Suppose each B$+-$tree node can hold up to $3($three$)$ pointers and two $(2)$ keys. Draw the B$+-$trees that would result after insertion $($a$)$ and deletion $($b$)$ operations as shown below $[25$ pts$].$

$($a$)$ Insertion $[8$ pts$]$

First, insert $19.$ Then, insert $27[$Show individual trees at each insertion$].$

$($b$)$ Deletion: Use the tree after inserting $27$ in part $($a$)[17$ pts$]$

First, delete $5$; then delete $9$; next, delete $12$; after that, delete $4$; and finally, delete $11$

$($Show individual trees at each deletion$].$