"""simple docstring"""





from collections.abc import Iterable
from typing import Any
class  _snake_case     :






						def __init__(       self      :			Optional[Any]							,					UpperCAmelCase      :			int | None = None    ):
													__lowerCamelCase					:		str		   =     value
													__lowerCamelCase					:		Node | None		   =     None  # Added in order to delete a node easier
													__lowerCamelCase					:		Node | None		   =     None
													__lowerCamelCase					:		Node | None		   =     None







						def __repr__(       self      :			str    ):
													from pprint import pformat

													if self.left is None and self.right is None:
																				return str(self.value    )
													return pformat({F"""{self.value}""": (self.left, self.right)}							,					indent=1    )

class  _snake_case     :






						def __init__(       self      :			str							,					UpperCAmelCase      :			Node | None = None    ):
													__lowerCamelCase					:		int		   =     root






						def __str__(       self      :			Optional[int]    ):
													return str(self.root    )






						def       lowerCamelCase__     (       self      :			List[str]							,					UpperCAmelCase      :			Node							,					UpperCAmelCase      :			Node | None    ):
													if new_children is not None:  # reset its kids
																				__lowerCamelCase					:		int		   =     node.parent
													if node.parent is not None:  # reset its parent
																				if self.is_right(UpperCAmelCase    ):  # If it is the right children
																											__lowerCamelCase					:		Optional[Any]		   =     new_children
																				else:
																											__lowerCamelCase					:		Any		   =     new_children
													else:
																				__lowerCamelCase					:		Dict		   =     new_children






						def       lowerCamelCase__     (       self      :			List[str]							,					UpperCAmelCase      :			Node    ):
													if node.parent and node.parent.right:
																				return node == node.parent.right
													return False






						def       lowerCamelCase__     (       self      :			List[Any]    ):
													return self.root is None






						def       lowerCamelCase__     (       self      :			Union[str, Any]							,					UpperCAmelCase      :			Tuple    ):
													__lowerCamelCase					:		List[Any]		   =     Node(UpperCAmelCase    )  # create a new Node
													if self.empty():  # if Tree is empty
																				__lowerCamelCase					:		Tuple		   =     new_node  # set its root
													else:  # Tree is not empty
																				__lowerCamelCase					:		int		   =     self.root  # from root
																				if parent_node is None:
																											return
																				while True:  # While we don't get to a leaf
																											if value < parent_node.value:  # We go left
																																		if parent_node.left is None:
																																									__lowerCamelCase					:		Dict		   =     new_node  # We insert the new node in a leaf
																																									break
																																		else:
																																									__lowerCamelCase					:		Tuple		   =     parent_node.left
																											else:
																																		if parent_node.right is None:
																																									__lowerCamelCase					:		List[str]		   =     new_node
																																									break
																																		else:
																																									__lowerCamelCase					:		Optional[int]		   =     parent_node.right
																				__lowerCamelCase					:		str		   =     parent_node






						def       lowerCamelCase__     (       self      :			Tuple							,					*UpperCAmelCase      :			Optional[int]    ):
													for value in values:
																				self.__insert(UpperCAmelCase    )






						def       lowerCamelCase__     (       self      :			str							,					UpperCAmelCase      :			Union[str, Any]    ):
													if self.empty():
																				raise IndexError("Warning: Tree is empty! please use another."    )
													else:
																				__lowerCamelCase					:		List[str]		   =     self.root
																				# use lazy evaluation here to avoid NoneType Attribute error
																				while node is not None and node.value is not value:
																											__lowerCamelCase					:		Union[str, Any]		   =     node.left if value < node.value else node.right
																				return node






						def       lowerCamelCase__     (       self      :			str							,					UpperCAmelCase      :			Node | None = None    ):
													if node is None:
																				if self.root is None:
																											return None
																				__lowerCamelCase					:		Any		   =     self.root

