Question $3$: Constructing and Balancing a Red$-$Black Tree

$3.$ Inserting Numbers in a Red$-$Black Tree:

Starting with an empty Red$-$Black Tree, insert the following sequence: $10,18,\backslash (7,15,16,30,25,40,60,2,1,70\backslash ).$

$-$ Draw the tree after each insertion, showing any necessary rotations or recoloring to maintain Red$-$Black Tree properties.

$-$ Explain how each adjustment helps preserve balance in the tree, ensuring efficient search and insertion operations.