$A=[5,8,2,6,3,1,4,7]$

$($a$)$ First, consider building the initial heap, where we insert each number one at a time into a heap $($that is initially empty$).$ Show the heap after each insert.

$($b$)$ Second, consider the for loop where we sort the array $A.$ Show the status of the heap after each Extract$-$Max.