$.(7$ points$)$ What's the return node of next$(45)$

$2.(10$ points$)$ Please draw the binary search tree after insert$(30)$

$3.(10$ points$)$ Still based on the original tree, please draw the binary search tree after delete$(15)$

$4.(10$ points$)$ Consider the original tree as an AVL tree, please draw the AVL tree after insert$(13)$

$5.(15$ points$)$ Consider the original tree as an AVL tree, please draw the AVL tree after insert$(9),$ and insert$(8)$