


'''simple docstring'''



from __future__ import annotations

import unittest
from collections.abc import Iterator





class 							__UpperCamelCase       :




	def __init__(     self		,       __a		,       __a							):

						'''simple docstring'''





						__a    : int      					=						label
						__a    : Optional[Any]      					=						parent
						__a    : Union[str, Any]      					=						None
						__a    : Tuple      					=						None





class 							__UpperCamelCase       :




	def __init__(     self							):

						'''simple docstring'''





						__a    : Dict      					=						None




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : List[Any]      					=						None




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						return self.root is None




	def    __UpperCAmelCase							(     self		,       __a							):

						'''simple docstring'''





						__a    : Optional[Any]      					=						self._put(self.root		,       a_							)




	def    __UpperCAmelCase							(     self		,       __a		,       __a		,       __a = None							):

						'''simple docstring'''





						if node is None:
											__a    : Optional[int]      					=						Node(a_		,       a_							)
						else:
											if label < node.label:
																__a    : List[Any]      					=						self._put(node.left		,       a_		,       a_							)
											elif label > node.label:
																__a    : Union[str, Any]      					=						self._put(node.right		,       a_		,       a_							)
											else:
																__a    : List[str]      					=						f"""Node with label {label} already exists"""
																raise Exception(a_							)

						return node




	def    __UpperCAmelCase							(     self		,       __a							):

						'''simple docstring'''





						return self._search(self.root		,       a_							)




	def    __UpperCAmelCase							(     self		,       __a		,       __a							):

						'''simple docstring'''





						if node is None:
											__a    : Optional[Any]      					=						f"""Node with label {label} does not exist"""
											raise Exception(a_							)
						else:
											if label < node.label:
																__a    : Optional[Any]      					=						self._search(node.left		,       a_							)
											elif label > node.label:
																__a    : str      					=						self._search(node.right		,       a_							)

						return node




	def    __UpperCAmelCase							(     self		,       __a							):

						'''simple docstring'''





						__a    : str      					=						self.search(a_							)
						if node.right and node.left:
											__a    : int      					=						self._get_lowest_node(node.right							)
											__a    : List[str]      					=						node.left
											__a    : Optional[int]      					=						node.right
											__a    : Union[str, Any]      					=						lowest_node
											if node.right:
																__a    : Optional[int]      					=						lowest_node
											self._reassign_nodes(a_		,       a_							)
						elif not node.right and node.left:
											self._reassign_nodes(a_		,       node.left							)
						elif node.right and not node.left:
											self._reassign_nodes(a_		,       node.right							)
						else:
											self._reassign_nodes(a_		,       a_							)




	def    __UpperCAmelCase							(     self		,       __a		,       __a							):

						'''simple docstring'''





						if new_children:
											__a    : Any      					=						node.parent

						if node.parent:
											if node.parent.right == node:
																__a    : List[str]      					=						new_children
											else:
																__a    : int      					=						new_children
						else:
											__a    : int      					=						new_children




	def    __UpperCAmelCase							(     self		,       __a							):

						'''simple docstring'''





						if node.left:
											__a    : Dict      					=						self._get_lowest_node(node.left							)
						else:
											__a    : int      					=						node
											self._reassign_nodes(a_		,       node.right							)

						return lowest_node




	def    __UpperCAmelCase							(     self		,       __a							):

						'''simple docstring'''





						try:
											self.search(a_							)
											return True
						except Exception:
											return False




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						if self.root is None:
											raise Exception('Binary search tree is empty'							)

						__a    : Optional[int]      					=						self.root
						while node.right is not None:
											__a    : Tuple      					=						node.right

						return node.label




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						if self.root is None:
											raise Exception('Binary search tree is empty'							)

						__a    : Optional[Any]      					=						self.root
						while node.left is not None:
											__a    : int      					=						node.left

						return node.label




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						return self._inorder_traversal(self.root							)




	def    __UpperCAmelCase							(     self		,       __a							):

						'''simple docstring'''





						if node is not None:
											yield from self._inorder_traversal(node.left							)
											yield node
											yield from self._inorder_traversal(node.right							)




