Consider the following format for floating point literals. Assume a fraction part consisting of a string of one or more decimal digits with an optional decimal point $($period$)$ that can be added immediately before or after any of the digits. In addition, an optional exponent can be appended to the fraction part, consisting of an e or E$,$ followed by an optional sign, followed by one or more decimal digits. A floating point literal must contain either a decimal point, or an exponent, or both.

Examples: $\mathrm{.}0,0.,0\mathrm{.}1,\mathrm{.}01$e$-01,01$E$00$

a$.$ Give a regular expression for this construct. You may use $.$

b$.$ Use Thompson$$s construction to translate the regular expression into an NFA.

Make sure that you don$$t accept integers