Maximum Depth of Binary Tree

Execution time limit is 1 second

Runtime memory usage limit is 128 megabytes

Given an array of integers. Create a Binary Search Tree from these numbers. If the inserted value equals to the current node, insert it to the right subtree.

Write a method MaxDepth that finds the maximum depth of a tree. The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Write the code according to the next interface:

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

class Tree
{
public:
  TreeNode *head;
  Tree() : head(NULL) {};
  void Insert(int val); // Insert number val into Binary Search Tree
  int MaxDepth(void); // return the maximum depth of Binary Search Tree
};

// Java
class TreeNode
{
  int val;
  TreeNode left;
  TreeNode right;
  TreeNode(int x)
  {
    val = x;
    left = null;
    right = null;
  }
}

class Tree
{
  TreeNode head;
  Tree();
  void Insert(int val); // Insert number val into Binary Search Tree
  int maxDepth() // return the maximum depth of Binary Search Tree
}

You can create (use) additional methods if needed.

Input

The first line contains number n (1 ≤ n ≤ 100). The second line contains n integers.

Output

Create the Binary Search Tree from input data. Find and print its maximum depth.

Examples

Input #1

Answer #1

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