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						return self._preorder_traversal(self.root							)





	def    __UpperCAmelCase							(     self		,       __a							):

						'''simple docstring'''





						if node is not None:
											yield node
											yield from self._preorder_traversal(node.left							)
											yield from self._preorder_traversal(node.right							)





class 							__UpperCamelCase       (	unittest.TestCase      ):




	@staticmethod
	def    __UpperCAmelCase							(     ):

						'''simple docstring'''





						__a    : str      					=						BinarySearchTree()
						t.put(8							)
						t.put(3							)
						t.put(6							)
						t.put(1							)
						t.put(10							)
						t.put(14							)
						t.put(13							)
						t.put(4							)
						t.put(7							)
						t.put(5							)

						return t




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : List[Any]      					=						BinarySearchTree()
						assert t.is_empty()

						t.put(8							)
						assert t.root is not None
						assert t.root.parent is None
						assert t.root.label == 8

						t.put(10							)
						assert t.root.right is not None
						assert t.root.right.parent == t.root
						assert t.root.right.label == 10

						t.put(3							)
						assert t.root.left is not None
						assert t.root.left.parent == t.root
						assert t.root.left.label == 3

						t.put(6							)
						assert t.root.left.right is not None
						assert t.root.left.right.parent == t.root.left
						assert t.root.left.right.label == 6

						t.put(1							)
						assert t.root.left.left is not None
						assert t.root.left.left.parent == t.root.left
						assert t.root.left.left.label == 1

						with self.assertRaises(a_							):  # noqa: B017
											t.put(1							)




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : Any      					=						self._get_binary_search_tree()

						__a    : Dict      					=						t.search(6							)
						assert node.label == 6

						__a    : str      					=						t.search(13							)
						assert node.label == 13

						with self.assertRaises(a_							):  # noqa: B017
											t.search(2							)




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : Union[str, Any]      					=						self._get_binary_search_tree()

						t.remove(13							)
						assert t.root is not None
						assert t.root.right is not None
						assert t.root.right.right is not None
						assert t.root.right.right.right is None
						assert t.root.right.right.left is None

						t.remove(7							)
						assert t.root.left is not None
						assert t.root.left.right is not None
						assert t.root.left.right.left is not None
						assert t.root.left.right.right is None
						assert t.root.left.right.left.label == 4

						t.remove(6							)
						assert t.root.left.left is not None
						assert t.root.left.right.right is not None
						assert t.root.left.left.label == 1
						assert t.root.left.right.label == 4
						assert t.root.left.right.right.label == 5
						assert t.root.left.right.left is None
						assert t.root.left.left.parent == t.root.left
						assert t.root.left.right.parent == t.root.left

						t.remove(3							)
						assert t.root is not None
						assert t.root.left.label == 4
						assert t.root.left.right.label == 5
						assert t.root.left.left.label == 1
						assert t.root.left.parent == t.root
						assert t.root.left.left.parent == t.root.left
						assert t.root.left.right.parent == t.root.left

						t.remove(4							)
						assert t.root.left is not None
						assert t.root.left.left is not None
						assert t.root.left.label == 5
						assert t.root.left.right is None
						assert t.root.left.left.label == 1
						assert t.root.left.parent == t.root
						assert t.root.left.left.parent == t.root.left




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : List[str]      					=						self._get_binary_search_tree()

						t.remove(3							)
						assert t.root is not None
						assert t.root.left is not None
						assert t.root.left.left is not None
						assert t.root.left.right is not None
						assert t.root.left.right.left is not None
						assert t.root.left.right.right is not None
						assert t.root.left.label == 4
						assert t.root.left.right.label == 6
						assert t.root.left.left.label == 1
						assert t.root.left.right.right.label == 7
						assert t.root.left.right.left.label == 5
						assert t.root.left.parent == t.root
						assert t.root.left.right.parent == t.root.left
						assert t.root.left.left.parent == t.root.left
						assert t.root.left.right.left.parent == t.root.left.right




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : str      					=						self._get_binary_search_tree()
						t.empty()
						assert t.root is None




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : List[str]      					=						self._get_binary_search_tree()
						assert not t.is_empty()

						t.empty()
						assert t.is_empty()




