



class 				a_    :

						def __init__(       self      :Any  ,		_lowercase      :Dict)						->   Optional[Any]:
												UpperCAmelCase_					=	val
												# Number of nodes in left subtree
												UpperCAmelCase_					=	0
												UpperCAmelCase_					=	None
												UpperCAmelCase_					=	None
												UpperCAmelCase_					=	None




						def       __a			(       self      :Optional[int]  ,		_lowercase      :Optional[Any])						->   str:
												assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

												if self.val < other.val:
																		UpperCAmelCase_					=	self.right
																		UpperCAmelCase_					=	None
																		if self.right:
																								UpperCAmelCase_					=	other
																		UpperCAmelCase_					=	other
																		UpperCAmelCase_					=	self.left_tree_size * 2 + 1
																		return self
												else:
																		UpperCAmelCase_					=	other.right
																		UpperCAmelCase_					=	None
																		if other.right:
																								UpperCAmelCase_					=	self
																		UpperCAmelCase_					=	self
																		UpperCAmelCase_					=	other.left_tree_size * 2 + 1
																		return other







class 				a_    :

						def __init__(       self      :Dict  ,		_lowercase      :Any=None  ,		_lowercase      :Optional[int]=None  ,		_lowercase      :Optional[int]=0)						->   Optional[Any]:
												UpperCAmelCase_					=	heap_size
												UpperCAmelCase_					=	bottom_root
												UpperCAmelCase_					=	min_node

						def       __a			(       self      :Optional[Any]  ,		_lowercase      :Union[str, Any])						->   Optional[Any]:

												# Empty heaps corner cases
												if other.size == 0:
																		return None
												if self.size == 0:
																		UpperCAmelCase_					=	other.size
																		UpperCAmelCase_					=	other.bottom_root
																		UpperCAmelCase_					=	other.min_node
																		return None
												# Update size
												UpperCAmelCase_					=	self.size + other.size

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

												# Order roots by left_subtree_size
												UpperCAmelCase_					=	[]
												UpperCAmelCase_				, UpperCAmelCase_					=	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))
																								UpperCAmelCase_					=	i.parent
																		else:
																								combined_roots_list.append((j, False))
																								UpperCAmelCase_					=	j.parent
        # Insert links between them
												for i in range(len(_lowercase) - 1):
																		if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
																								UpperCAmelCase_					=	combined_roots_list[i + 1][0]
																								UpperCAmelCase_					=	combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
												UpperCAmelCase_					=	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
																								UpperCAmelCase_					=	i.left
																								UpperCAmelCase_					=	i.parent.parent

																								# Merging trees
																								UpperCAmelCase_					=	i.merge_trees(i.parent)

																								# Updating links
																								UpperCAmelCase_					=	previous_node
																								UpperCAmelCase_					=	next_node
																								if previous_node:
																														UpperCAmelCase_					=	i
																								if next_node:
																														UpperCAmelCase_					=	i
																		else:
																								UpperCAmelCase_					=	i.parent
        # Updating self.bottom_root
												while i.left:
																		UpperCAmelCase_					=	i.left
												UpperCAmelCase_					=	i

												# Update other
												UpperCAmelCase_					=	self.size
												UpperCAmelCase_					=	self.bottom_root
												UpperCAmelCase_					=	self.min_node

												# Return the merged heap
												return self

						def       __a			(       self      :Optional[Any]  ,		_lowercase      :str)						->   Union[str, Any]:
												if self.size == 0:
																		UpperCAmelCase_					=	Node(_lowercase)
																		UpperCAmelCase_					=	1
																		UpperCAmelCase_					=	self.bottom_root
												else:
																		# Create new node
																		UpperCAmelCase_					=	Node(_lowercase)

																		# Update size
																		self.size += 1

																		# update min_node
																		if val < self.min_node.val:
																								UpperCAmelCase_					=	new_node
																		# Put new_node as a bottom_root in heap
																		UpperCAmelCase_					=	new_node
																		UpperCAmelCase_					=	self.bottom_root
																		UpperCAmelCase_					=	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
																								UpperCAmelCase_					=	self.bottom_root.parent.parent

