Is it a search tree?

Return True if the tree is a binary search tree (lesson 4): for every node, all keys in its left subtree are smaller than its key, and all keys in its right subtree are bigger. Keys must be different, so equal keys mean False.

tree [8, 3, 10, 1, 6, None, 14]   ->  True
tree [5, 1, 4, None, None, 3, 6]  ->  False
tree [5, 4, 6, None, None, 3, 7]  ->  False

In the second tree, 4 is the right child of 5 but smaller than 5. In the third tree, every node is fine next to its own children, but 3 is in the right subtree of 5 and is smaller than 5.

The tests write a tree as a level-order list: the values level by level, left to right, with None where a child is missing. So [3, 9, 20, None, None, 15, 7] is 3 with children 9 and 20, where 20 has children 15 and 7. An empty tree is None.

Limits

• Up to 100,000 nodes, at most about 50 levels deep. Keys are whole numbers of any size.