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.left = self.right = self.parent = None

class BST:
	def __init__(self):
		self.root = None
	
	def insert(self, key):
		parent = None
		current = self.root
		while current != None:
			parent = current
			if key < current.key:
				current = current.left
			else:
				current = current.right
		new = Node(key)
		new.parent = parent
		if parent == None:
			self.root = new
		elif key < parent.key:
			parent.left = new
		else:
			parent.right = new		
	
	def find(self, key):
		current = self.root
		while current != None:
			if key == current.key:
				return current
			if key < current.key:
				current = current.left
			else:
				current = current.right
		return None
		
	def delete(self, key):
		return
	
	def print(self):
		self.print_in_order(self.root)
		print()
		self.print_pre_order(self.root)
		print()
		
	def print_in_order(self, node):
		if node != None:
			self.print_in_order(node.left)
			print(' ' + str(node.key), end='')
			self.print_in_order(node.right)
		
	def print_pre_order(self, node):
		if node != None:
			print(' ' + str(node.key), end='')
			self.print_pre_order(node.left)
			self.print_pre_order(node.right)		

n = int(input())
bst = BST()
for i in range(n):
	cmd = list(map(str, input().split()))
	if cmd[0] == 'print':
		bst.print()
	else:
		key = int(cmd[1])
		if cmd[0] == 'insert':
			bst.insert(key)
		elif cmd[0] == 'find':
			if bst.find(key) != None:
				print('yes')
			else:
				print('no')
		else:
			bst.delete(key)