code: 
  
  
  from __future__ import annotations
  
  from abc import abstractmethod
  from collections.abc import Iterable
  from typing import Generic, Protocol, TypeVar
  
  
  
  
  class 					_UpperCamelCase (      lowerCamelCase__	):
  
  
  
  
  
  
  
  							'''simple docstring'''
  
  
  
  
  
  
  
  							@abstractmethod
  							def __lt__(		self  :				T		,				SCREAMING_SNAKE_CASE_  :				T		):
  													pass
  
  
  
  
  
  
  
  							@abstractmethod
  							def __gt__(		self  :				T		,				SCREAMING_SNAKE_CASE_  :				T		):
  													pass
  
  
  
  
  
  
  
  							@abstractmethod
  							def __eq__(		self  :				T		,				SCREAMING_SNAKE_CASE_  :				object		):
  													pass
  
  
  
  
  lowercase_								=    TypeVar('T', bound=Comparable)
  
  
  
  
  class 					_UpperCamelCase (      Generic[T]	):
  
  
  
  
  
  
  
  							'''simple docstring'''
  
  
  
  
  
  
  
  							def __init__(		self  :				Any		):
  													_a     =			[]
  													_a     =			0
  
  
  
  
  
  
  
  							def __repr__(		self  :				List[str]		):
  													return str(self.h		)
  
  
  
  
  
  
  
  							def 		_UpperCAmelCase	(		self  :				Optional[int]		,				SCREAMING_SNAKE_CASE_  :				int		):
  													if child_idx > 0:
  																			return (child_idx - 1) // 2
  													return None
  
  
  
  
  
  
  
  							def 		_UpperCAmelCase	(		self  :				int		,				SCREAMING_SNAKE_CASE_  :				int		):
  													_a     =			2 * parent_idx + 1
  													if left_child_index < self.heap_size:
  																			return left_child_index
  													return None
  
  
  
  
  
  
  
  							def 		_UpperCAmelCase	(		self  :				Any		,				SCREAMING_SNAKE_CASE_  :				int		):
  													_a     =			2 * parent_idx + 2
  													if right_child_index < self.heap_size:
  																			return right_child_index
  													return None
  
  
  
  
  
  
  
  							def 		_UpperCAmelCase	(		self  :				str		,				SCREAMING_SNAKE_CASE_  :				int		):
  													if index < self.heap_size:
  																			_a     =			index
  																			_a     =			self.left_child_idx(SCREAMING_SNAKE_CASE_		)
  																			_a     =			self.right_child_idx(SCREAMING_SNAKE_CASE_		)
  																			# check which child is larger than its parent
  																			if left_child is not None and self.h[left_child] > self.h[violation]:
  																									_a     =			left_child
  																			if right_child is not None and self.h[right_child] > self.h[violation]:
  																									_a     =			right_child
  																			# if violation indeed exists
  																			if violation != index:
  																									# swap to fix the violation
  																									_a ,	_a     =			self.h[index], self.h[violation]
  																									# fix the subsequent violation recursively if any
  																									self.max_heapify(SCREAMING_SNAKE_CASE_		)
  
  
  
  
  
  
  
  							def 		_UpperCAmelCase	(		self  :				Dict		,				SCREAMING_SNAKE_CASE_  :				Iterable[T]		):
  													_a     =			list(SCREAMING_SNAKE_CASE_		)
  													_a     =			len(self.h		)
  													if self.heap_size > 1:
  																			# max_heapify from right to left but exclude leaves (last level)
  																			for i in range(self.heap_size // 2 - 1		,				-1		,				-1		):
  																									self.max_heapify(SCREAMING_SNAKE_CASE_		)
  
  
  
  
  
  
  
  							def 		_UpperCAmelCase	(		self  :				Optional[Any]		):
  													if self.heap_size >= 2:
  																			_a     =			self.h[0]
  																			_a     =			self.h.pop(-1		)
  																			self.heap_size -= 1
  																			self.max_heapify(0		)
  																			return me
  													elif self.heap_size == 1:
  																			self.heap_size -= 1
  																			return self.h.pop(-1		)
  													else:
  																			raise Exception('Empty heap'		)
  
