Determine if a Binary Tree is a Binary Search Tree (BST)

You are given a binary tree in level-order traversal format. The tree is represented as a sequence of tokens separated by spaces. Each token is either an integer (representing the node's value) or the string null (representing a missing node). Your task is to determine whether the given binary tree satisfies the properties of a Binary Search Tree (BST).

A BST must satisfy the following condition for every node:

• All nodes in its left subtree have values strictly less than the node's value.
• All nodes in its right subtree have values strictly greater than the node's value.

If the binary tree is empty, it should be considered as a valid BST.

Note: The input is provided via standard input (stdin) and the result should be printed to standard output (stdout) as either True or False.

Tree Construction Hint: Interpret the input tokens as the level order traversal of the tree. For example, the input 10 5 15 2 7 12 18 represents the following tree:

         10
        /  \
       5    15
      / \   / \
     2   7 12  18

inputFormat

The input is a single line containing a space-separated list of tokens representing the level-order traversal of a binary tree. Each token is either an integer or the string null. An empty input indicates an empty tree.

outputFormat

Output a single line to stdout: True if the binary tree is a valid BST, or False if it is not.

## sample

True