"""simple docstring"""







import importlib.util
import json
import os
import warnings
from dataclasses import dataclass, field

import torch

from ..training_args import TrainingArguments
from ..utils import cached_property, is_sagemaker_dp_enabled, logging


__SCREAMING_SNAKE_CASE    	=logging.get_logger(__name__)



def 			lowercase__(       ):
     lowercase_	:				str													=	os.getenv('SM_HP_MP_PARAMETERS'     ,			'{}'      )
     try:
          # Parse it and check the field "partitions" is included, it is required for model parallel.
          lowercase_	:				Union[str, Any]													=	json.loads(lowerCAmelCase_      )
          if "partitions" not in smp_options:
               return False
     except json.JSONDecodeError:
          return False

     # Get the sagemaker specific framework parameters from mpi_options variable.
     lowercase_	:				List[Any]													=	os.getenv('SM_FRAMEWORK_PARAMS'     ,			'{}'      )
     try:
          # Parse it and check the field "sagemaker_distributed_dataparallel_enabled".
          lowercase_	:				Tuple													=	json.loads(lowerCAmelCase_      )
          if not mpi_options.get('sagemaker_mpi_enabled'     ,			lowerCAmelCase_      ):
               return False
     except json.JSONDecodeError:
          return False
     # Lastly, check if the `smdistributed` module is present.
     return importlib.util.find_spec('smdistributed'      ) is not None


if is_sagemaker_model_parallel_available():
       import smdistributed.modelparallel.torch as smp

       smp.init()







@dataclass
class        UpperCamelCase		(			lowercase_  ):
   lowercase							=  field(
       default=''						,      metadata={'help': 'Used by the SageMaker launcher to send mp-specific args. Ignored in SageMakerTrainer'}						,      )
   def 			_UpperCAmelCase   (			self			)	->      Any:


        '''simple docstring'''


        super().__post_init__()
        warnings.warn(
            '`SageMakerTrainingArguments` is deprecated and will be removed in v5 of Transformers. You can use '
            '`TrainingArguments` instead.'     ,UpperCAmelCase__     ,)
   @cached_property
   def 			_UpperCAmelCase   (			self			)	->      "torch.device":


        '''simple docstring'''


        logger.info('PyTorch: setting up devices'			)
        if torch.distributed.is_available() and torch.distributed.is_initialized() and self.local_rank == -1:
             logger.warning(
                 'torch.distributed process group is initialized, but local_rank == -1. '
                 'In order to use Torch DDP, launch your script with `python -m torch.distributed.launch'			)
        if self.no_cuda:
             lowercase_	:				List[str]													=	torch.device('cpu'			)
             lowercase_	:				Optional[Any]													=	0
        elif is_sagemaker_model_parallel_available():
             lowercase_	:				Dict													=	smp.local_rank()
             lowercase_	:				Union[str, Any]													=	torch.device('cuda'     ,UpperCAmelCase__			)
             lowercase_	:				Optional[int]													=	1
        elif is_sagemaker_dp_enabled():
             import smdistributed.dataparallel.torch.torch_smddp  # noqa: F401

             torch.distributed.init_process_group(backend='smddp'     ,timeout=self.ddp_timeout_delta			)
             lowercase_	:				Dict													=	int(os.getenv('SMDATAPARALLEL_LOCAL_RANK'			)			)
             lowercase_	:				Any													=	torch.device('cuda'     ,self.local_rank			)
             lowercase_	:				List[Any]													=	1
        elif self.local_rank == -1:
             # if n_gpu is > 1 we'll use nn.DataParallel.
             # If you only want to use a specific subset of GPUs use `CUDA_VISIBLE_DEVICES=0`
             # Explicitly set CUDA to the first (index 0) CUDA device, otherwise `set_device` will
             # trigger an error that a device index is missing. Index 0 takes into account the
             # GPUs available in the environment, so `CUDA_VISIBLE_DEVICES=1,2` with `cuda:0`
             # will use the first GPU in that env, i.e. GPU#1
             lowercase_	:				Union[str, Any]													=	torch.device('cuda:0' if torch.cuda.is_available() else 'cpu'			)
             # Sometimes the line in the postinit has not been run before we end up here, so just checking we're not at
             # the default value.
             lowercase_	:				List[Any]													=	torch.cuda.device_count()
        else:
             # Here, we'll use torch.distributed.
             # Initializes the distributed backend which will take care of synchronizing nodes/GPUs
             if not torch.distributed.is_initialized():
                  torch.distributed.init_process_group(backend='nccl'     ,timeout=self.ddp_timeout_delta			)
             lowercase_	:				Any													=	torch.device('cuda'     ,self.local_rank			)
             lowercase_	:				Any													=	1

        if device.type == "cuda":
             torch.cuda.set_device(UpperCAmelCase__			)

        return device
   @property
   def 			_UpperCAmelCase   (			self			)	->      Any:


        '''simple docstring'''


        if is_sagemaker_model_parallel_available():
             return smp.dp_size()

        return super().world_size
   @property
   def 			_UpperCAmelCase   (			self			)	->      List[Any]:


        '''simple docstring'''


        return not is_sagemaker_model_parallel_available()







   @property
   def 			_UpperCAmelCase   (			self			)	->      int:


        '''simple docstring'''


        return False





"""simple docstring"""







def    UpperCAmelCase__       (lowerCAmelCase_ = 100_0000   ):




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						   =				set(range(3  ,						lowerCAmelCase_  ,						2   )   )
					primes.add(2   )
					for p in range(3  ,						lowerCAmelCase_  ,						2   ):
										if p not in primes:
															continue
										primes.difference_update(set(range(p * p  ,						lowerCAmelCase_  ,						lowerCAmelCase_   )   )   )

					__SCREAMING_SNAKE_CASE						   =				[float(lowerCAmelCase_   ) for n in range(limit + 1   )]

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

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


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