Construct an extended BNF grammar for floating$-$point numbers with the following

features:

$($i$)$ floating$-$point$-$number longrightarrowf$-$sign frac$-$part e$-$sign exponent

$($ii$)f-$sign is optional $($i$.$e$.,$ it can be omitted for positive values$).$

$($iii$)$ frac$-$part longrightarrowx.$y$

$($iv$)x$ is a non$-$empty digit string $($i$.$e$.,.222$ is invalid$).$

$($v$)y$ is a non$-$empty digit string $($i$.$e$.,222.$ is invalid$).$

$($vi$)x$ and $y$ have lengths no more than $8.$

$($vii$)$ e$-$sign is optional $($i$.$e$.,$ can be omitted for positive values$).$

$($viii$)$ exponent has length $2.$

$($ix$)$ e$-$sign exponent is optional $($i$.$e$.,-0\mathrm{.}555$ is valid$).$