"""simple docstring"""






class   UpperCAmelCase__				:


	"""simple docstring"""







	def __init__(			self       ,     _SCREAMING_SNAKE_CASE )    ->	Union[str, Any]:
							a_							:			List[str]     		=					val
							# Number of nodes in left subtree
							a_							:			Union[str, Any]     		=					0
							a_							:			Union[str, Any]     		=					None
							a_							:			Tuple     		=					None
							a_							:			Dict     		=					None







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE )    ->	Dict:
							assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

							if self.val < other.val:
													a_							:			str     		=					self.right
													a_							:			int     		=					None
													if self.right:
																			a_							:			Any     		=					other
													a_							:			str     		=					other
													a_							:			str     		=					self.left_tree_size * 2 + 1
													return self
							else:
													a_							:			List[str]     		=					other.right
													a_							:			Optional[Any]     		=					None
													if other.right:
																			a_							:			str     		=					self
													a_							:			Optional[int]     		=					self
													a_							:			List[str]     		=					other.left_tree_size * 2 + 1
													return other




class   UpperCAmelCase__				:


	"""simple docstring"""







	def __init__(			self       ,     _SCREAMING_SNAKE_CASE=None       ,     _SCREAMING_SNAKE_CASE=None       ,     _SCREAMING_SNAKE_CASE=0 )    ->	str:
							a_							:			Any     		=					heap_size
							a_							:			Tuple     		=					bottom_root
							a_							:			str     		=					min_node







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE )    ->	List[Any]:

							# Empty heaps corner cases
							if other.size == 0:
													return None
							if self.size == 0:
													a_							:			Tuple     		=					other.size
													a_							:			Any     		=					other.bottom_root
													a_							:			Optional[Any]     		=					other.min_node
													return None
							# Update size
							a_							:			Optional[int]     		=					self.size + other.size

							# Update min.node
							if self.min_node.val > other.min_node.val:
													a_							:			Dict     		=					other.min_node
							# Merge

							# Order roots by left_subtree_size
							a_							:			Tuple     		=					[]
							a_		,					a_							:			Tuple     		=					self.bottom_root, other.bottom_root
							while i or j:
													if i and ((not j) or i.left_tree_size < j.left_tree_size):
																			combined_roots_list.append((i, True) )
																			a_							:			Optional[int]     		=					i.parent
													else:
																			combined_roots_list.append((j, False) )
																			a_							:			Dict     		=					j.parent
        # Insert links between them
							for i in range(len(_SCREAMING_SNAKE_CASE ) - 1 ):
													if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
																			a_							:			Optional[Any]     		=					combined_roots_list[i + 1][0]
																			a_							:			Any     		=					combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
							a_							:			str     		=					combined_roots_list[0][0]
							while i.parent:
													if (
													    (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
													) or (
													    i.left_tree_size == i.parent.left_tree_size
													    and i.left_tree_size != i.parent.parent.left_tree_size
													):
																			# Neighbouring Nodes
																			a_							:			List[str]     		=					i.left
																			a_							:			Optional[int]     		=					i.parent.parent

																			# Merging trees
																			a_							:			str     		=					i.merge_trees(i.parent )

																			# Updating links
																			a_							:			Union[str, Any]     		=					previous_node
																			a_							:			Union[str, Any]     		=					next_node
																			if previous_node:
																									a_							:			str     		=					i
																			if next_node:
																									a_							:			Tuple     		=					i
													else:
																			a_							:			Union[str, Any]     		=					i.parent
        # Updating self.bottom_root
							while i.left:
													a_							:			Any     		=					i.left
							a_							:			List[Any]     		=					i

							# Update other
							a_							:			Optional[Any]     		=					self.size
							a_							:			List[str]     		=					self.bottom_root
							a_							:			int     		=					self.min_node

							# Return the merged heap
							return self







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE )    ->	Optional[Any]:
							if self.size == 0:
													a_							:			Optional[int]     		=					Node(_SCREAMING_SNAKE_CASE )
													a_							:			Any     		=					1
													a_							:			Dict     		=					self.bottom_root
							else:
													# Create new node
													a_							:			Dict     		=					Node(_SCREAMING_SNAKE_CASE )

													# Update size
													self.size += 1

													# update min_node
													if val < self.min_node.val:
																			a_							:			Optional[int]     		=					new_node
													# Put new_node as a bottom_root in heap
													a_							:			Optional[Any]     		=					new_node
													a_							:			str     		=					self.bottom_root
													a_							:			List[str]     		=					new_node

													# Consecutively merge roots with same left_tree_size
													while (
													    self.bottom_root.parent
													    and self.bottom_root.left_tree_size
													    == self.bottom_root.parent.left_tree_size
													):
																			# Next node
																			a_							:			str     		=					self.bottom_root.parent.parent

																			# Merge
																			a_							:			List[Any]     		=					self.bottom_root.merge_trees(self.bottom_root.parent )

																			# Update Links
																			a_							:			Optional[Any]     		=					next_node
																			a_							:			List[str]     		=					None
																			if next_node:
																									a_							:			Any     		=					self.bottom_root







	def       A    (			self )    ->	List[str]:
							return self.min_node.val







	def       A    (			self )    ->	List[Any]:
							return self.size == 0







	def       A    (			self )    ->	Optional[int]:
							a_							:			Dict     		=					self.min_node.val

