


from __future__ import annotations

import queue






class       _UpperCamelCase    :

				"""simple docstring"""







				def __init__(						self				,   a__   )	->				Dict:
					A								=				data
					A								=				None
					A								=				None





def   _lowerCAmelCase				(   ) ->   TreeNode:





	"""simple docstring"""







	print("""\n********Press N to stop entering at any point of time********\n"""						)
	A								=				input("""Enter the value of the root node: """						).strip().lower()
	A								=				queue.Queue()
	A								=				TreeNode(int(UpperCamelCase__						)						)
	q.put(UpperCamelCase__						)
	while not q.empty():
		A								=				q.get()
		A								=				f'Enter the left node of {node_found.data}: '
		A								=				input(UpperCamelCase__						).strip().lower() or """n"""
		if check == "n":
			return tree_node
		A								=				TreeNode(int(UpperCamelCase__						)						)
		A								=				left_node
		q.put(UpperCamelCase__						)
		A								=				f'Enter the right node of {node_found.data}: '
		A								=				input(UpperCamelCase__						).strip().lower() or """n"""
		if check == "n":
			return tree_node
		A								=				TreeNode(int(UpperCamelCase__						)						)
		A								=				right_node
		q.put(UpperCamelCase__						)
	raise





def   _lowerCAmelCase				(   UpperCamelCase__:     Dict						) ->   None:





	"""simple docstring"""







	if not isinstance(UpperCamelCase__							,					UpperCamelCase__						) or not node:
		return
	print(node.data							,					end=""","""						)
	pre_order(node.left						)
	pre_order(node.right						)





def   _lowerCAmelCase				(   UpperCamelCase__:     Optional[int]						) ->   None:





	"""simple docstring"""







	if not isinstance(UpperCamelCase__							,					UpperCamelCase__						) or not node:
		return
	in_order(node.left						)
	print(node.data							,					end=""","""						)
	in_order(node.right						)





def   _lowerCAmelCase				(   UpperCamelCase__:     Union[str, Any]						) ->   None:





	"""simple docstring"""







	if not isinstance(UpperCamelCase__							,					UpperCamelCase__						) or not node:
		return
	post_order(node.left						)
	post_order(node.right						)
	print(node.data							,					end=""","""						)





def   _lowerCAmelCase				(   UpperCamelCase__:     Dict						) ->   None:





	"""simple docstring"""







	if not isinstance(UpperCamelCase__							,					UpperCamelCase__						) or not node:
		return
	A								=				queue.Queue()
	q.put(UpperCamelCase__						)
	while not q.empty():
		A								=				q.get()
		print(node_dequeued.data							,					end=""","""						)
		if node_dequeued.left:
			q.put(node_dequeued.left						)
		if node_dequeued.right:
			q.put(node_dequeued.right						)





def   _lowerCAmelCase				(   UpperCamelCase__:     List[str]						) ->   None:





	"""simple docstring"""







	if not isinstance(UpperCamelCase__							,					UpperCamelCase__						) or not node:
		return
	A								=				queue.Queue()
	q.put(UpperCamelCase__						)
	while not q.empty():
		A								=				[]
		while not q.empty():
			A								=				q.get()
			print(node_dequeued.data							,					end=""","""						)
			if node_dequeued.left:
				list_.append(node_dequeued.left						)
			if node_dequeued.right:
				list_.append(node_dequeued.right						)
		print()
		for node in list_:
			q.put(UpperCamelCase__						)





def   _lowerCAmelCase				(   UpperCamelCase__:     Dict						) ->   None:





	"""simple docstring"""







	if not isinstance(UpperCamelCase__							,					UpperCamelCase__						) or not node:
		return
	A								=				[]
	A								=				node
	while n or stack:
		while n:  # start from root node, find its left child
			print(n.data							,					end=""","""						)
			stack.append(UpperCamelCase__						)
			A								=				n.left
		# end of while means current node doesn't have left child
		A								=				stack.pop()
		# start to traverse its right child
		A								=				n.right





def   _lowerCAmelCase				(   UpperCamelCase__:     List[str]						) ->   None:





	"""simple docstring"""







	if not isinstance(UpperCamelCase__							,					UpperCamelCase__						) or not node:
		return
	A								=				[]
	A								=				node
	while n or stack:
		while n:
			stack.append(UpperCamelCase__						)
			A								=				n.left
		A								=				stack.pop()
		print(n.data							,					end=""","""						)
		A								=				n.right





def   _lowerCAmelCase				(   UpperCamelCase__:     Dict						) ->   None:





	"""simple docstring"""







	if not isinstance(UpperCamelCase__							,					UpperCamelCase__						) or not node:
		return
	A					,			A								=				[], []
	A								=				node
	stacka.append(UpperCamelCase__						)
	while stacka:  # to find the reversed order of post order, store it in stack2
		A								=				stacka.pop()
		if n.left:
			stacka.append(n.left						)
		if n.right:
			stacka.append(n.right						)
		stacka.append(UpperCamelCase__						)
	while stacka:  # pop up from stack2 will be the post order
		print(stacka.pop().data							,					end=""","""						)





def   _lowerCAmelCase				(   UpperCamelCase__:     Union[str, Any] = ""							,					UpperCamelCase__:     Optional[int]=50							,					UpperCamelCase__:     str="*"						) ->   str:





	"""simple docstring"""







	if not s:
		return "\n" + width * char
	A					,			A								=				divmod(width - len(UpperCamelCase__						) - 2							,					2						)
	return f'{left * char} {s} {(left + extra) * char}'