																								# Merge
																								UpperCAmelCase_					=	self.bottom_root.merge_trees(self.bottom_root.parent)

																								# Update Links
																								UpperCAmelCase_					=	next_node
																								UpperCAmelCase_					=	None
																								if next_node:
																														UpperCAmelCase_					=	self.bottom_root

						def       __a			(       self      :Tuple)						->   Tuple:
												return self.min_node.val

						def       __a			(       self      :int)						->   str:
												return self.size == 0

						def       __a			(       self      :str)						->   int:
												UpperCAmelCase_					=	self.min_node.val

												# Last element in heap corner case
												if self.size == 1:
																		# Update size
																		UpperCAmelCase_					=	0

																		# Update bottom root
																		UpperCAmelCase_					=	None

																		# Update min_node
																		UpperCAmelCase_					=	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
																		UpperCAmelCase_					=	self.bottom_root.parent
																		UpperCAmelCase_					=	None

																		# Update min_node
																		UpperCAmelCase_					=	self.bottom_root
																		UpperCAmelCase_					=	self.bottom_root.parent
																		while i:
																								if i.val < self.min_node.val:
																														UpperCAmelCase_					=	i
																								UpperCAmelCase_					=	i.parent
																		return min_value
												# General case
												# Find the BinomialHeap of the right subtree of min_node
												UpperCAmelCase_					=	self.min_node.right
												UpperCAmelCase_					=	None
												UpperCAmelCase_					=	bottom_of_new
												UpperCAmelCase_					=	1

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

												# Update size
												UpperCAmelCase_					=	self.size - 1 - size_of_new

												# Neighbour nodes
												UpperCAmelCase_					=	self.min_node.left
												UpperCAmelCase_					=	self.min_node.parent

												# Initialize new bottom_root and min_node
												UpperCAmelCase_					=	previous_node or next_node
												UpperCAmelCase_					=	next_node

												# Update links of previous_node and search below for new min_node and
												# bottom_root
												if previous_node:
																		UpperCAmelCase_					=	next_node

																		# Update bottom_root and search for min_node below
																		UpperCAmelCase_					=	previous_node
																		UpperCAmelCase_					=	previous_node
																		while self.bottom_root.left:
																								UpperCAmelCase_					=	self.bottom_root.left
																								if self.bottom_root.val < self.min_node.val:
																														UpperCAmelCase_					=	self.bottom_root
												if next_node:
																		UpperCAmelCase_					=	previous_node

																		# Search for new min_node above min_node
																		UpperCAmelCase_					=	next_node
																		while i:
																								if i.val < self.min_node.val:
																														UpperCAmelCase_					=	i
																								UpperCAmelCase_					=	i.parent
        # Merge heaps
												self.merge_heaps(_lowercase)

												return min_value

						def       __a			(       self      :Dict)						->   Union[str, Any]:
												UpperCAmelCase_					=	self.bottom_root
												while top_root.parent:
																		UpperCAmelCase_					=	top_root.parent
												# preorder
												UpperCAmelCase_					=	[]
												self.__traversal(_lowercase  ,		_lowercase)
												return heap_pre_order

						def       __a			(       self      :int  ,		_lowercase      :int  ,		_lowercase      :int  ,		_lowercase      :int=0)						->   Union[str, Any]:
												if curr_node:
																		preorder.append((curr_node.val, level))
																		self.__traversal(curr_node.left  ,		_lowercase  ,		level + 1)
																		self.__traversal(curr_node.right  ,		_lowercase  ,		level + 1)
												else:
																		preorder.append(('''#''', level))




						def __str__(       self      :int)						->   Dict:
												if self.is_empty():
																		return ""
												UpperCAmelCase_					=	self.pre_order()

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


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

							doctest.testmod()










import math







def 							A     (						__UpperCAmelCase      )			->			str:



