Java class TreeNode is defined as below:

public class TreeNode { public int val; public TreeNode left, right; public TreeNode(int x) { val = x; } }

Suppose you only have the reference of the root, please write a method that returns true if the binary tree is binary search tree; false otherwise.

Please be careful! Checking every node for "greater than the left child and smaller than the right child" is insufficient. The binary tree below is not a binary search tree and your algorithm should correctly detect it.

You may write a private recursive method then a wrapper method.

The code should be in java.