A red$-$black tree is a binary$-$search tree such that the following hold:

$1.$ Every node is either red or black.

$2.$ The root and the leaves are black.

$3.$ If a node is red, then both its children are black.

$4.$ For each node, all simple paths from the node to descendant leaves have the same

number of black nodes.

$($a$)(5$ points$)$ Draw a red$-$black tree with the keys $6,18,10,28,8,12$ so that no two internal

nodes contain the same key, and that the black height of the tree is $2.$ Make sure that

the nodes with the keys $8$ and $28$ are red. What is the height of this tree? Please explain

briefly.