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 Python (judge verdict: Wrong Answer)

class Node:
  def __init__(self, label):
    self.label = label
    self.left = None
    self.right = None

class BinaryTree:
  def __init__(self):
    self.root = Node(None)

  def insert_node(self, node, n):
    if node.label == None:
      node.label = n
    elif n < node.label:
      if node.left == None:
        node.left = Node(n)
      else:
        node.left = self.insert_node(node.left, n)
    else:
      if node.right == None:
        node.right = Node(n)
      else:
        node.right = self.insert_node(node.right, n)
    return node

  def node_printer(self, node):
    labels = []
    if node.left != None:
      labels.extend(self.node_printer(node.left))
    labels.append(node.label)
    if node.right != None:
      labels.extend(self.node_printer(node.right))
    return labels

  def node_printer_c(self, node):
    labels = []
    labels.append(node.label)
    if node.left != None:
      labels.extend(self.node_printer_c(node.left))
    if node.right != None:
      labels.extend(self.node_printer_c(node.right))
    return labels

  def find_node(self, node, x):
    if node == None:
      return False
    elif node.label == x:
      return True
    elif x < node.label:
      return self.find_node(node.left, x)
    elif node.label < x:
      return self.find_node(node.right, x)

  def find_minimum_node(self, node):
    if node.label == None:
      return -1
    elif node.left == None:
      return node.label
    else:
      return self.find_minimum_node(node.left)

  def delete_node(self, node, x):
    if node.label == None:
      return node
    elif node.label == x:
     if node.left == None and node.right == None:
       return None
     elif node.left != None and node.right != None:
       minnode = self.find_minimum_node(node.left)
       node.label = minnode
       node.left = self.delete_node(node.left, minnode)
     else:
       if node.left != None:
         return node.left
       else:
         return node.right
    elif x < node.label:
      node.left = self.delete_node(node.left, x)
    else:
      node.right = self.delete_node(node.right, x)
    return node

  # functions
  def insert(self, x):
    return self.insert_node(self.root, x)
  def printer(self):
    return self.node_printer(self.root)
  def printer_c(self):
    return self.node_printer_c(self.root)
  def find(self, x):
    return self.find_node(self.root, x)
  def delete(self, x):
    return self.delete_node(self.root, x)

btree = BinaryTree()
n = int(raw_input())
for _ in xrange(n):
  op = raw_input().split()
  if op[0] == "insert":
    btree.insert(int(op[1]))
  elif op[0] == "print":
    print " "+" ".join(map(str, btree.printer()))
    print " "+" ".join(map(str, btree.printer_c()))
  elif op[0] == "find":
    judge = btree.find(int(op[1]))
    if judge:
      print "yes"
    else:
      print "no"
  elif op[0] == "delete":
    btree.delete(int(op[1]))