"""simple docstring"""


from __future__ import annotations

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






class        lowercase__ (      __SCREAMING_SNAKE_CASE  ):

			"""simple docstring"""







			@abstractmethod
			def __lt__(			self	,      _A						):






									'''simple docstring'''







									pass







			@abstractmethod
			def __gt__(			self	,      _A						):






									'''simple docstring'''







									pass







			@abstractmethod
			def __eq__(			self	,      _A						):






									'''simple docstring'''







									pass


__magic_name__					:				Union[str, Any]	= TypeVar("""T""", bound=Comparable)






class        lowercase__ (      Generic[T]  ):

			"""simple docstring"""







			def __init__(			self						):






									'''simple docstring'''







									UpperCamelCase							:		list[T]							      = []
									UpperCamelCase							:		int							      = 0







			def __repr__(			self						):






									'''simple docstring'''







									return str(self.h						)







			def      _a			(			self	,      _A						):






									'''simple docstring'''







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







			def      _a			(			self	,      _A						):






									'''simple docstring'''







									UpperCamelCase							:		Any							      = 2 * parent_idx + 1
									if left_child_index < self.heap_size:
															return left_child_index
									return None







			def      _a			(			self	,      _A						):






									'''simple docstring'''







									UpperCamelCase							:		Any							      = 2 * parent_idx + 2
									if right_child_index < self.heap_size:
															return right_child_index
									return None







			def      _a			(			self	,      _A						):






									'''simple docstring'''







									if index < self.heap_size:
															UpperCamelCase							:		int							      = index
															UpperCamelCase							:		int							      = self.left_child_idx(_A						)
															UpperCamelCase							:		int							      = self.right_child_idx(_A						)
															# check which child is larger than its parent
															if left_child is not None and self.h[left_child] > self.h[violation]:
																					UpperCamelCase							:		Dict							      = left_child
															if right_child is not None and self.h[right_child] > self.h[violation]:
																					UpperCamelCase							:		List[Any]							      = right_child
															# if violation indeed exists
															if violation != index:
																					# swap to fix the violation
																					UpperCamelCase							:		Tuple							      = self.h[index], self.h[violation]
																					# fix the subsequent violation recursively if any
																					self.max_heapify(_A						)







			def      _a			(			self	,      _A						):






									'''simple docstring'''







									UpperCamelCase							:		Dict							      = list(_A						)
									UpperCamelCase							:		List[str]							      = 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(_A						)







			def      _a			(			self						):






									'''simple docstring'''







									if self.heap_size >= 2:
															UpperCamelCase							:		int							      = self.h[0]
															UpperCamelCase							:		Tuple							      = 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      _a			(			self	,      _A						):






									'''simple docstring'''







									self.h.append(_A						)
									UpperCamelCase							:		Tuple							      = (self.heap_size - 1) // 2
									self.heap_size += 1
									while idx >= 0:
															self.max_heapify(_A						)
															UpperCamelCase							:		Tuple							      = (idx - 1) // 2







			def      _a			(			self						):






									'''simple docstring'''







									UpperCamelCase							:		Union[str, Any]							      = self.heap_size
									for j in range(size - 1	,      0	,      -1						):
															UpperCamelCase							:		Optional[int]							      = self.h[j], self.h[0]
															self.heap_size -= 1
															self.max_heapify(0						)
									UpperCamelCase							:		Tuple							      = 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, 1_0, 8],
		    [1_0_3, 9, 1, 7, 1_1, 1_5, 2_5, 2_0_1, 2_0_9, 1_0_7, 5],
		    [-4_5, -2, -5],
		]:
				print(f'''unsorted array: {unsorted}''')

				__magic_name__					:				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(1_0_0)
				print(f'''after new value 100 inserted: {heap}''')

				heap.heap_sort()
				print(f'''heap-sorted array: {heap}\n''')










"""simple docstring"""


def     UpperCamelCase       (SCREAMING_SNAKE_CASE = 1000    ):
						UpperCamelCase							:		List[str]							      = []
						UpperCamelCase							:		int							      = []
						UpperCamelCase							:		Dict							      = 3
						UpperCamelCase							:		Dict							      = 5
						UpperCamelCase							:		Optional[int]							      = 1
						while True:
												UpperCamelCase							:		int							      = z * temp
												if result < n:
																		zmulti.append(SCREAMING_SNAKE_CASE    )
																		temp += 1
												else:
																		UpperCamelCase							:		Optional[int]							      = 1
																		break
						while True:
												UpperCamelCase							:		Any							      = x * temp
												if result < n:
																		xmulti.append(SCREAMING_SNAKE_CASE    )
																		temp += 1
												else:
																		break
						UpperCamelCase							:		List[Any]							      = list(set(xmulti + zmulti    )    )
						return sum(SCREAMING_SNAKE_CASE    )


if __name__ == "__main__":
		print(f'''{solution() = }''')



