





import inspect
import unittest


class 						lowerCamelCase       (unittest.TestCase      ):







							"""simple docstring"""




							def  A_     ( self     :					str						)				->			Union[str, Any]:





														"""simple docstring"""
														try:
																					import diffusers  # noqa: F401
														except ImportError:
																					assert False






							def  A_     ( self     :					List[str]						)				->			List[str]:





														"""simple docstring"""
														import diffusers
														from diffusers.dependency_versions_table import deps

														SCREAMING_SNAKE_CASE__       :      str     =						inspect.getmembers(_UpperCAmelCase,			inspect.isclass						)

														for cls_name, cls_module in all_classes:
																					if "dummy_" in cls_module.__module__:
																												for backend in cls_module._backends:
																																			if backend == "k_diffusion":
																																										SCREAMING_SNAKE_CASE__       :      Any     =						"k-diffusion"
																																			elif backend == "invisible_watermark":
																																										SCREAMING_SNAKE_CASE__       :      Dict     =						"invisible-watermark"
																																			assert backend in deps, F'''{backend} is not in the deps table!'''













def _a (  SCREAMING_SNAKE_CASE__      :  int = 50_00_00_00       )	->    int:

							'''simple docstring'''






							SCREAMING_SNAKE_CASE__       :      str     =						set()
							SCREAMING_SNAKE_CASE__       :      Dict     =						int((limit - 24) ** (1 / 2)       )

							SCREAMING_SNAKE_CASE__       :      Any     =						set(range(3			,				prime_square_limit + 1			,				2       )       )
							primes.add(2       )
							for p in range(3			,				prime_square_limit + 1			,				2       ):
														if p not in primes:
																					continue
														primes.difference_update(set(range(p * p			,				prime_square_limit + 1			,				SCREAMING_SNAKE_CASE__       )       )       )

							for primea in primes:
														SCREAMING_SNAKE_CASE__       :      Optional[int]     =						primea * primea
														for primea in primes:
																					SCREAMING_SNAKE_CASE__       :      Union[str, Any]     =						primea * primea * primea
																					if square + cube >= limit - 16:
																												break
																					for primea in primes:
																												SCREAMING_SNAKE_CASE__       :      List[str]     =						primea * primea * primea * primea
																												SCREAMING_SNAKE_CASE__       :      Optional[int]     =						square + cube + tetr
																												if total >= limit:
																																			break
																												ret.add(SCREAMING_SNAKE_CASE__       )

							return len(SCREAMING_SNAKE_CASE__       )


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






