Given a binary tree, find 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.

Definition of a tree:

// Java
class TreeNode
{
public:
  int val;
  TreeNode left;
  TreeNode right;
  TreeNode(int x) {
    val = x;
    left = NULL; 
    right = NULL;
};

// C++
class TreeNode
{
public:
  int val;
  TreeNode *left;
  TreeNode *right;
  TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};

Implement function maxDepth that returns the maximum depth of the tree.

// Java
int maxDepth(TreeNode tree)

// C++
int maxDepth(TreeNode *tree)

Example

Function maxDepth returns 3 because the longest path from the root 5 to the farthest leaf 1 contains 3 nodes.