Insert node 13 in the following red-black tree using the given RB_insert function. Show all the transformations necessary (with explanations from the code) and show the changes in the tree after each transformation. (z pointer shows the node to be inserted.)

12 16 10 15 6 21 7 RB-INSERT (T, Z) TREE-INSERT (T, z) z.color = RED 1 while z# T.root and z.p.color == RED 2 if z.p == z.p.p.left 3 y = z.p.p.right 4 if y.color == RED 5 z.p.color = BLACK 6 y.color = BLACK 7 z.p.p.color = RED 8 2 = 2.P.P 9 else 10 if z == z.p.right 11 z = z.p 12 LEFT-ROTATE(T, z) 13 RIGHT-ROTATE(T, z.p.p) else (same as then clause with "right" and "left" exchanged) 15 T.root.color = BLACK // case 1 // case 1 Il case 1 // case 1 Il case 2 Il case 2 Il case 3 14