Problem:
Binary Search Tree II

Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$ or print are given.

Output

For each find $k$ operation, print "yes" if $T$ has a node containing $k$, "no" if not.

In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key.

Constraints

The number of operations $\leq 500,000$

The number of print operations $\leq 10$.

$-2,000,000,000 \leq key \leq 2,000,000,000$

The height of the binary tree does not exceed 100 if you employ the above pseudo code.

The keys in the binary search tree are all different.

Sample Input 1

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Ruby (judge verdict: Time Limit Exceeded)

class Node
  def initialize(parent, key)
    @key = key
    @parent = parent
    @left = nil
    @right = nil
  end

  attr_accessor :left, :right, :parent
  attr_reader :key
end

class BinarySearchTree
  def initialize
    @first = nil
    @visited_node = []
    @keys = []
  end

  def insert(node)
    unless @first.nil?
      current = @first
      until current.nil?
        node.parent = current
        if node.key < current.key
          current = current.left
        else
          current = current.right
        end
      end
    end
    if @first.nil?
      @first = node
    elsif node.key < node.parent.key
      node.parent.left = node
    else
      node.parent.right = node
    end
    @keys << node.key
  end

  def find(key)
    if @keys.include? key
      puts 'yes'
    else
      puts 'no'
    end
  end

  def preorder_tree_walk(node)
    @visited_node << node.key
    return if node.nil?
    preorder_tree_walk node.left unless node.left.nil?
    preorder_tree_walk node.right unless node.right.nil?
  end

  def inorder_tree_walk(node)
    return if node.nil?
    inorder_tree_walk node.left unless node.left.nil?
    @visited_node << node.key
    inorder_tree_walk node.right unless node.right.nil?
  end

  def print
    inorder_tree_walk @first
    puts " #{@visited_node.join ' '}"
    @visited_node = []
    preorder_tree_walk @first
    puts " #{@visited_node.join ' '}"
    @visited_node = []
  end
end

n = gets.to_i
tree = BinarySearchTree.new
n.times do
  input = gets.split ' '
  case input[0]
  when 'insert'
    tree.insert Node.new nil, input[1].to_i
  when 'find'
    tree.find input[1].to_i
  when 'print'
    tree.print
  end
end