$($Palindromes and DFA are bad news $)$ A string $w$ is palindromic if it is the same read forwards and backwards $-$ e$.$g$.,10101,111,$ racecar, neveroddoreven $($Never odd or even$).$

a$.$ Construct a deterministic finite$-$state automaton with fixed input length $`=3($all words$/$strings are of length $3)$ that recognizes the palindromic bit$-$strings of length $3(000,010,101,111).($Solve with $7$ states or fewer.$)$