Exploring the pre$-$trained Transformer Architecture

a$.$ Utilize the Enron$1$ dataset to provide few$-$shot examples to the $$gpt$-3\mathrm{.}5-$turbo' Large Language Model $($LLM$).$ Develop a prompt specifically designed for the model to classify input text as either legitimate $("$Ham$")$ or unwanted $("$Spam$").$ Test is with $10$ data $(5$ spam and $5$ ham$)$ and report the accuracy.

b$.$ Compare and contrast the functionalities and applications of encoder$-$only models such as BERT, decoder$-$only models such as GPT$-2,$ and encoder$-$decoder models such as T$5,$ particularly considering their implementations accessible through the Hugging Face Transformers library?

c$.$ How do these models differ in their architectures, training objectives, and typical use cases in natural language processing tasks?