PLEASE PLEASE DON'T EVER ANSWER FROM CHATGPT I NEED YOUR OWN ANSWER?

You are given the following Treap, where nodes are $($key$,$priority$)$ tuples:

Which of the following, when inserted into the above Treap, will result in a perfectly balanced Treap and will cause exactly $2$

AVL rotations during the insertion? Select all that apply.

$($A$,11)$

$($D$,38)$

$($K$,25)$

$($Y$,31)$

$($Y$,14)$

$($A$,22)$

$($J$,27)$

$($D$,22)$

$(0,44)$

$($J$,38)$