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				print(prompt("Binary Tree Traversals"))

				_lowercase       :      TreeNode	=	build_tree()
				print(prompt("Pre Order Traversal"))
				pre_order(node)
				print(prompt() + "\n")

				print(prompt("In Order Traversal"))
				in_order(node)
				print(prompt() + "\n")

				print(prompt("Post Order Traversal"))
				post_order(node)
				print(prompt() + "\n")

				print(prompt("Level Order Traversal"))
				level_order(node)
				print(prompt() + "\n")

				print(prompt("Actual Level Order Traversal"))
				level_order_actual(node)
				print("*" * 50 + "\n")

				print(prompt("Pre Order Traversal - Iteration Version"))
				pre_order_iter(node)
				print(prompt() + "\n")

				print(prompt("In Order Traversal - Iteration Version"))
				in_order_iter(node)
				print(prompt() + "\n")

				print(prompt("Post Order Traversal - Iteration Version"))
				post_order_iter(node)
				print(prompt())



from __future__ import annotations

from typing import Any






class       _UpperCamelCase    :

				"""simple docstring"""







				def __init__(						self				,   a__				,   a__				,   a__ = 0   )	->				None:
					A					,			A								=				row, column
					A								=				[[default_value for c in range(a__   )] for r in range(a__   )]

				def __str__(						self   )	->				str:
					A								=				f'Matrix consist of {self.row} rows and {self.column} columns\n'

					# Make string identifier
					A								=				0
					for row_vector in self.array:
						for obj in row_vector:
							A								=				max(a__				,   len(str(a__   )   )   )
					A								=				f'%{max_element_length}s'

					# Make string and return
					def single_line(a__   ) -> str:
						nonlocal string_format_identifier
						A								=				"""["""
						line += ", ".join(string_format_identifier % (obj,) for obj in row_vector   )
						line += "]"
						return line

					s += "\n".join(single_line(a__   ) for row_vector in self.array   )
					return s

				def __repr__(						self   )	->				str:
					return str(self   )

				def      _UpperCAmelCase					(						self				,   a__   )	->				bool:
					if not (isinstance(a__				,   (list, tuple)   ) and len(a__   ) == 2):
						return False
					elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
						return False
					else:
						return True

				def __getitem__(						self				,   a__   )	->				Any:
					assert self.validate_indicies(a__   )
					return self.array[loc[0]][loc[1]]

				def __setitem__(						self				,   a__				,   a__   )	->				None:
					assert self.validate_indicies(a__   )
					A								=				value

				def __add__(						self				,   a__   )	->				Matrix:
					assert isinstance(a__				,   a__   )
					assert self.row == another.row and self.column == another.column

					# Add
					A								=				Matrix(self.row				,   self.column   )
					for r in range(self.row   ):
						for c in range(self.column   ):
							A								=				self[r, c] + another[r, c]
					return result

				def __neg__(						self   )	->				Matrix:
					A								=				Matrix(self.row				,   self.column   )
					for r in range(self.row   ):
						for c in range(self.column   ):
							A								=				-self[r, c]
					return result

				def __sub__(						self				,   a__   )	->				Matrix:
					return self + (-another)

				def __mul__(						self				,   a__   )	->				Matrix:

					if isinstance(a__				,   (int, float)   ):  # Scalar multiplication
						A								=				Matrix(self.row				,   self.column   )
						for r in range(self.row   ):
							for c in range(self.column   ):
								A								=				self[r, c] * another
						return result
					elif isinstance(a__				,   a__   ):  # Matrix multiplication
						assert self.column == another.row
						A								=				Matrix(self.row				,   another.column   )
						for r in range(self.row   ):
							for c in range(another.column   ):
								for i in range(self.column   ):
									result[r, c] += self[r, i] * another[i, c]
						return result
					else:
						A								=				f'Unsupported type given for another ({type(a__   )})'
						raise TypeError(a__   )

				def      _UpperCAmelCase					(						self   )	->				Matrix:
					A								=				Matrix(self.column				,   self.row   )
					for r in range(self.row   ):
						for c in range(self.column   ):
							A								=				self[r, c]
					return result

				def      _UpperCAmelCase					(						self				,   a__				,   a__   )	->				Any:
					assert isinstance(a__				,   a__   ) and isinstance(a__				,   a__   )
					assert self.row == self.column == u.row == v.row  # u, v should be column vector
					assert u.column == v.column == 1  # u, v should be column vector

					# Calculate
					A								=				v.transpose()
					A								=				(v_t * self * u)[0, 0] + 1
					if numerator_factor == 0:
						return None  # It's not invertable
					return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":





				def   _lowerCAmelCase				(   ) ->   None:





					"""simple docstring"""







					A								=				Matrix(3							,					3							,					0						)
					for i in range(3						):
						A								=				1
					print(f'a^(-1) is {ainv}'						)
					# u, v
					A								=				Matrix(3							,					1							,					0						)
					A					,			A					,			A								=				1, 2, -3
					A								=				Matrix(3							,					1							,					0						)
					A					,			A					,			A								=				4, -2, 5
					print(f'u is {u}'						)
					print(f'v is {v}'						)
					print(f'uv^T is {u * v.transpose()}'						)
					# Sherman Morrison
					print(f'(a + uv^T)^(-1) is {ainv.sherman_morrison(UpperCamelCase__							,					UpperCamelCase__						)}'						)





				def   _lowerCAmelCase				(   ) ->   None:





					"""simple docstring"""







					import doctest

					doctest.testmod()
				testa()



