Write a function that determines if a given binary tree is a valid binary search tree $($BST$).$ A valid BST is defined as a binary tree in which every node follows these rules:

The left subtree of a node contains only nodes with keys less than the node$$s key.The right subtree of a node contains only nodes with keys greater than the node$$s key.Both the left and right subtrees must also be binary search trees.

Write a method to determine the depth of a given node in a Binary Search Tree $($BST$).$

The depth of a node is the number of edges from the root to the node. If the node does not exist in the tree, return $-1.$