$($a$)$ Given the same input, i$.$e$.,$ a sequence of characters starting with $ andending with #$,$ and any combination of $0$s and $1$s in$-$between, specify aset of rewrite rules that determine whether the string contains an evennumber of $0$s$.$Here is some sample output:$$0011$# should be rewritten as $0011$ A$$10001$# should be rewritten as $10001$ B$$110110$# should be rewritten as $110110$ A$$0001100$# should be rewritten as $0001100$ B$($b$)$ Is there only one rewrite rule that can be applied at any step of yourrewrite process $($using your defined rewriting rules$)?$ Explain.$($c$)$ Show the steps of your rewrite system for the input strings $$0101$# and$$1000$#$.$