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : Dict      					=						self._get_binary_search_tree()

						assert t.exists(6							)
						assert not t.exists(-1							)




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : int      					=						self._get_binary_search_tree()

						assert t.get_max_label() == 14

						t.empty()
						with self.assertRaises(a_							):  # noqa: B017
											t.get_max_label()




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : Optional[int]      					=						self._get_binary_search_tree()

						assert t.get_min_label() == 1

						t.empty()
						with self.assertRaises(a_							):  # noqa: B017
											t.get_min_label()




	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : Dict      					=						self._get_binary_search_tree()

						__a    : Any      					=						[i.label for i in t.inorder_traversal()]
						assert inorder_traversal_nodes == [1, 3, 4, 5, 6, 7, 8, 10, 13, 14]





	def    __UpperCAmelCase							(     self							):

						'''simple docstring'''





						__a    : Optional[int]      					=						self._get_binary_search_tree()

						__a    : List[str]      					=						[i.label for i in t.preorder_traversal()]
						assert preorder_traversal_nodes == [8, 3, 1, 6, 4, 5, 7, 10, 14, 13]






def 						lowerCamelCase							():
					__a    : Any      					=						BinarySearchTree()
					t.put(8     )
					t.put(3     )
					t.put(6     )
					t.put(1     )
					t.put(10     )
					t.put(14     )
					t.put(13     )
					t.put(4     )
					t.put(7     )
					t.put(5     )

					print(
					    '\n            8\n           / \\\n          3   10\n         / \\    \\\n        1   6    14\n           / \\   /\n          4   7 13\n           \\\n            5\n        '     )

					print('Label 6 exists:'		,   t.exists(6     )     )
					print('Label 13 exists:'		,   t.exists(13     )     )
					print('Label -1 exists:'		,   t.exists(-1     )     )
					print('Label 12 exists:'		,   t.exists(12     )     )

					# Prints all the elements of the list in inorder traversal
					__a    : Union[str, Any]      					=						[i.label for i in t.inorder_traversal()]
					print('Inorder traversal:'		,   UpperCamelCase__     )

					# Prints all the elements of the list in preorder traversal
					__a    : Dict      					=						[i.label for i in t.preorder_traversal()]
					print('Preorder traversal:'		,   UpperCamelCase__     )

					print('Max. label:'		,   t.get_max_label()     )
					print('Min. label:'		,   t.get_min_label()     )

					# Delete elements
					print('\nDeleting elements 13, 10, 8, 3, 6, 14'     )
					print(
					    '\n          4\n         / \\\n        1   7\n             \\\n              5\n        '     )
					t.remove(13     )
					t.remove(10     )
					t.remove(8     )
					t.remove(3     )
					t.remove(6     )
					t.remove(14     )

					# Prints all the elements of the list in inorder traversal after delete
					__a    : str      					=						[i.label for i in t.inorder_traversal()]
					print('Inorder traversal after delete:'		,   UpperCamelCase__     )

					# Prints all the elements of the list in preorder traversal after delete
					__a    : Tuple      					=						[i.label for i in t.preorder_traversal()]
					print('Preorder traversal after delete:'		,   UpperCamelCase__     )

					print('Max. label:'		,   t.get_max_label()     )
					print('Min. label:'		,   t.get_min_label()     )


if __name__ == "__main__":
							binary_search_tree_example()







'''simple docstring'''



import itertools






def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int = 1_000_000     ):
					__a    : str      					=						[1]

					for i in itertools.count(len(_SCREAMING_SNAKE_CASE     )     ):
										__a    : Dict      					=						0
										for j in itertools.count(1     ):
															__a    : int      					=						-1 if j % 2 == 0 else +1
															__a    : Optional[int]      					=						(j * j * 3 - j) // 2
															if index > i:
																				break
															item += partitions[i - index] * sign
															item %= number
															index += j
															if index > i:
																				break
															item += partitions[i - index] * sign
															item %= number

										if item == 0:
															return i
										partitions.append(_SCREAMING_SNAKE_CASE     )

					return 0


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	print(f'''{solution() = }''')



