Suppose the key sequence is $\{2,1,4,5,9,3,6,7\}$

$($a$)[6$ points$]$ Following the above order, please insert each key and build an AVL tree

$($Hint: You can keep some important intermediate results to get some points if the final result

is wrong$)$

$($b$)[4$ points$]$ Draw the AVL tree after removing key $4.$