L$\_1=\{$a$^$i b$^$j c$^$k d$^|$ i$,$ j$,$ k$,$ in $,$ j$=$k or i$=\}$

Exercise $20$ Design a pushdown automaton for L$\_1.$Exercise $19$ Design a context$-$free grammar for the following language

L$\_1=\{$a$^$i b$^$j c$^$k d$^|$ i$,$ j$,$ k$,$ in $,$ j$=$k or i$=\}$

Informally describe your construction.