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)

Node = Struct.new(:key, :left, :right)

class Tree
  def initialize
    @root = nil
  end
  
  def insert(key)
    unless @root
      @root = Node.new(key)
      return
    end
    node = @root
    while node
      if key < node.key
        if node.left
          node = node.left
        else
          node.left = Node.new(key)
          break
        end
      else
        if node.right
          node = node.right
        else
          node.right = Node.new(key)
          break
        end
      end
    end
  end
  
  def search(key)
    node = @root
    while node
      if key < node.key
        node = node.left
      elsif key > node.key
        node = node.right
      else
        return node
      end
    end
    nil
  end
  
  def preorder
    traverse = ->(node) {
      if node
        yield(node.key)
        traverse.(node.left)
        traverse.(node.right)
      end
    }
    traverse.(@root)
  end
  
  def inorder
    traverse = ->(node) {
      if node
        traverse.(node.left)
        yield(node.key)
        traverse.(node.right)
      end
    }
    traverse.(@root)
  end
end

t = Tree.new

$<.gets.to_i.times do
  com, key = $<.gets.split
  case com
  when "insert" then t.insert(key.to_i)
  when "print"
    t.inorder  {|key| print " #{key}"}
    puts
    t.preorder {|key| print " #{key}"}
    puts
  when "find"
    puts t.search(key.to_i) ? "yes" : "no"
  end
end