insert the given value into an AVL tree. For each insertion, first list any rotations that were performed, one per line, with the direction $($L or R$)$ first and then the value of the node where the rotation was performed. Following that, enter the nodes in the tree level by level, with one space between each pair of values, and zeros where nodes are missing. For example, the tree below would be entered as:

$2$

$17$

$0068$

If the node with eight was deleted, the tree would be entered as $($note the trailing zero!$)$:

$2$

$17$

$0060$

Starting with an empty tree,

$1)$ insert the value $1$

$1$

$2)$ Insert $17$

$1$

$017$

$3)$ Insert $6$

$4)$Insert $4$

$5)$Insert $5$

$6)$Insert $10$

$7)$Insert $15$

$8)$Insert $13$

$9)$Insert $12$

$10)$ Insert $11$