Construct npda's that accept the following languages on $=\{a,b,c\}$ :

$($f$)L=\{a^n{b}^m$:$nm3n\}.$

$($g$)L=\{w$:$n_a(w)=n_b(w)+1\}.$

$($h$)L=\{w$:$n_a(w)=2n_b(w)\}.$

$($i$)L=\{w$:$n_a(w)+n_b(w)=n_c(w)\}.$

Chapter $7$ Pushdown Automata

$($j$)L=\{w$:$2n_a(w)n_b(w)3n_a(w)\}.$

Please solve all and make their state graph

$($k$)$