Largest Sum of a BST Rooted Subtree

### Problem Among rooted subtrees of the native binary tree, find the largest sum whose entire subtree is a strict binary search tree. Every left descendant must be smaller than its ancestor and every right descendant greater. The empty BST with sum 0 is also allowed, as in the original all-negative example. Return the maximum sum. ```cpp class Solution { public: int maxSumBST(TreeNode* root); }; ``` ### Examples **Example 1:** ```text Input: root = [4,2,6,1,3] Output: 16 Explanation: The entire tree is a BST and sums to4+2+6+1+3=16. ``` **Example 2:** ```text Input: root = [-2,-3,-1] Output: 0 Explanation: Every nonempty candidate has negative sum; the allowed empty BST gives0. ``` ### Constraints - The tree has 1 to 40000 nodes. - Each key is an integer in `[-40000,40000]`. - Strict BST ordering is required; the original example explicitly permits the empty BST. ### Contract considerations Keep the native TreeNode interface and allow the empty candidate when all valid nonempty sums are negative. ```hint Read the boundary condition A rooted subtree includes all of its descendants. Check strict ordering, duplicate keys, negative values, and the permitted empty candidate. ``` ### Boundary reminders Keep the native TreeNode interface and allow the empty candidate when all valid nonempty sums are negative.