Maximum Sum BST in Binary Tree

Given a binary tree root, return the maximum sum of all keys of any subtree 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

          1
        /   \
       4     3
      / \   / \
     2   4 2   5
              / \
             4   6

Inputroot = [1,4,3,2,4,2,5,null,null,null,null,null,null,4,6]

Output20

Maximum sum in a valid Binary Search Tree is obtained in the subtree rooted at the node with key equal to 3.

Example 2

Inputroot = [4,3,null,1,2]

Output2

Maximum sum in a valid Binary Search Tree is obtained in a single-node subtree with key equal to 2.

Constraints