





from dataclasses import dataclass

_lowercase		:     Tuple 					='''0.1'''
_lowercase		:     Optional[Any] 					='''Lucia Harcekova'''






@dataclass
class 	UpperCamelCase_     :
     _a			:	int
     _a			:	int
     _a			:	str



     def __repr__(		self    :    int	):
       return F"({self.offset}, {self.length}, {self.indicator})"






class 	UpperCamelCase_     :



     def __init__(		self    :    Dict					,			lowerCamelCase    :    int = 13					,			lowerCamelCase    :    int = 6	):
       lowerCamelCase_  :    Optional[int]   	=			window_size
       lowerCamelCase_  :    Optional[Any]   	=			lookahead_buffer_size
       lowerCamelCase_  :    Union[str, Any]   	=			self.window_size - self.lookahead_buffer_size



     def      __a    (		self    :    Optional[int]					,			lowerCamelCase    :    str	):
       lowerCamelCase_  :    List[Any]   	=			[]
       lowerCamelCase_  :    Optional[int]   	=			''

       # while there are still characters in text to compress
       while text:
         # find the next encoding phrase
         # - triplet with offset, length, indicator (the next encoding character)
         lowerCamelCase_  :    int   	=			self._find_encoding_token(_A					,			_A	)

         # update the search buffer:
         # - add new characters from text into it
         # - check if size exceed the max search buffer size, if so, drop the
         #   oldest elements
         search_buffer += text[: token.length + 1]
         if len(_A	) > self.search_buffer_size:
           lowerCamelCase_  :    List[Any]   	=			search_buffer[-self.search_buffer_size :]

         # update the text
         lowerCamelCase_  :    Tuple   	=			text[token.length + 1 :]

         # append the token to output
         output.append(_A	)

       return output



     def      __a    (		self    :    Tuple					,			lowerCamelCase    :    list[Token]	):
       lowerCamelCase_  :    Tuple   	=			''

       for token in tokens:
         for _ in range(token.length	):
           output += output[-token.offset]
         output += token.indicator

       return output



     def      __a    (		self    :    Optional[int]					,			lowerCamelCase    :    str					,			lowerCamelCase    :    str	):

       if not text:
         raise ValueError('We need some text to work with.'	)

       # Initialise result parameters to default values
       lowerCamelCase_  :    Tuple   	=			0, 0

       if not search_buffer:
         return Token(_A					,			_A					,			text[length]	)

       for i, character in enumerate(_A	):
         lowerCamelCase_  :    List[str]   	=			len(_A	) - i
         if character == text[0]:
           lowerCamelCase_  :    Any   	=			self._match_length_from_index(_A					,			_A					,			0					,			_A	)
           # if the found length is bigger than the current or if it's equal,
           # which means it's offset is smaller: update offset and length
           if found_length >= length:
             lowerCamelCase_  :    Tuple   	=			found_offset, found_length

       return Token(_A					,			_A					,			text[length]	)





     def      __a    (		self    :    str					,			lowerCamelCase    :    str					,			lowerCamelCase    :    str					,			lowerCamelCase    :    int					,			lowerCamelCase    :    int	):
       if not text or text[text_index] != window[window_index]:
         return 0
       return 1 + self._match_length_from_index(
           _A					,			window + text[text_index]					,			text_index + 1					,			window_index + 1	)


if __name__ == "__main__":
  from doctest import testmod

  testmod()
  # Initialize compressor class
  _lowercase		:     List[Any] 					=LZaaCompressor(window_size=13, lookahead_buffer_size=6)

  # Example
  _lowercase		:     List[str] 					='''cabracadabrarrarrad'''
  _lowercase		:     Dict 					=lzaa_compressor.compress(TEXT)
  print(lzaa_compressor.compress("""ababcbababaa"""))
  _lowercase		:     Tuple 					=lzaa_compressor.decompress(compressed_text)
  assert decompressed_text == TEXT, "The LZ77 algorithm returned the invalid result."







class 	UpperCamelCase_     :



					def __init__(		self    :    List[Any]					,			lowerCamelCase    :    int	):
							lowerCamelCase_  :    Union[str, Any]   	=			val
							# Number of nodes in left subtree
							lowerCamelCase_  :    Dict   	=			0
							lowerCamelCase_  :    str   	=			None
							lowerCamelCase_  :    int   	=			None
							lowerCamelCase_  :    Dict   	=			None





					def      __a    (		self    :    Optional[int]					,			lowerCamelCase    :    List[Any]	):
							assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

