def  _lowerCamelCase					(   a_				: int = 50_00_00_00):
			lowerCamelCase						:int						  =     set()
			lowerCamelCase						:Union[str, Any]						  =     int((limit - 24) ** (1 / 2))

			lowerCamelCase						:Optional[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						,			a_)))

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

			return len(a_)


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




import inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_huggingface_suite,
    require_multi_gpu,
    require_single_gpu,
)
from accelerate.utils import patch_environment
@require_huggingface_suite
class   _lowerCAmelCase		(     unittest.TestCase				):







							def 				snake_case  (				self     :    Tuple		):
										lowerCamelCase						:List[Any]						  =     inspect.getfile(accelerate.test_utils		)
										lowerCamelCase						:Dict						  =     os.path.sep.join(
										    mod_file.split(os.path.sep		)[:-1] + ['''scripts''', '''external_deps''', '''test_metrics.py''']		)

										from accelerate.test_utils.scripts.external_deps import test_metrics  # noqa: F401

										lowerCamelCase						:Any						  =     test_metrics







							@require_cpu
							def 				snake_case  (				self     :    Dict		):
										debug_launcher(self.test_metrics.main	,					num_processes=1		)







							@require_cpu
							def 				snake_case  (				self     :    int		):
										debug_launcher(self.test_metrics.main		)







							@require_single_gpu
							def 				snake_case  (				self     :    Any		):
										self.test_metrics.main()







							@require_multi_gpu
							def 				snake_case  (				self     :    Optional[int]		):
										print(F"Found {torch.cuda.device_count()} devices."		)
										lowerCamelCase						:Optional[int]						  =     ['''torchrun''', F"--nproc_per_node={torch.cuda.device_count()}", self.test_file_path]
										with patch_environment(omp_num_threads=1		):
													execute_subprocess_async(__snake_case	,					env=os.environ.copy()		)