							# Last element in heap corner case
							if self.size == 1:
													# Update size
													a_							:			Optional[Any]     		=					0

													# Update bottom root
													a_							:			Tuple     		=					None

													# Update min_node
													a_							:			Tuple     		=					None

													return min_value
							# No right subtree corner case
							# The structure of the tree implies that this should be the bottom root
							# and there is at least one other root
							if self.min_node.right is None:
													# Update size
													self.size -= 1

													# Update bottom root
													a_							:			str     		=					self.bottom_root.parent
													a_							:			List[str]     		=					None

													# Update min_node
													a_							:			Optional[Any]     		=					self.bottom_root
													a_							:			Optional[Any]     		=					self.bottom_root.parent
													while i:
																			if i.val < self.min_node.val:
																									a_							:			List[str]     		=					i
																			a_							:			Dict     		=					i.parent
													return min_value
							# General case
							# Find the BinomialHeap of the right subtree of min_node
							a_							:			Optional[int]     		=					self.min_node.right
							a_							:			Tuple     		=					None
							a_							:			str     		=					bottom_of_new
							a_							:			Optional[int]     		=					1

							# Size, min_node and bottom_root
							while bottom_of_new.left:
													a_							:			Union[str, Any]     		=					size_of_new * 2 + 1
													a_							:			Any     		=					bottom_of_new.left
													if bottom_of_new.val < min_of_new.val:
																			a_							:			str     		=					bottom_of_new
        # Corner case of single root on top left path
							if (not self.min_node.left) and (not self.min_node.parent):
													a_							:			Union[str, Any]     		=					size_of_new
													a_							:			Optional[int]     		=					bottom_of_new
													a_							:			str     		=					min_of_new
													# print("Single root, multiple nodes case")
													return min_value
							# Remaining cases
							# Construct heap of right subtree
							a_							:			List[str]     		=					BinomialHeap(
							    bottom_root=_SCREAMING_SNAKE_CASE       ,     min_node=_SCREAMING_SNAKE_CASE       ,     heap_size=_SCREAMING_SNAKE_CASE )

							# Update size
							a_							:			str     		=					self.size - 1 - size_of_new

							# Neighbour nodes
							a_							:			Dict     		=					self.min_node.left
							a_							:			int     		=					self.min_node.parent

							# Initialize new bottom_root and min_node
							a_							:			List[str]     		=					previous_node or next_node
							a_							:			Tuple     		=					next_node

							# Update links of previous_node and search below for new min_node and
							# bottom_root
							if previous_node:
													a_							:			Union[str, Any]     		=					next_node

													# Update bottom_root and search for min_node below
													a_							:			str     		=					previous_node
													a_							:			Dict     		=					previous_node
													while self.bottom_root.left:
																			a_							:			List[str]     		=					self.bottom_root.left
																			if self.bottom_root.val < self.min_node.val:
																									a_							:			Tuple     		=					self.bottom_root
							if next_node:
													a_							:			List[str]     		=					previous_node

													# Search for new min_node above min_node
													a_							:			str     		=					next_node
													while i:
																			if i.val < self.min_node.val:
																									a_							:			str     		=					i
																			a_							:			Union[str, Any]     		=					i.parent
        # Merge heaps
							self.merge_heaps(_SCREAMING_SNAKE_CASE )

							return min_value







	def       A    (			self )    ->	Union[str, Any]:
							a_							:			Dict     		=					self.bottom_root
							while top_root.parent:
													a_							:			Dict     		=					top_root.parent
							# preorder
							a_							:			Optional[int]     		=					[]
							self.__traversal(_SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE )
							return heap_pre_order







	def       A    (			self       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE       ,     _SCREAMING_SNAKE_CASE=0 )    ->	List[Any]:
							if curr_node:
													preorder.append((curr_node.val, level) )
													self.__traversal(curr_node.left       ,     _SCREAMING_SNAKE_CASE       ,     level + 1 )
													self.__traversal(curr_node.right       ,     _SCREAMING_SNAKE_CASE       ,     level + 1 )
							else:
													preorder.append(("#", level) )







	def __str__(			self )    ->	Optional[Any]:
							if self.is_empty():
													return ""
							a_							:			str     		=					self.pre_order()

							return "\n".join(("-" * level + str(_SCREAMING_SNAKE_CASE )) for value, level in preorder_heap )


# Unit Tests
if __name__ == "__main__":
				import doctest

				doctest.testmod()





"""simple docstring"""






def  lowerCAmelCase_      (_SCREAMING_SNAKE_CASE	:str  )				-> int:
						a_							:			Optional[int]     		=					0
						for letter in data:
												a_							:			Union[str, Any]     		=					(hash_ << 4) + ord(_SCREAMING_SNAKE_CASE  )
												a_							:			Optional[int]     		=					hash_ & 0xf000_0000
												if x != 0:
																		hash_ ^= x >> 24
												hash_ &= ~x
						return hash_


if __name__ == "__main__":
				import doctest

				doctest.testmod()




