Is it a Search Tree?

Given a binary tree, can you determine if it is a proper Binary Search Tree?

In a binary search tree, every descendant to the right of node P must be greater than P, and every descendant to the left of P must be less than P.

The input will be given as a list, as discussed in Trees.

Here's a good Binary Search Tree:

...and here's a bad one:

This tree is not a proper BST for 2 reasons:

• The 8 is smaller than the 9, even though it is in a right subtree of 9.
• The 6 is smaller than the 7, even though it is in a right subtree of 7.