Problem:
Binary Search Tree III

Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.

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

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

delete $k$: Delete a node containing $k$.

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

The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:

If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).

If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.

If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.

Input

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

18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print

Sample Output 1

yes
yes
yes
no
no
no
yes
yes
1 2 3 7 8 22
8 2 1 3 7 22
1 2 8 22
8 2 1 22

Reference

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

Solution in Ruby (judge verdict: Wrong Answer)

class Node
  attr_accessor :key, :left, :right, :parent
  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
  def in
    left.in if left
    $a << self
  end
end

def insert
  z = Node.new $key
  x = $root
  while x
    y = x
    x = z.key < x.key ? x.left : x.right
  end
  z.parent=y
  unless y
    $root = z
  else
    z.key < y.key ? y.left = z : y.right = z
  end
end

def find root
  if root == nil
    puts 'no'
  elsif $key == root.key
    puts 'yes'
  elsif $key < root.key
    find root.left
  else
    find root.right
  end
end

def delete root
  left = root.left
  right = root.right
  if $key == root.key
    parent = root.parent
    pleft = parent.left if parent
    if (left || right) == nil
      if parent.left
        $key == pleft.key ? parent.left = nil : parent.right = nil
      else
        parent.right = nil
      end
    elsif left && right
      $a=[]
      right.in
      root.key = $key = $a[0].key
      delete $a[0]
    elsif left
      if parent
        $key == pleft.key ? parent.left = left : parent.right = left
      else
        $root = left
      end
      left.parent = parent
    else
      if parent
        $key == parent.right.key ? parent.left = right : parent.right = right
      else
        $root = right
      end
      right.parent = parent
    end
  elsif $key < root.key
    delete left
  else
    delete right
  end
end
gets.to_i.times {
    command, $key = gets.split
    $key=$key.to_i
    case command
    when 'insert'
      insert
    when 'find'
      find $root
    when 'delete'
      delete $root
    else
      $root.inorder
      puts
      $root.preorder
      puts
    end
}