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






class 	UpperCamelCase_     :



					def __init__(		self    :    List[str]					,			lowerCamelCase    :    Optional[int]=None					,			lowerCamelCase    :    str=None					,			lowerCamelCase    :    List[Any]=0	):
							lowerCamelCase_  :    Any   	=			heap_size
							lowerCamelCase_  :    int   	=			bottom_root
							lowerCamelCase_  :    Any   	=			min_node



					def      __a    (		self    :    int					,			lowerCamelCase    :    int	):

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

							# Update min.node
							if self.min_node.val > other.min_node.val:
									lowerCamelCase_  :    Optional[Any]   	=			other.min_node
							# Merge

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

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

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

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

							# Return the merged heap
							return self



					def      __a    (		self    :    Any					,			lowerCamelCase    :    Dict	):
							if self.size == 0:
									lowerCamelCase_  :    Tuple   	=			Node(lowerCamelCase	)
									lowerCamelCase_  :    Optional[int]   	=			1
									lowerCamelCase_  :    Optional[int]   	=			self.bottom_root
							else:
									# Create new node
									lowerCamelCase_  :    List[Any]   	=			Node(lowerCamelCase	)

									# Update size
									self.size += 1

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

											# Merge
											lowerCamelCase_  :    int   	=			self.bottom_root.merge_trees(self.bottom_root.parent	)

											# Update Links
											lowerCamelCase_  :    Dict   	=			next_node
											lowerCamelCase_  :    Optional[Any]   	=			None
											if next_node:
													lowerCamelCase_  :    Union[str, Any]   	=			self.bottom_root



					def      __a    (		self    :    Dict	):
							return self.min_node.val



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



					def      __a    (		self    :    List[Any]	):
							lowerCamelCase_  :    Tuple   	=			self.min_node.val

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

									# Update bottom root
									lowerCamelCase_  :    Any   	=			None

									# Update min_node
									lowerCamelCase_  :    List[str]   	=			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
									lowerCamelCase_  :    Union[str, Any]   	=			self.bottom_root.parent
									lowerCamelCase_  :    Union[str, Any]   	=			None

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

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

							# Update size
							lowerCamelCase_  :    Union[str, Any]   	=			self.size - 1 - size_of_new

							# Neighbour nodes
							lowerCamelCase_  :    Union[str, Any]   	=			self.min_node.left
							lowerCamelCase_  :    Optional[Any]   	=			self.min_node.parent

							# Initialize new bottom_root and min_node
							lowerCamelCase_  :    Optional[int]   	=			previous_node or next_node
							lowerCamelCase_  :    Tuple   	=			next_node

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

									# Update bottom_root and search for min_node below
									lowerCamelCase_  :    int   	=			previous_node
									lowerCamelCase_  :    Tuple   	=			previous_node
									while self.bottom_root.left:
											lowerCamelCase_  :    Union[str, Any]   	=			self.bottom_root.left
											if self.bottom_root.val < self.min_node.val:
													lowerCamelCase_  :    Any   	=			self.bottom_root
							if next_node:
									lowerCamelCase_  :    Any   	=			previous_node

									# Search for new min_node above min_node
									lowerCamelCase_  :    List[str]   	=			next_node
									while i:
											if i.val < self.min_node.val:
													lowerCamelCase_  :    List[Any]   	=			i
											lowerCamelCase_  :    Dict   	=			i.parent
        # Merge heaps
							self.merge_heaps(lowerCamelCase	)

							return min_value



					def      __a    (		self    :    Optional[int]	):
							lowerCamelCase_  :    List[Any]   	=			self.bottom_root
							while top_root.parent:
									lowerCamelCase_  :    Tuple   	=			top_root.parent
							# preorder
							lowerCamelCase_  :    str   	=			[]
							self.__traversal(lowerCamelCase					,			lowerCamelCase	)
							return heap_pre_order



					def      __a    (		self    :    Dict					,			lowerCamelCase    :    Tuple					,			lowerCamelCase    :    Dict					,			lowerCamelCase    :    List[str]=0	):
							if curr_node:
									preorder.append((curr_node.val, level)	)
									self.__traversal(curr_node.left					,			lowerCamelCase					,			level + 1	)
									self.__traversal(curr_node.right					,			lowerCamelCase					,			level + 1	)
							else:
									preorder.append(('#', level)	)





					def __str__(		self    :    List[Any]	):
							if self.is_empty():
									return ""
							lowerCamelCase_  :    str   	=			self.pre_order()

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


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

		doctest.testmod()
