code: 
  '''simple docstring'''
  
  from __future__ import annotations
  
  from abc import abstractmethod
  from collections.abc import Iterable
  from typing import Generic, Protocol, TypeVar
  
  class 			UpperCAmelCase				(					a_ ):
  
  
  
  
  
  		"""simple docstring"""
  
  
  
  
  
  		@abstractmethod
  		def __lt__(    self  ,					_snake_case     )				->    bool:
  				pass
  		@abstractmethod
  		def __gt__(    self  ,					_snake_case     )				->    bool:
  				pass
  
  
  
  
  		@abstractmethod
  		def __eq__(    self  ,					_snake_case     )				->    bool:
  				pass
  
  
  
  
  
  
  
  _UpperCAmelCase   :      int 						=  TypeVar("""T""", bound=Comparable)
  
  class 			UpperCAmelCase				(					Generic[T] ):
  
  
  
  
  
  		"""simple docstring"""
  
  
  
  
  
  		def __init__(    self     )				->    None:
  				_UpperCamelCase       : list[T]    =      []
  				_UpperCamelCase       : int    =      0
  		def __repr__(    self     )				->    str:
  				return str(self.h     )
  		def _lowercase  (    self  ,					_snake_case     )				->    int | None:
  				if child_idx > 0:
  						return (child_idx - 1) // 2
  				return None
  		def _lowercase  (    self  ,					_snake_case     )				->    int | None:
  				_UpperCamelCase       : Any    =      2 * parent_idx + 1
  				if left_child_index < self.heap_size:
  						return left_child_index
  				return None
  		def _lowercase  (    self  ,					_snake_case     )				->    int | None:
  				_UpperCamelCase       : List[Any]    =      2 * parent_idx + 2
  				if right_child_index < self.heap_size:
  						return right_child_index
  				return None
  		def _lowercase  (    self  ,					_snake_case     )				->    None:
  				if index < self.heap_size:
  						_UpperCamelCase       : int    =      index
  						_UpperCamelCase       : int    =      self.left_child_idx(_snake_case     )
  						_UpperCamelCase       : int    =      self.right_child_idx(_snake_case     )
  						# check which child is larger than its parent
  						if left_child is not None and self.h[left_child] > self.h[violation]:
  								_UpperCamelCase       : Optional[Any]    =      left_child
  						if right_child is not None and self.h[right_child] > self.h[violation]:
  								_UpperCamelCase       : int    =      right_child
  						# if violation indeed exists
  						if violation != index:
  								# swap to fix the violation
  								_UpperCamelCase,							_UpperCamelCase       : Any    =      self.h[index], self.h[violation]
  								# fix the subsequent violation recursively if any
  								self.max_heapify(_snake_case     )
  		def _lowercase  (    self  ,					_snake_case     )				->    None:
  				_UpperCamelCase       : Optional[int]    =      list(_snake_case     )
  				_UpperCamelCase       : Union[str, Any]    =      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(_snake_case     )
  		def _lowercase  (    self     )				->    T:
  				if self.heap_size >= 2:
  						_UpperCamelCase       : Optional[Any]    =      self.h[0]
  						_UpperCamelCase       : 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 _lowercase  (    self  ,					_snake_case     )				->    None:
  				self.h.append(_snake_case     )
  				_UpperCamelCase       : Tuple    =      (self.heap_size - 1) // 2
  				self.heap_size += 1
  				while idx >= 0:
  						self.max_heapify(_snake_case     )
  						_UpperCamelCase       : List[Any]    =      (idx - 1) // 2
  
  
  
  
  		def _lowercase  (    self     )				->    None:
  				_UpperCamelCase       : List[str]    =      self.heap_size
  				for j in range(size - 1  ,					0  ,					-1     ):
  						_UpperCamelCase,							_UpperCamelCase       : str    =      self.h[j], self.h[0]
  						self.heap_size -= 1
  						self.max_heapify(0     )
  				_UpperCamelCase       : 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],
  	    [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
  	    [-45, -2, -5],
  	]:
  		print(f"""unsorted array: {unsorted}""")
  
  		_UpperCAmelCase   :      Heap[int] 						=  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(100)
  		print(f"""after new value 100 inserted: {heap}""")
  
  		heap.heap_sort()
  		print(f"""heap-sorted array: {heap}\n""")
  
  
  
  
  
  
style_context: 
  '''simple docstring'''
  
  import os
  
  
  
  
  
  
  
  def 						snake_case__	(      ) ->      Tuple:
  		_UpperCamelCase       : Dict    =      os.path.dirname(os.path.realpath(UpperCamelCase	)	)
  		_UpperCamelCase       : str    =      os.path.join(UpperCamelCase			,'''triangle.txt'''	)
  
  		with open(UpperCamelCase	) as f:
  				_UpperCamelCase       : Optional[Any]    =      f.readlines()
  
  		_UpperCamelCase       : List[str]    =      [[int(UpperCamelCase	) for y in x.rstrip('''\r\n'''	).split(''' '''	)] for x in triangle]
  
  		for i in range(1			,len(UpperCamelCase	)	):
  				for j in range(len(a[i]	)	):
  						_UpperCamelCase       : str    =      a[i - 1][j] if j != len(a[i - 1]	) else 0
  						_UpperCamelCase       : Any    =      a[i - 1][j - 1] if j > 0 else 0
  						a[i][j] += max(UpperCamelCase			,UpperCamelCase	)
  		return max(a[-1]	)
  
  
  if __name__ == "__main__":
  	print(solution())
  
  
  
  
  
  