Problem

At Dropbox, a service stores hierarchical folder metadata as a binary tree. Given the root of a binary tree, return its maximum depth.

The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Formal Specification

• Input: root, the root node of a binary tree, or null for an empty tree.
• Output: An integer representing the maximum depth of the tree.

You should solve this as a standard binary tree traversal problem.

Examples

Example 1

Input: root = [3,9,20,null,null,15,7]
Output: 3

Explanation: The longest root-to-leaf path is 3 -> 20 -> 15 (or 3 -> 20 -> 7), which contains 3 nodes.

Example 2

Input: root = [1,null,2]
Output: 2

Explanation: The longest path is 1 -> 2, so the depth is 2.

Constraints

• The number of nodes in the tree is in the range [0, 10^4]
• -100 <= Node.val <= 100
• The tree may be empty
• A leaf is a node with no children

Assume the binary tree is already constructed and passed as root using nodes with val, left, and right attributes.