You are given a binary tree in a peculiar string representation. Each node is written in the form (lr), where l corresponds to the left child and r corresponds to the right child.
If either l or r is null, it will be represented as a zero. Otherwise, it will be represented by a new (lr) pair.
Here are a few examples:
A root node with no children: (00)A root node with two children: ((00)(00))An unbalanced tree with three consecutive left children: ((((00)0)0)0)
Given this representation, determine the depth of the tree.