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)

node = Struct.new(:key, :parent, :left, :right)
root = nil

insert = ->(z) {
  pa = nil
  x = root
  while x
    pa = x
    x = (z.key < x.key) ? x.left : x.right
  end
  z.parent = pa
  
  if pa.nil?
    root = z
  elsif z.key < pa.key
    pa.left  = z
  else
    pa.right = z
  end
}

inorder = ->(x) {
  a = x.left
  inorder.(a) if a
  print " " + x.key.to_s
  a = x.right
  inorder.(a) if a
}

preorder = ->(x) {
  print " " + x.key.to_s
  a = x.left
  preorder.(a) if a
  a = x.right
  preorder.(a) if a
}

find = ->(x, k) {
  f = false
  try = ->(node) {
    if node.key == k
      f = true
    else
      a = node.left
      try.(a) if a && !f
      a = node.right
      try.(a) if a && !f
    end
  }
  try.(x) 
  puts f ? "yes" : "no" 
}

gets.to_i.times do
  command = gets.split(" ")
  case command[0]
  when "insert"
    z = node.new
    z.key = command[1].to_i
    insert.(z)
  when "print"
    inorder .(root)
    puts
    preorder.(root)
    puts
  when "find"
    find.(root, command[1].to_i)
  end
end