Consider a collection made of $500000$ documents, each containing on average $800$ tokens and $6$ characters per token. The number of different terms is estimated to $700000$ and there are $70,000,000$ non$-$positional posting lists.

a$)$ If $20$ fixed bytes are used for terms, $4$ bytes for term frequency and $4$ bytes for storing the pointer to postings list, compute the memory usage for dictionary.

b$)$ What is the minimum number of bits required for document identifiers and the total size of the collection?

c$)$ What is the size of the uncompressed posting list?