Consider the following query in the context of mini$-$project $2.$ r:great p:camera

Suppose the full reviews are stored in file reviews.txt; further assume the review terms

$($rterms$)$ are organized as a B$+$ tree and the product terms $($pterms$)$ are organized as a sorted file. The index entries for both rterms and pterms are in the form of $($term$,$reviewid,pid$)$ where pid is the address of the page in reviews.txt where the full record of the respective review is stored.

Suppose each page of both the B$+$ tree index and the sorted file stores $100$ index entries, whereas each page of the file reviews.txt stores $50$ records. Suppose $5\%$ of the review records satisfy the predicate r:great, $2\%$ of the records satisfy the predicate p:camera and $1\%$ of the records satisfy both predicates. Let N denotes the number of records in reviews.txt$,20$N denotes the number of index entries in rterms and $3$N denotes the number of index entries in pterms.

a$)[4$ marks $]$ What is the cost $($in terms of the number of I$/$Os$)$ of evaluating the query if the query predicates r:great and p:camera are respectively evaluated using the B$+$ tree index and the sorted file, before retrieving the matching records from reviews.txt$?$ Assume both the B$+$ tree and the sorted file are unclustered. Show your work.