<p>Given a <strong>binary tree</strong> <code>root</code>, return <em>the maximum sum of all keys of <strong>any</strong> sub-tree which is also a Binary Search Tree (BST)</em>.</p> <p>Assume a BST is defined as follows:</p> <ul> <li>The left subtree of a node contains only nodes with keys <strong>less than</strong> the node's key.</li> <li>The right subtree of a node contains only nodes with keys <strong>greater than</strong> the node's key.</li> <li>Both the left and right subtrees must also be binary search trees.</li> </ul> <p> </p> <p><strong class="example">Example 1:</strong></p> <p><img alt="" src="https://assets.leetcode.com/uploads/2020/01/30/sample_1_1709.png" style="width: 320px; height: 250px;" /></p> <pre> <strong>Input:</strong> root = [1,4,3,2,4,2,5,null,null,null,null,null,null,4,6] <strong>Output:</strong> 20 <strong>Explanation:</strong> Maximum sum in a valid Binary search tree is obtained in root node with key equal to 3. </pre> <p><strong class="example">Example 2:</strong></p> <p><img alt="" src="https://assets.leetcode.com/uploads/2020/01/30/sample_2_1709.png" style="width: 134px; height: 180px;" /></p> <pre> <strong>Input:</strong> root = [4,3,null,1,2] <strong>Output:</strong> 2 <strong>Explanation:</strong> Maximum sum in a valid Binary search tree is obtained in a single root node with key equal to 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> root = [-4,-2,-5] <strong>Output:</strong> 0 <strong>Explanation:</strong> All values are negatives. Return an empty BST. </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li>The number of nodes in the tree is in the range <code>[1, 4 * 10<sup>4</sup>]</code>.</li> <li><code>-4 * 10<sup>4</sup> <= Node.val <= 4 * 10<sup>4</sup></code></li> </ul>