![\"\"](\"https://assets.leetcode.com/uploads/2020/01/30/sample_1_1709.png\")
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:
\n\n\n
Example 1:
\n\n
\nInput: root = [1,4,3,2,4,2,5,null,null,null,null,null,null,4,6]\nOutput: 20\nExplanation: Maximum sum in a valid Binary search tree is obtained in root node with key equal to 3.\n\n\n
Example 2:
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2020/01/30/sample_2_1709.png\")
\nInput: root = [4,3,null,1,2]\nOutput: 2\nExplanation: Maximum sum in a valid Binary search tree is obtained in a single root node with key equal to 2.\n\n\n
Example 3:
\n\n\nInput: root = [-4,-2,-5]\nOutput: 0\nExplanation: All values are negatives. Return an empty BST.\n\n\n
\n
Constraints:
\n\n[1, 4 * 104].-4 * 104 <= Node.val <= 4 * 104给你一棵以 root 为根的 二叉树 ，请你返回 任意 二叉搜索子树的最大键值和。
二叉搜索树的定义如下：
\n\n\n\n
示例 1：
\n\n![\"\"](\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/03/07/sample_1_1709.png\")
\n输入：root = [1,4,3,2,4,2,5,null,null,null,null,null,null,4,6]\n输出：20\n解释：键值为 3 的子树是和最大的二叉搜索树。\n\n\n
示例 2：
\n\n![\"\"](\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/03/07/sample_2_1709.png\")
\n输入：root = [4,3,null,1,2]\n输出：2\n解释：键值为 2 的单节点子树是和最大的二叉搜索树。\n\n\n
示例 3：
\n\n\n输入：root = [-4,-2,-5]\n输出：0\n解释：所有节点键值都为负数，和最大的二叉搜索树为空。\n\n\n
示例 4：
\n\n\n输入：root = [2,1,3]\n输出：6\n\n\n
示例 5：
\n\n\n输入：root = [5,4,8,3,null,6,3]\n输出：7\n\n\n
\n\n
提示：
\n\n1 到 40000 个节点。[-4 * 10^4 , 4 * 10^4] 之间。\\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\"],\"java\":[\"Java\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u88ab\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5305\\u542b Pair \\u7c7b: https:\\/\\/docs.oracle.com\\/javase\\/8\\/javafx\\/api\\/javafx\\/util\\/Pair.html <\\/p>\"],\"python\":[\"Python\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982\\uff1aarray<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\" \\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n 1. 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