  
  
  
  
  
  
  							def 		_UpperCAmelCase	(		self  :				int		,				SCREAMING_SNAKE_CASE_  :				T		):
  													self.h.append(SCREAMING_SNAKE_CASE_		)
  													_a     =			(self.heap_size - 1) // 2
  													self.heap_size += 1
  													while idx >= 0:
  																			self.max_heapify(SCREAMING_SNAKE_CASE_		)
  																			_a     =			(idx - 1) // 2
  
  
  
  
  
  
  
  							def 		_UpperCAmelCase	(		self  :				int		):
  													_a     =			self.heap_size
  													for j in range(size - 1		,				0		,				-1		):
  																			_a ,	_a     =			self.h[j], self.h[0]
  																			self.heap_size -= 1
  																			self.max_heapify(0		)
  													_a     =			size
  
  
  if __name__ == "__main__":
  		import doctest
  
  		# run doc test
  		doctest.testmod()
  
  		# demo
  		for unsorted in [
  		    [0],
  		    [2],
  		    [3, 5],
  		    [5, 3],
  		    [5, 5],
  		    [0, 0, 0, 0],
  		    [1, 1, 1, 1],
  		    [2, 2, 3, 5],
  		    [0, 2, 2, 3, 5],
  		    [2, 5, 3, 0, 2, 3, 0, 3],
  		    [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
  		    [1_03, 9, 1, 7, 11, 15, 25, 2_01, 2_09, 1_07, 5],
  		    [-45, -2, -5],
  		]:
  				print(f"""unsorted array: {unsorted}""")
  
  				lowercase_								=    Heap()
  				heap.build_max_heap(unsorted)
  				print(f"""after build heap: {heap}""")
  
  				print(f"""max value: {heap.extract_max()}""")
  				print(f"""after max value removed: {heap}""")
  
  				heap.insert(1_00)
  				print(f"""after new value 100 inserted: {heap}""")
  
  				heap.heap_sort()
  				print(f"""heap-sorted array: {heap}\n""")
  
style_context: 
  
  
  from typing import TYPE_CHECKING
  
  from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available
  
  
  lowercase_								=    {
      'configuration_codegen': ['CODEGEN_PRETRAINED_CONFIG_ARCHIVE_MAP', 'CodeGenConfig', 'CodeGenOnnxConfig'],
      'tokenization_codegen': ['CodeGenTokenizer'],
  }
  
  try:
  		if not is_tokenizers_available():
  				raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
  		pass
  else:
  		lowercase_								=    ['CodeGenTokenizerFast']
  
  try:
  		if not is_torch_available():
  				raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
  		pass
  else:
  		lowercase_								=    [
  		    'CODEGEN_PRETRAINED_MODEL_ARCHIVE_LIST',
  		    'CodeGenForCausalLM',
  		    'CodeGenModel',
  		    'CodeGenPreTrainedModel',
  		]
  
  if TYPE_CHECKING:
  		from .configuration_codegen import CODEGEN_PRETRAINED_CONFIG_ARCHIVE_MAP, CodeGenConfig, CodeGenOnnxConfig
  		from .tokenization_codegen import CodeGenTokenizer
  
  		try:
  				if not is_tokenizers_available():
  						raise OptionalDependencyNotAvailable()
  		except OptionalDependencyNotAvailable:
  				pass
  		else:
  				from .tokenization_codegen_fast import CodeGenTokenizerFast
  
  		try:
  				if not is_torch_available():
  						raise OptionalDependencyNotAvailable()
  		except OptionalDependencyNotAvailable:
  				pass
  		else:
  				from .modeling_codegen import (
  				    CODEGEN_PRETRAINED_MODEL_ARCHIVE_LIST,
  				    CodeGenForCausalLM,
  				    CodeGenModel,
  				    CodeGenPreTrainedModel,
  				)
  
  else:
  		import sys
  
  		lowercase_								=    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
  
  
  