													if not self.empty():
																				while node.right is not None:
																											__lowerCamelCase					:		Optional[Any]		   =     node.right
													return node






						def       lowerCamelCase__     (       self      :			Optional[int]							,					UpperCAmelCase      :			Node | None = None    ):
													if node is None:
																				__lowerCamelCase					:		Optional[int]		   =     self.root
													if self.root is None:
																				return None
													if not self.empty():
																				__lowerCamelCase					:		str		   =     self.root
																				while node.left is not None:
																											__lowerCamelCase					:		str		   =     node.left
													return node






						def       lowerCamelCase__     (       self      :			str							,					UpperCAmelCase      :			int    ):
													__lowerCamelCase					:		Tuple		   =     self.search(UpperCAmelCase    )  # Look for the node with that label
													if node is not None:
																				if node.left is None and node.right is None:  # If it has no children
																											self.__reassign_nodes(UpperCAmelCase							,					UpperCAmelCase    )
																				elif node.left is None:  # Has only right children
																											self.__reassign_nodes(UpperCAmelCase							,					node.right    )
																				elif node.right is None:  # Has only left children
																											self.__reassign_nodes(UpperCAmelCase							,					node.left    )
																				else:
																											__lowerCamelCase					:		List[str]		   =     self.get_max(
																											    node.left    )  # Gets the max value of the left branch
																											self.remove(tmp_node.value    )  # type: ignore
																											__lowerCamelCase					:		Tuple		   =     (
																											    tmp_node.value  # type: ignore
																											)  # Assigns the value to the node to delete and keep tree structure






						def       lowerCamelCase__     (       self      :			int							,					UpperCAmelCase      :			Node | None    ):
													if node is not None:
																				yield node  # Preorder Traversal
																				yield from self.preorder_traverse(node.left    )
																				yield from self.preorder_traverse(node.right    )






						def       lowerCamelCase__     (       self      :			Union[str, Any]							,					UpperCAmelCase      :			Any=None    ):
													if traversal_function is None:
																				return self.preorder_traverse(self.root    )
													else:
																				return traversal_function(self.root    )






						def       lowerCamelCase__     (       self      :			Any							,					UpperCAmelCase      :			list							,					UpperCAmelCase      :			Node | None    ):
													if node:
																				self.inorder(UpperCAmelCase							,					node.left    )
																				arr.append(node.value    )
																				self.inorder(UpperCAmelCase							,					node.right    )







						def       lowerCamelCase__     (       self      :			Optional[int]							,					UpperCAmelCase      :			int							,					UpperCAmelCase      :			Node    ):
													__lowerCamelCase					:		list[int]		   =     []
													self.inorder(UpperCAmelCase							,					UpperCAmelCase    )  # append all values to list using inorder traversal
													return arr[k - 1]


def    lowercase_   (   _lowerCamelCase:	Node | None      ) ->      list[Node]:



							'''simple docstring'''

							__lowerCamelCase					:		Dict		   =     []
							if curr_node is not None:
														__lowerCamelCase					:		Optional[Any]		   =     postorder(curr_node.left      ) + postorder(curr_node.right      ) + [curr_node]
							return node_list


def    lowercase_   (   ) ->      None:



							'''simple docstring'''

							__lowerCamelCase					:		List[str]		   =     (8, 3, 6, 1, 10, 14, 13, 4, 7)
							__lowerCamelCase					:		Optional[Any]		   =     BinarySearchTree()
							for i in testlist:
														t.insert(_lowerCamelCase      )

							# Prints all the elements of the list in order traversal
							print(_lowerCamelCase      )

							if t.search(6      ) is not None:
														print("The value 6 exists"      )
							else:
														print("The value 6 doesn't exist"      )

							if t.search(-1      ) is not None:
														print("The value -1 exists"      )
							else:
														print("The value -1 doesn't exist"      )

							if not t.empty():
														print("Max Value: "						,   t.get_max().value      )  # type: ignore
														print("Min Value: "						,   t.get_min().value      )  # type: ignore

							for i in testlist:
														t.remove(_lowerCamelCase      )
														print(_lowerCamelCase      )