						'''simple docstring'''






						if number == 0:
												UpperCAmelCase_					=	'''Zero'''
												return words
						else:
												UpperCAmelCase_					=	math.logaa(__UpperCAmelCase      )
												UpperCAmelCase_					=	digits + 1
												UpperCAmelCase_					=	{}
												UpperCAmelCase_					=	''''''
												UpperCAmelCase_					=	'''One'''
												UpperCAmelCase_					=	'''Two'''
												UpperCAmelCase_					=	'''Three'''
												UpperCAmelCase_					=	'''Four'''
												UpperCAmelCase_					=	'''Five'''
												UpperCAmelCase_					=	'''Six'''
												UpperCAmelCase_					=	'''Seven'''
												UpperCAmelCase_					=	'''Eight'''
												UpperCAmelCase_					=	'''Nine'''

												UpperCAmelCase_					=	{}
												UpperCAmelCase_					=	''''''
												UpperCAmelCase_					=	'''Twenty'''
												UpperCAmelCase_					=	'''Thirty'''
												UpperCAmelCase_					=	'''Forty'''
												UpperCAmelCase_					=	'''Fifty'''
												UpperCAmelCase_					=	'''Sixty'''
												UpperCAmelCase_					=	'''Seventy'''
												UpperCAmelCase_					=	'''Eighty'''
												UpperCAmelCase_					=	'''Ninety'''

												UpperCAmelCase_					=	{}
												UpperCAmelCase_					=	'''Ten'''
												UpperCAmelCase_					=	'''Eleven'''
												UpperCAmelCase_					=	'''Twelve'''
												UpperCAmelCase_					=	'''Thirteen'''
												UpperCAmelCase_					=	'''Fourteen'''
												UpperCAmelCase_					=	'''Fifteen'''
												UpperCAmelCase_					=	'''Sixteen'''
												UpperCAmelCase_					=	'''Seventeen'''
												UpperCAmelCase_					=	'''Eighteen'''
												UpperCAmelCase_					=	'''Nineteen'''

												UpperCAmelCase_					=	{}
												UpperCAmelCase_					=	'''Hundred,'''
												UpperCAmelCase_					=	'''Thousand,'''
												UpperCAmelCase_					=	'''Lakh,'''
												UpperCAmelCase_					=	'''Crore,'''

												UpperCAmelCase_					=	number
												UpperCAmelCase_					=	''''''
												UpperCAmelCase_					=	0
												UpperCAmelCase_					=	int(__UpperCAmelCase      )
												while counter < digits:
																		UpperCAmelCase_					=	temp_num % 10
																		if counter % 2 == 0:
																								UpperCAmelCase_					=	''''''
																								if counter in placevalue and current != 0:
																														UpperCAmelCase_					=	placevalue[counter]
																								if counter == 2:
																														UpperCAmelCase_					=	singles[current] + addition + words
																								elif counter == 0:
																														if ((temp_num % 100) // 10) == 1:
																																				UpperCAmelCase_					=	teens[current] + addition + words
																																				UpperCAmelCase_					=	temp_num // 10
																																				counter += 1
																														else:
																																				UpperCAmelCase_					=	singles[current] + addition + words

																								else:
																														UpperCAmelCase_					=	doubles[current] + addition + words

																		else:
																								if counter == 1:
																														if current == 1:
																																				UpperCAmelCase_					=	teens[number % 10] + words
																														else:
																																				UpperCAmelCase_					=	''''''
																																				if counter in placevalue:
																																										UpperCAmelCase_					=	placevalue[counter]
																																				UpperCAmelCase_					=	doubles[current] + addition + words
																								else:
																														UpperCAmelCase_					=	''''''
																														if counter in placevalue:
																																				if current == 0 and ((temp_num % 100) // 10) == 0:
																																										UpperCAmelCase_					=	''''''
																																				else:
																																										UpperCAmelCase_					=	placevalue[counter]
																														if ((temp_num % 100) // 10) == 1:
																																				UpperCAmelCase_					=	teens[current] + addition + words
																																				UpperCAmelCase_					=	temp_num // 10
																																				counter += 1
																														else:
																																				UpperCAmelCase_					=	singles[current] + addition + words
																		counter += 1
																		UpperCAmelCase_					=	temp_num // 10
						return words


if __name__ == "__main__":
							import doctest

							doctest.testmod()





