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 Node
  attr_accessor :key, :left, :right
  def initialize key
    @key = key
  end
  
  def inorder
    left.inorder if left
    print " ", key
    right.inorder if right
  end
  
  def preorder
    print " ", key
    left.preorder if left
    right.preorder if right
  end
end
  
def insert
  z = Node.new $key.to_i
  x = $root
  while x
    y = x
    x = z.key < x.key ? x.left : x.right
  end
  
  unless y
    $root = z
  else
    z.key < y.key ? y.left = z : y.right = z
  end
end

def find(x)
  y = $root
  while y
    if y.key == x
      puts "yes"
      return
    end
    z = y
    y = x < y.key ? y.left : y.right
  end
  puts "no"
end

n = gets.to_i
n.times do
  command, $key = gets.split
  if command == "insert"
    insert
  elsif command == "find"
    find($key.to_i)
  else
    $root.inorder
    puts
    $root.preorder
    puts
  end
end