$30$ points$)$ Find the S$-$Box output of the input which you will obtain by following the steps:

$($a$)$ Take the number $34326917$ and take mod $2$ of each digit.

$($b$)$ Convert $34326917$ to binary string of length $8($by padding the first digits with $0$s if

needed$).$

$($c$)$ XOR these two binary strings.

$($d$)$ Find this binary string$$s correspondent polynomial in the filed F$28=$ F$2[$x$]/<$ x$8+$ x$4+$ x$3+$ x $+1>.($e$)$ Find the inverse of this polynomial in F$28$ and convert it to binary.