Recall that a treap combines BST properties (left < parent < right) with heap properties (parent > children). How can you leverage both properties to maintain balance probabilistically?

Consider how rotations in BSTs preserve BST order. How might you use rotations to maintain both BST and heap properties after an insertion?

Given the random priority assigned to each node, how would you modify standard BST insertion to ensure the heap property is maintained while preserving BST order?