Given the root of a binary tree, determine if it is a valid binary search tree $($BST$).$

A valid 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.

Output: false

Explanation: The root node's value is $5$ but its right child's value is $4.$

Constraints:

The number of nodes in the tree is in the range $[1,104].$

$-2^{31}$ Node.val $2^{31}-1$

PLEASE DON'T USE INBUILT FUNCTION,LIBRARY.

DON'T USE VECTOR.

DON'T USE STL