Consider the alphabet $\{$A$,$ G$,$ T$,$ C$\}$ of nucleotide bases.

$$ Design a regular expression that recognizes all strings of nucleotide bases that have at least three

T nucleotides which are non$-$consecutive $($two characters are non$-$consecutive if there is at least one

character between them$).$

$$ Explain how your regular expression recognizes the string AT GGT T CAT AAA by clearly identifying

which parts of the string match to the components of your regular expression.