Given a binary tree `root`, return the maximum sum of all keys of any sub-tree which is also a Binary Search Tree (BST).

Assume a BST is defined as follows:

- 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.

Example 1:

    Input: root = [1,4,3,2,4,2,5,null,null,null,null,null,null,4,6]
    Output: 20
    Explanation: Maximum sum in a valid Binary search tree is obtained in root node with key equal to 3.

Example 2:

    Input: root = [4,3,null,1,2]
    Output: 2
    Explanation: Maximum sum in a valid Binary search tree is obtained in a single root node with key equal to 2.

Example 3:

    Input: root = [-4,-2,-5]
    Output: 0
    Explanation: All values are negatives. Return an empty BST.

Constraints:

- The number of nodes in the tree is in the range `[1, 4 * 104]`.
- `-4 * 104 <= Node.val <= 4 * 104`