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)
"""simple docstring"""





import gc
import threading
import time

import psutil
import torch
class  _snake_case     :






						def __init__(       self      :			str    ):
													__lowerCamelCase					:		Optional[Any]		   =     psutil.Process()
													__lowerCamelCase					:		List[Any]		   =     False






						def       lowerCamelCase__     (       self      :			str    ):
													__lowerCamelCase					:		List[Any]		   =     -1

													while True:
																				__lowerCamelCase					:		Union[str, Any]		   =     max(self.process.memory_info().rss							,					self.cpu_memory_peak    )

																				# can't sleep or will not catch the peak right (this comment is here on purpose)
																				if not self.peak_monitoring:
																											break






						def       lowerCamelCase__     (       self      :			Any    ):
													__lowerCamelCase					:		Optional[Any]		   =     True
													__lowerCamelCase					:		Union[str, Any]		   =     threading.Thread(target=self.peak_monitor    )
													__lowerCamelCase					:		Optional[Any]		   =     True
													self.thread.start()







						def       lowerCamelCase__     (       self      :			Dict    ):
													__lowerCamelCase					:		str		   =     False
													self.thread.join()
													return self.cpu_memory_peak

__A  =				PeakCPUMemory()


def    lowercase_   (   ) ->      Union[str, Any]:



							'''simple docstring'''

							__lowerCamelCase					:		Any		   =     {"time": time.time()}

							gc.collect()
							torch.cuda.empty_cache()

							# CPU mem
							__lowerCamelCase					:		Optional[int]		   =     psutil.Process().memory_info().rss
							cpu_peak_tracker.start()

							# GPU mem
							for i in range(torch.cuda.device_count()      ):
														__lowerCamelCase					:		int		   =     torch.cuda.memory_allocated(_lowerCamelCase      )
							torch.cuda.reset_peak_memory_stats()

							return measures


def    lowercase_   (   _lowerCamelCase:	Optional[Any]      ) ->      Tuple:



							'''simple docstring'''

							__lowerCamelCase					:		Tuple		   =     {"time": time.time() - start_measures["time"]}

							gc.collect()
							torch.cuda.empty_cache()

							# CPU mem
							__lowerCamelCase					:		Dict		   =     (psutil.Process().memory_info().rss - start_measures["cpu"]) / 2**20
							__lowerCamelCase					:		Tuple		   =     (cpu_peak_tracker.stop() - start_measures["cpu"]) / 2**20

							# GPU mem
							for i in range(torch.cuda.device_count()      ):
														__lowerCamelCase					:		Any		   =     (torch.cuda.memory_allocated(_lowerCamelCase      ) - start_measures[str(_lowerCamelCase      )]) / 2**20
														__lowerCamelCase					:		Optional[int]		   =     (torch.cuda.max_memory_allocated(_lowerCamelCase      ) - start_measures[str(_lowerCamelCase      )]) / 2**20

							return measures







def    lowercase_   (   _lowerCamelCase:	int						,   _lowerCamelCase:	List[Any]      ) ->      Optional[int]:



							'''simple docstring'''

							print(F"""{description}:"""      )
							print(F"""- Time: {measures["time"]:.2f}s"""      )
							for i in range(torch.cuda.device_count()      ):
														print(F"""- GPU {i} allocated: {measures[str(_lowerCamelCase      )]:.2f}MiB"""      )
														__lowerCamelCase					:		List[Any]		   =     measures[F"""{i}-peak"""]
														print(F"""- GPU {i} peak: {peak:.2f}MiB"""      )
							print(F"""- CPU RAM allocated: {measures["cpu"]:.2f}MiB"""      )
							print(F"""- CPU RAM peak: {measures["cpu-peak"]:.2f}MiB"""      )