$ w $=$ w$\}$:

This is the set of all palindromic strings over the alphabet $\{0,1\}.$

$4.\{01|$ n $>=1\}$:

This language consists of strings where the number of $0$s is equal to the number of $1$s$,$ with all the $0$s appearing before the $1$s$.$

Provide the CFGs for each of these languages.