Deletion in Red$-$Black Trees

Consider a red$-$black tree formed by inserting the following keys in the given order: $20,15,25,10,18,$

$22,$ and $30.$ After constructing the tree, perform successive deletions of the keys in the following order:

$15,22,$ and $18.$

For each deletion:

Draw the resulting red$-$black tree.

Indicate any necessary rotations and recoloring.

Provide a brief rationale for each operation performed