





from math import isqrt, loga

def     __A      (			a_						:List[Any])		->		list[int]:
				__a :						Tuple			       =  [True] * max_number
				for i in range(2   ,       isqrt(max_number - 1) + 1):
								if is_prime[i]:
												for j in range(i**2   ,       a_   ,       a_):
																__a :						Any			       =  False

				return [i for i in range(2   ,       a_) if is_prime[i]]

def     __A      (			a_						:int = 80_08_00   ,       a_						:List[str] = 80_08_00)		->		int:
				__a :						List[Any]			       =  degree * loga(a_)
				__a :						int			       =  int(a_)
				__a :						int			       =  calculate_prime_numbers(a_)

				__a :						Any			       =  0
				__a :						Union[str, Any]			       =  0
				__a :						int			       =  len(a_) - 1
				while left < right:
								while (
								    prime_numbers[right] * loga(prime_numbers[left])
								    + prime_numbers[left] * loga(prime_numbers[right])
								    > upper_bound
								):
												right -= 1
								hybrid_integers_count += right - left
								left += 1

				return hybrid_integers_count


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






"""simple docstring"""






from __future__ import annotations

from collections import deque
from collections.abc import Iterator
from dataclasses import dataclass




@dataclass
class 				__lowercase			:







					'''simple docstring'''




					__lowerCAmelCase  =  42
					__lowerCAmelCase  =  42






class 				__lowercase			:







					'''simple docstring'''




					def __init__(						self	,			_UpperCAmelCase     ):
									__a :						list[list[Edge]]			       =  [[] for _ in range(_UpperCAmelCase     )]
									__a :						Dict			       =  size







					def __getitem__(						self	,			_UpperCAmelCase     ):
									return iter(self._graph[vertex]     )







					@property
					def  _lowerCamelCase		(						self     ):
									return self._size







					def  _lowerCamelCase		(						self	,			_UpperCAmelCase	,			_UpperCAmelCase	,			_UpperCAmelCase     ):
									if weight not in (0, 1):
													raise ValueError('''Edge weight must be either 0 or 1.'''     )

									if to_vertex < 0 or to_vertex >= self.size:
													raise ValueError('''Vertex indexes must be in [0; size).'''     )

									self._graph[from_vertex].append(Edge(_UpperCAmelCase	,			_UpperCAmelCase     )     )







					def  _lowerCamelCase		(						self	,			_UpperCAmelCase	,			_UpperCAmelCase     ):
									__a :						List[str]			       =  deque([start_vertex]     )
									__a :						list[int | None]			       =  [None] * self.size
									__a :						int			       =  0

									while queue:
													__a :						Any			       =  queue.popleft()
													__a :						Tuple			       =  distances[current_vertex]
													if current_distance is None:
																	continue

													for edge in self[current_vertex]:
																	__a :						List[str]			       =  current_distance + edge.weight
																	__a :						str			       =  distances[edge.destination_vertex]
																	if (
																	    isinstance(_UpperCAmelCase	,			_UpperCAmelCase     )
																	    and new_distance >= dest_vertex_distance
																	):
																					continue
																	__a :						str			       =  new_distance
																	if edge.weight == 0:
																					queue.appendleft(edge.destination_vertex     )
																	else:
																					queue.append(edge.destination_vertex     )

									if distances[finish_vertex] is None:
													raise ValueError('''No path from start_vertex to finish_vertex.'''     )

									return distances[finish_vertex]


if __name__ == "__main__":
		import doctest

		doctest.testmod()