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: Accepted)

class BinaryTree
  attr_accessor :root

  class Node
    attr_accessor :parent, :left, :right, :key

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

  def initialize
    @root = nil
  end

  def insert(key)
    n = Node.new(key)
    y = nil
    x = @root

    while x != nil
      y = x
      x = if n.key < x.key
            x.left
          else
            x.right
          end
    end
    n.parent = y

    if y == nil
      @root = n
    elsif n.key < y.key
      y.left = n
    else
      y.right = n
    end
  end

  def find(key)
    n = @root
    while n != nil
      return true if n.key == key
      n = if key < n.key
        n.left
      else
        n.right
      end
    end
    return false
  end

  def inorder(n)
    return unless n
    inorder(n.left)
    print " #{n.key}"
    inorder(n.right)
  end

  def preorder(n)
    return unless n
    print " #{n.key}"
    preorder(n.left)
    preorder(n.right)
  end

  def dump
    inorder(@root)
    print "\n"
    preorder(@root)
    print "\n"
  end
end

n = gets.to_i
bt = BinaryTree.new

n.times do |i|
  cmd, v = gets.split
  case cmd
  when "insert"
    bt.insert(v.to_i)
  when "find"
    puts bt.find(v.to_i) ? "yes" : "no"
  when "print"
    bt.dump
  end
end