




'''simple docstring'''






class  A		:




				'''simple docstring'''





				def __init__(self			,  _UpperCAmelCase      )     ->	Optional[int]:
							__UpperCamelCase				:      Tuple									=       val
							# Number of nodes in left subtree
							__UpperCamelCase				:      List[str]									=       0
							__UpperCamelCase				:      Optional[Any]									=       None
							__UpperCamelCase				:      List[str]									=       None
							__UpperCamelCase				:      Optional[Any]									=       None





				def 	a_	(self			,  _UpperCAmelCase      )     ->	Union[str, Any]:
							assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

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







class  A		:




				'''simple docstring'''





				def __init__(self			,  _UpperCAmelCase=None			,  _UpperCAmelCase=None			,  _UpperCAmelCase=0      )     ->	List[str]:
							__UpperCamelCase				:      Dict									=       heap_size
							__UpperCamelCase				:      str									=       bottom_root
							__UpperCamelCase				:      str									=       min_node
				def 	a_	(self			,  _UpperCAmelCase      )     ->	List[str]:

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

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

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

													# Merging trees
													__UpperCamelCase				:      Optional[int]									=       i.merge_trees(i.parent      )

													# Updating links
													__UpperCamelCase				:      Any									=       previous_node
													__UpperCamelCase				:      List[Any]									=       next_node
													if previous_node:
																__UpperCamelCase				:      List[str]									=       i
													if next_node:
																__UpperCamelCase				:      Dict									=       i
										else:
													__UpperCamelCase				:      List[str]									=       i.parent
        # Updating self.bottom_root
							while i.left:
										__UpperCamelCase				:      Optional[Any]									=       i.left
							__UpperCamelCase				:      List[str]									=       i

							# Update other
							__UpperCamelCase				:      Tuple									=       self.size
							__UpperCamelCase				:      Tuple									=       self.bottom_root
							__UpperCamelCase				:      str									=       self.min_node

							# Return the merged heap
							return self
				def 	a_	(self			,  _UpperCAmelCase      )     ->	str:
							if self.size == 0:
										__UpperCamelCase				:      int									=       Node(_UpperCAmelCase      )
										__UpperCamelCase				:      List[str]									=       1
										__UpperCamelCase				:      Any									=       self.bottom_root
							else:
										# Create new node
										__UpperCamelCase				:      List[str]									=       Node(_UpperCAmelCase      )

										# Update size
										self.size += 1

										# update min_node
										if val < self.min_node.val:
													__UpperCamelCase				:      Optional[Any]									=       new_node
										# Put new_node as a bottom_root in heap
										__UpperCamelCase				:      Optional[Any]									=       new_node
										__UpperCamelCase				:      Dict									=       self.bottom_root
										__UpperCamelCase				:      Dict									=       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				:      Optional[int]									=       self.bottom_root.parent.parent

													# Merge
													__UpperCamelCase				:      Tuple									=       self.bottom_root.merge_trees(self.bottom_root.parent      )

													# Update Links
													__UpperCamelCase				:      str									=       next_node
													__UpperCamelCase				:      str									=       None
													if next_node:
																__UpperCamelCase				:      str									=       self.bottom_root
				def 	a_	(self      )     ->	Any:
							return self.min_node.val
				def 	a_	(self      )     ->	Dict:
							return self.size == 0
				def 	a_	(self      )     ->	str:
							__UpperCamelCase				:      Optional[Any]									=       self.min_node.val

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

										# Update bottom root
										__UpperCamelCase				:      str									=       None

										# Update min_node
										__UpperCamelCase				:      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
										__UpperCamelCase				:      str									=       self.bottom_root.parent
										__UpperCamelCase				:      Optional[int]									=       None

