




from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar




class    snake_case__							(UpperCamelCase_       ):
				"""simple docstring"""



				@abstractmethod
				def __lt__(				self    :					T ,				__lowerCamelCase    :					T							) ->					bool:
							pass





				@abstractmethod
				def __gt__(				self    :					T ,				__lowerCamelCase    :					T							) ->					bool:
							pass





				@abstractmethod
				def __eq__(				self    :					T ,				__lowerCamelCase    :					object							) ->					bool:
							pass

__lowerCAmelCase		:    Tuple	      =		TypeVar('T', bound=Comparable)




class    snake_case__							(Generic[T]       ):
				"""simple docstring"""



				def __init__(				self    :					Optional[Any]							) ->					None:
							a   =      []
							a   =      0





				def __repr__(				self    :					int							) ->					str:
							return str(self.h							)





				def 							__UpperCAmelCase							(				self    :					str ,				__lowerCamelCase    :					int							) ->					int | None:




							if child_idx > 0:
										return (child_idx - 1) // 2
							return None





				def 							__UpperCAmelCase							(				self    :					Union[str, Any] ,				__lowerCamelCase    :					int							) ->					int | None:
							a   =      2 * parent_idx + 1
							if left_child_index < self.heap_size:
										return left_child_index
							return None





				def 							__UpperCAmelCase							(				self    :					List[str] ,				__lowerCamelCase    :					int							) ->					int | None:
							a   =      2 * parent_idx + 2
							if right_child_index < self.heap_size:
										return right_child_index
							return None





				def 							__UpperCAmelCase							(				self    :					Any ,				__lowerCamelCase    :					int							) ->					None:




							if index < self.heap_size:
										a   =      index
										a   =      self.left_child_idx(lowercase_							)
										a   =      self.right_child_idx(lowercase_							)
										# 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   =      self.h[index], self.h[violation]
													# fix the subsequent violation recursively if any
													self.max_heapify(lowercase_							)





				def 							__UpperCAmelCase							(				self    :					int ,				__lowerCamelCase    :					Iterable[T]							) ->					None:
							a   =      list(lowercase_							)
							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(lowercase_							)





				def 							__UpperCAmelCase							(				self    :					Dict							) ->					T:




							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    :					Tuple ,				__lowerCamelCase    :					T							) ->					None:
							self.h.append(lowercase_							)
							a   =      (self.heap_size - 1) // 2
							self.heap_size += 1
							while idx >= 0:
										self.max_heapify(lowercase_							)
										a   =      (idx - 1) // 2





				def 							__UpperCAmelCase							(				self    :					Optional[Any]							) ->					None:
							a   =      self.heap_size
							for j in range(size - 1 ,				0 ,				-1							):
										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],
		    [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
		    [-45, -2, -5],
		]:
				print(F'''unsorted array: {unsorted}''')

				__lowerCAmelCase		:    Optional[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''')












def       __magic_name__    (			A		: float       ):






			'''simple docstring'''







			return -num if num < 0 else num




def       __magic_name__    (			A		: list[int]       ):






			'''simple docstring'''







			if len(A       ) == 0:
						raise ValueError("abs_min() arg is an empty sequence"       )
			a   =      x[0]
			for i in x:
						if abs_val(A       ) < abs_val(A       ):
									a   =      i
			return j




def       __magic_name__    (			A		: list[int]       ):






			'''simple docstring'''







			if len(A       ) == 0:
						raise ValueError("abs_max() arg is an empty sequence"       )
			a   =      x[0]
			for i in x:
						if abs(A       ) > abs(A       ):
									a   =      i
			return j




def       __magic_name__    (			A		: list[int]       ):






			'''simple docstring'''







			if len(A       ) == 0:
						raise ValueError("abs_max_sort() arg is an empty sequence"       )
			return sorted(A,  key=A       )[-1]




def       __magic_name__    (			):






			'''simple docstring'''







			assert abs_val(0       ) == 0
			assert abs_val(34       ) == 34
			assert abs_val(-100000000000       ) == 100000000000

			a   =      [-3, -1, 2, -11]
			assert abs_max(A       ) == -11
			assert abs_max_sort(A       ) == -11
			assert abs_min(A       ) == -1


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		test_abs_val()
		print(abs_val(-34))  # --> 34






