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 Python3 (judge verdict: Accepted)

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

class BST:
  root = None
  def insert(self, key):
    x = self.root
    y = None
    z = Node(key)
    while x != None:
      y = x
      if(z.key < y.key):
        x = x.left
      elif(y.key < z.key):
        x = x.right
    
    if y is None:
      # 初回
      self.root = z
    else:
      if z.key < y.key:
        y.left = z
      elif y.key < z.key:
        y.right = z
        
  def preorder(self, par):
    if par is not None:
      print(" {}".format(par.key), end="")
      self.preorder(par.left)
      self.preorder(par.right)
  
  def inorder(self, par):
    if par is not None:
      self.inorder(par.left)
      print(" {}".format(par.key), end="")
      self.inorder(par.right)
      
  def find(self, key):
    x = self.root
    y = None
    z = Node(key)
    flag = False
    while x != None: 
      y = x
      if(z.key < y.key):
        x = x.left
      elif(y.key < z.key):
        x = x.right
      else:
        flag = True
        break
    return flag
    
  
n = int(input())
bst = BST()
for _ in range(n):
  query = input().split()
  if query[0] == "insert":
    bst.insert(int(query[1]))
  elif query[0] == "find":
    print("yes" if bst.find(int(query[1])) else "no")
  elif query[0] == "print":
    # 中間巡回順, 先行巡回順
    root = bst.root
    bst.inorder(root)
    print()
    bst.preorder(root)
    print()