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

							# Size, min_node and bottom_root
							while bottom_of_new.left:
										__UpperCamelCase				:      List[Any]									=       size_of_new * 2 + 1
										__UpperCamelCase				:      Tuple									=       bottom_of_new.left
										if bottom_of_new.val < min_of_new.val:
													__UpperCamelCase				:      Optional[Any]									=       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				:      List[Any]									=       size_of_new
										__UpperCamelCase				:      List[str]									=       bottom_of_new
										__UpperCamelCase				:      Optional[int]									=       min_of_new
										# print("Single root, multiple nodes case")
										return min_value
							# Remaining cases
							# Construct heap of right subtree
							__UpperCamelCase				:      List[Any]									=       BinomialHeap(
							    bottom_root=_UpperCAmelCase			,  min_node=_UpperCAmelCase			,  heap_size=_UpperCAmelCase      )

							# Update size
							__UpperCamelCase				:      Dict									=       self.size - 1 - size_of_new

							# Neighbour nodes
							__UpperCamelCase				:      Dict									=       self.min_node.left
							__UpperCamelCase				:      Optional[Any]									=       self.min_node.parent

							# Initialize new bottom_root and min_node
							__UpperCamelCase				:      int									=       previous_node or next_node
							__UpperCamelCase				:      Union[str, Any]									=       next_node

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

										# Update bottom_root and search for min_node below
										__UpperCamelCase				:      Optional[int]									=       previous_node
										__UpperCamelCase				:      int									=       previous_node
										while self.bottom_root.left:
													__UpperCamelCase				:      Dict									=       self.bottom_root.left
													if self.bottom_root.val < self.min_node.val:
																__UpperCamelCase				:      int									=       self.bottom_root
							if next_node:
										__UpperCamelCase				:      str									=       previous_node

										# Search for new min_node above min_node
										__UpperCamelCase				:      List[Any]									=       next_node
										while i:
													if i.val < self.min_node.val:
																__UpperCamelCase				:      int									=       i
													__UpperCamelCase				:      int									=       i.parent
        # Merge heaps
							self.merge_heaps(_UpperCAmelCase      )

							return min_value
				def 	a_	(self      )     ->	List[str]:
							__UpperCamelCase				:      Dict									=       self.bottom_root
							while top_root.parent:
										__UpperCamelCase				:      int									=       top_root.parent
							# preorder
							__UpperCamelCase				:      Union[str, Any]									=       []
							self.__traversal(_UpperCAmelCase			,  _UpperCAmelCase      )
							return heap_pre_order
				def 	a_	(self			,  _UpperCAmelCase			,  _UpperCAmelCase			,  _UpperCAmelCase=0      )     ->	Optional[int]:
							if curr_node:
										preorder.append((curr_node.val, level)      )
										self.__traversal(curr_node.left			,  _UpperCAmelCase			,  level + 1      )
										self.__traversal(curr_node.right			,  _UpperCAmelCase			,  level + 1      )
							else:
										preorder.append(("#", level)      )





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

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


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

				doctest.testmod()









'''simple docstring'''






from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_lowerCAmelCase				     = {'''configuration_visual_bert''': ['''VISUAL_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''VisualBertConfig''']}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				_lowerCAmelCase				     = [
				    '''VISUAL_BERT_PRETRAINED_MODEL_ARCHIVE_LIST''',
				    '''VisualBertForMultipleChoice''',
				    '''VisualBertForPreTraining''',
				    '''VisualBertForQuestionAnswering''',
				    '''VisualBertForRegionToPhraseAlignment''',
				    '''VisualBertForVisualReasoning''',
				    '''VisualBertLayer''',
				    '''VisualBertModel''',
				    '''VisualBertPreTrainedModel''',
				]


if TYPE_CHECKING:
				from .configuration_visual_bert import VISUAL_BERT_PRETRAINED_CONFIG_ARCHIVE_MAP, VisualBertConfig

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_visual_bert import (
								    VISUAL_BERT_PRETRAINED_MODEL_ARCHIVE_LIST,
								    VisualBertForMultipleChoice,
								    VisualBertForPreTraining,
								    VisualBertForQuestionAnswering,
								    VisualBertForRegionToPhraseAlignment,
								    VisualBertForVisualReasoning,
								    VisualBertLayer,
								    VisualBertModel,
								    VisualBertPreTrainedModel,
								)


else:
				import sys

				_lowerCAmelCase				     = _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



