code: 
  
  
  from __future__ import annotations
  
  from abc import abstractmethod
  from collections.abc import Iterable
  from typing import Generic, Protocol, TypeVar
  
  
  
  
  
  
  
  class 				__SCREAMING_SNAKE_CASE   (			A__   ):
  
  
        @abstractmethod
        def __lt__(							self							,						SCREAMING_SNAKE_CASE__		):
              pass
  
  
        @abstractmethod
        def __gt__(							self							,						SCREAMING_SNAKE_CASE__		):
              pass
  
  
  
  
  
  
        @abstractmethod
        def __eq__(							self							,						SCREAMING_SNAKE_CASE__		):
              pass
  
  
  
  
  
  __a   				=      TypeVar('''T''', bound=Comparable)
  
  
  
  
  
  
  
  class 				__SCREAMING_SNAKE_CASE   (			Generic[T]   ):
  
  
        def __init__(							self		):
              lowercase			:   list[T]					   =		[]
              lowercase			:   int					   =		0
  
  
        def __repr__(							self		):
              return str(self.h		)
  
  
        def        __lowerCamelCase			(							self							,						SCREAMING_SNAKE_CASE__		):
              if child_idx > 0:
                    return (child_idx - 1) // 2
              return None
  
  
        def        __lowerCamelCase			(							self							,						SCREAMING_SNAKE_CASE__		):
              lowercase			:   int					   =		2 * parent_idx + 1
              if left_child_index < self.heap_size:
                    return left_child_index
              return None
  
  
        def        __lowerCamelCase			(							self							,						SCREAMING_SNAKE_CASE__		):
              lowercase			:   List[Any]					   =		2 * parent_idx + 2
              if right_child_index < self.heap_size:
                    return right_child_index
              return None
  
  
        def        __lowerCamelCase			(							self							,						SCREAMING_SNAKE_CASE__		):
              if index < self.heap_size:
                    lowercase			:   int					   =		index
                    lowercase			:   Dict					   =		self.left_child_idx(SCREAMING_SNAKE_CASE__		)
                    lowercase			:   Dict					   =		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]:
                          lowercase			:   List[Any]					   =		left_child
                    if right_child is not None and self.h[right_child] > self.h[violation]:
                          lowercase			:   Tuple					   =		right_child
                    # if violation indeed exists
                    if violation != index:
                          # swap to fix the violation
                          lowercase   ,			lowercase			:   str					   =		self.h[index], self.h[violation]
                          # fix the subsequent violation recursively if any
                          self.max_heapify(SCREAMING_SNAKE_CASE__		)
  
  
        def        __lowerCamelCase			(							self							,						SCREAMING_SNAKE_CASE__		):
              lowercase			:   int					   =		list(SCREAMING_SNAKE_CASE__		)
              lowercase			:   Dict					   =		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        __lowerCamelCase			(							self		):
              if self.heap_size >= 2:
                    lowercase			:   Any					   =		self.h[0]
                    lowercase			:   Optional[int]					   =		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        __lowerCamelCase			(							self							,						SCREAMING_SNAKE_CASE__		):
              self.h.append(SCREAMING_SNAKE_CASE__		)
              lowercase			:   Any					   =		(self.heap_size - 1) // 2
              self.heap_size += 1
              while idx >= 0:
                    self.max_heapify(SCREAMING_SNAKE_CASE__		)
                    lowercase			:   Tuple					   =		(idx - 1) // 2
  
  
  
  
  
  
        def        __lowerCamelCase			(							self		):
              lowercase			:   Union[str, Any]					   =		self.heap_size
              for j in range(size - 1							,						0							,						-1		):
                    lowercase   ,			lowercase			:   Any					   =		self.h[j], self.h[0]
                    self.heap_size -= 1
                    self.max_heapify(0		)
              lowercase			:   List[str]					   =		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}''')
  
      __a   				=      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_torch_available
  
  
  __a   				=      {
      '''configuration_decision_transformer''': [
          '''DECISION_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP''',
          '''DecisionTransformerConfig''',
      ],
  }
  
  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    __a   				=      [
        '''DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''DecisionTransformerGPT2Model''',
        '''DecisionTransformerGPT2PreTrainedModel''',
        '''DecisionTransformerModel''',
        '''DecisionTransformerPreTrainedModel''',
    ]
  
  
  if TYPE_CHECKING:
    from .configuration_decision_transformer import (
        DECISION_TRANSFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
        DecisionTransformerConfig,
    )
  
    try:
      if not is_torch_available():
        raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
      pass
    else:
      from .modeling_decision_transformer import (
          DECISION_TRANSFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
          DecisionTransformerGPTaModel,
          DecisionTransformerGPTaPreTrainedModel,
          DecisionTransformerModel,
          DecisionTransformerPreTrainedModel,
      )
  
  
  else:
    import sys
  
    __a   				=      _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
  
  