Write an efficient program that checks if a binary tree is BST. In the program, first add the code structure that will create the tree with object-oriented programming logic.

Binary search tree (BST) is a node-based binary tree data structure with the following features.

A node's left subtree contains only those nodes whose keys are less than the node's key. A node's right subtree contains only nodes with keys larger than the node's key. Both left and right subtrees must also be binary search trees.