<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&#39;s key.</li>
	<li>The right subtree of a node contains only nodes with keys <strong>greater than</strong> the node&#39;s key.</li>
	<li>Both the left and right subtrees must also be binary search trees.</li>
</ul>

<p>&nbsp;</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>&nbsp;</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> &lt;= Node.val &lt;= 4 * 10<sup>4</sup></code></li>
</ul>

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    //int maxSumBST(TreeNode* root) {
pair<pair<int,int>,pair<int,int>> print0(TreeNode * b,int &c){
    if(b==NULL){
        pair<pair<int,int>,pair<int,int>> temp0;
        temp0.first.first=INT_MAX;
        temp0.first.second=0;
        temp0.second.first=INT_MIN;
        temp0.second.second=0;
        return temp0;
    }
    pair<pair<int,int>,pair<int,int>> temp2=print0(b->left,c);
    pair<pair<int,int>,pair<int,int>> temp12=print0(b->right,c);
    pair<pair<int,int>,pair<int,int>> temp18;
    if(temp2.first.second==0 && temp12.first.second==0){
           if(b->val>temp2.second.first && b->val<temp12.first.first){
                  temp18.first.first=min(temp2.first.first,min(temp12.first.first,b->val));
                  temp18.second.first=max(temp2.second.first,max(temp12.second.first,b->val));
                  temp18.second.second=temp2.second.second+temp12.second.second+b->val;
                  //cout<<endl;
                  temp18.first.second=0;
                  c=max(c,temp18.second.second);
           }
           else if(b->val<=temp2.second.first || b->val>=temp12.first.first){
            temp18.first.first=-1;
            temp18.first.second=1;
            temp18.second.first=-1;
            temp18.second.second=-1;
           }
    } 
    else if(temp2.first.second==1 || temp12.first.second==1){
        temp18.first.first=-1;
        temp18.first.second=1;
        temp18.second.second=-1;
        temp18.second.second=-1;
    }
                  //cout<<temp18.first.second<<" ";
                  //cout<<temp18.second.second<<" ";
                  //cout<<temp2.second.second<<" ";
                  //cout<<temp12.second.second<<" ";
                  //cout<<endl;
    return temp18;
}
int maxSumBST(TreeNode * b){
  int c=INT_MIN;
  int e=0;
  int temp0=0;
  pair<pair<int,int>,pair<int,int>> temp2;
  temp2=print0(b,c);
  e=c;
  if(e<0){
    e=0;
  }
  return e;
    }
};
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