$(20$ points$)$ Answer the following questions about binary search trees $($BSTs$).$

$($a$)$ Draw the final BST after inserting elements $60,25,15,8,35,27,82,73,50,40,77,92,88,90$ in that order.

$($b$)$ Draw the tree after deleting $15$ from the BST in $($a$).$

$($c$)$ Draw the tree after deleting $60$ from the resulting tree of $($b$)$ using the largest element in the left subtree for replacement.

$($d$)$ Draw the tree after deleting $82$ from the resulting tree of $($c$)$ using the smallest element in the right subtree for replacement.

$($e$)$ List the elements of pre$-$order, in$-$order, and post$-$order traversals of the resulting tree of $($d$).$