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: Accepted)

class BinarySearchTree
	class Node
		attr_accessor :key, :left, :right
		def initialize(key)
			@key = key
		end
	end

	attr_accessor :root

	def insert(key)
		parent  = nil
		current = @root
		while current
			parent = current
			if key < current.key
				current = current.left
			else
				current = current.right
			end
		end

		new_node = Node.new(key)
		if !parent
			@root = new_node
		elsif key < parent.key
			parent.left = new_node
		else
			parent.right = new_node
		end
	end

	def find(key)
		current = @root
		while current
			return true if key == current.key
			if key < current.key
				current = current.left
			else
				current = current.right
			end
		end
		false
	end

	def keys_inorder
		inorder_helper(@root)
	end

	def keys_preorder
		preorder_helper(@root)
	end

	private
	def inorder_helper(node)
		return [] unless node
		result = []
		result.concat(inorder_helper(node.left))
		result << node.key
		result.concat(inorder_helper(node.right))
	end

	def preorder_helper(node)
		return [] unless node
		result = [node.key]
		result.concat(preorder_helper(node.left))
		result.concat(preorder_helper(node.right))
	end

end

tree = BinarySearchTree.new
n = STDIN.gets.to_i
n.times do
	command, param = STDIN.gets.split[0..1]
	if command == "insert"
		tree.insert(param.to_i)
	elsif command == "find"
		puts (tree.find(param.to_i) ? "yes" : "no")
	elsif command == "print"
		puts " #{tree.keys_inorder.join(" ")}"
		puts " #{tree.keys_preorder.join(" ")}"
	else
		raise "Unexpected input #{command}, #{param}"
	end
end