"""simple docstring"""







def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     Any = 1_00_00_00      ):
     lowercase_	:				Union[str, Any]													=	set(range(3     ,			_snake_case     ,			2      )      )
     primes.add(2      )
     for p in range(3     ,			_snake_case     ,			2      ):
          if p not in primes:
               continue
          primes.difference_update(set(range(p * p     ,			_snake_case     ,			_snake_case      )      )      )

     lowercase_	:				int													=	[float(_snake_case      ) for n in range(limit + 1      )]

     for p in primes:
          for n in range(_snake_case     ,			limit + 1     ,			_snake_case      ):
               phi[n] *= 1 - 1 / p

     return int(sum(phi[2:]      )      )


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



"""simple docstring"""




import pickle
import unittest

import torch

from accelerate import Accelerator
from accelerate.state import AcceleratorState
from accelerate.test_utils import require_cpu



@require_cpu
class 	lowerCAmelCase_						(unittest.TestCase  ):


				"""simple docstring"""



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



											"""simple docstring"""




											SCREAMING_SNAKE_CASE__						:       List[Any]           =   torch.nn.Linear(10   ,       10    )
											SCREAMING_SNAKE_CASE__						:       Optional[int]           =   torch.optim.SGD(model.parameters()   ,       0.1    )
											SCREAMING_SNAKE_CASE__						:       int           =   Accelerator()
											SCREAMING_SNAKE_CASE__						:       List[Any]           =   accelerator.prepare(SCREAMING_SNAKE_CASE__    )
											try:
																		pickle.loads(pickle.dumps(SCREAMING_SNAKE_CASE__    )    )
											except Exception as e:
																		self.fail(F'''Accelerated optimizer pickling failed with {e}'''    )
											AcceleratorState._reset_state()




