

from __future__ import annotations

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




class      SCREAMING_SNAKE_CASE__  (			_a      ):





	'''simple docstring'''



	@abstractmethod
	def __lt__(						self			:					T    ,						lowercase			:					T			):


				'''simple docstring'''


				pass



	@abstractmethod
	def __gt__(						self			:					T    ,						lowercase			:					T			):


				'''simple docstring'''


				pass





	@abstractmethod
	def __eq__(						self			:					T    ,						lowercase			:					object			):


				'''simple docstring'''


				pass




_lowerCamelCase :       Dict     					=    TypeVar('''T''', bound=Comparable)




class      SCREAMING_SNAKE_CASE__  (			Generic[T]      ):





	'''simple docstring'''



	def __init__(						self			:					List[str]			):


				'''simple docstring'''


				_snake_case						=    []
				_snake_case						=    0



	def __repr__(						self			:					Tuple			):


				'''simple docstring'''


				return str(self.h			)



	def 				A							(						self			:					Any    ,						lowercase			:					int			):


				'''simple docstring'''


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



	def 				A							(						self			:					List[str]    ,						lowercase			:					int			):


				'''simple docstring'''


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



	def 				A							(						self			:					Tuple    ,						lowercase			:					int			):


				'''simple docstring'''


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



	def 				A							(						self			:					str    ,						lowercase			:					int			):


				'''simple docstring'''


				if index < self.heap_size:
							_snake_case						=    index
							_snake_case						=    self.left_child_idx(lowercase			)
							_snake_case						=    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]:
										_snake_case						=    left_child
							if right_child is not None and self.h[right_child] > self.h[violation]:
										_snake_case						=    right_child
							# if violation indeed exists
							if violation != index:
										# swap to fix the violation
										_snake_case			,      _snake_case						=    self.h[index], self.h[violation]
										# fix the subsequent violation recursively if any
										self.max_heapify(lowercase			)



	def 				A							(						self			:					int    ,						lowercase			:					Iterable[T]			):


				'''simple docstring'''


				_snake_case						=    list(lowercase			)
				_snake_case						=    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 				A							(						self			:					Any			):


				'''simple docstring'''


				if self.heap_size >= 2:
							_snake_case						=    self.h[0]
							_snake_case						=    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			:					Dict    ,						lowercase			:					T			):


				'''simple docstring'''


				self.h.append(lowercase			)
				_snake_case						=    (self.heap_size - 1) // 2
				self.heap_size += 1
				while idx >= 0:
							self.max_heapify(lowercase			)
							_snake_case						=    (idx - 1) // 2





	def 				A							(						self			:					int			):


				'''simple docstring'''


				_snake_case						=    self.heap_size
				for j in range(size - 1    ,						0    ,						-1			):
							_snake_case			,      _snake_case						=    self.h[j], self.h[0]
							self.heap_size -= 1
							self.max_heapify(0			)
				_snake_case						=    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 :       str     					=    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  a_	( __lowercase     :			int				)				->						bool:
			_snake_case						=    9

			while num > 0:
						if num % 10 != digit:
									return False
						num //= 100
						digit -= 1

			return True






def  a_	( )				->						int:
			_snake_case						=    138_902_663

			while not is_square_form(num * num				):
						if num % 10 == 3:
									num -= 6  # (3 - 6) % 10 = 7
						else:
									num -= 4  # (7 - 4) % 10 = 3

			return num * 10


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