



"""simple docstring"""


from itertools import compress, repeat
from math import ceil, sqrt

def 				_lowerCAmelCase   (     lowercase_		):

						if num <= 2:
												return []
						if num == 3:
												return [2]

						# Odd sieve for numbers in range [3, num - 1]
						UpperCAmelCase    =				bytearray(B'\x01'		) * ((num >> 1) - 1)

						for i in range(3	,			int(sqrt(lowercase_		)		) + 1	,			2		):
												if sieve[(i >> 1) - 1]:
																		UpperCAmelCase    =				i**2
																		UpperCAmelCase    =				repeat(
																		    0	,			ceil((num - i_squared) / (i << 1)		)		)

						return [2] + list(compress(range(3	,			lowercase_	,			2		)	,			lowercase_		)		)


if __name__ == "__main__":
				import doctest

				doctest.testmod()










"""simple docstring"""


from __future__ import annotations

import random
from collections.abc import Iterable
from typing import Any, Generic, TypeVar

snake_case_         = TypeVar("""T""", bound=bool)







class    A_    (  Generic[T]       ):



						"""simple docstring"""






						def __init__(      self				:str     ,						lowercase_				:T      )       ->    None:
												UpperCAmelCase    =				value
												UpperCAmelCase    =				None
												UpperCAmelCase    =				None






						@property
						def 			UpperCAmelCase__  (      self				:Any      )       ->    T:
												return self._value






						@staticmethod
						def 			UpperCAmelCase__  (      lowercase_				:RandomizedHeapNode[T] | None     ,						lowercase_				:RandomizedHeapNode[T] | None      )       ->    RandomizedHeapNode[T] | None:
												if not roota:
																		return roota

												if not roota:
																		return roota

												if roota.value > roota.value:
																		UpperCAmelCase   ,					UpperCAmelCase    =				roota, roota

												if random.choice([True, False]      ):
																		UpperCAmelCase   ,					UpperCAmelCase    =				roota.right, roota.left

												UpperCAmelCase    =				RandomizedHeapNode.merge(roota.left     ,						lowercase_      )

												return roota







class    A_    (  Generic[T]       ):



						"""simple docstring"""






						def __init__(      self				:Optional[Any]     ,						lowercase_				:Iterable[T] | None = ()      )       ->    None:
												UpperCAmelCase    =				None

												if data:
																		for item in data:
																								self.insert(lowercase_      )






						def 			UpperCAmelCase__  (      self				:Dict     ,						lowercase_				:T      )       ->    None:
												UpperCAmelCase    =				RandomizedHeapNode.merge(self._root     ,						RandomizedHeapNode(lowercase_      )      )






						def 			UpperCAmelCase__  (      self				:Dict      )       ->    T | None:
												UpperCAmelCase    =				self.top()

												if self._root is None:
																		return None

												UpperCAmelCase    =				RandomizedHeapNode.merge(self._root.left     ,						self._root.right      )

												return result






						def 			UpperCAmelCase__  (      self				:Tuple      )       ->    T:
												if not self._root:
																		raise IndexError('Can\'t get top element for the empty heap.'      )
												return self._root.value






						def 			UpperCAmelCase__  (      self				:Dict      )       ->    None:
												UpperCAmelCase    =				None






						def 			UpperCAmelCase__  (      self				:Union[str, Any]      )       ->    list[Any]:
												UpperCAmelCase    =				[]
												while self:
																		result.append(self.pop()      )

												return result






						def __bool__(      self				:Optional[Any]      )       ->    bool:
												return self._root is not None


if __name__ == "__main__":
				import doctest

				doctest.testmod()





