$(10$ points$)$ Suppose that Artist $($A$)$ has $9000$ tuples stored in $100$ disk blocks and Recorded$\_$by $($R$)$ has $60000$ tuples stored in $600$ disk blocks.

The following information is provided for access paths:

$102$ buffer caches $($pages$)$ are available.

The relation Recorded$\_$by has the secondary Index on aID with index level $=3$

The relation Artist has the secondary index on aID with index level $=2$

Each Artist tuple matches with exactly $4$ Recorded$\_$by tuples.

What is the IO costs for the join Artist $|||><mi>|</mi><mi>|</mi><mi>|</mi>$ Recorded$\_$by: Artist.aID $=$ Recorded$\_$by$.$aID using

$($a$)$ index based nested loop join $A|||><mi>|</mi><mi>R</mi><mi>|</mi><mi>|</mi>$

$($b$)$ index based nested loop join $R|||><mi>|</mi><mi>A</mi><mi>|</mi><mi>|</mi>$

$($Show all work$)$