




def 					_a							(					lowerCAmelCase = 10 )->	List[Any]:
		if not isinstance(UpperCamelCase_    ,						UpperCamelCase_ ) or n < 0:
				raise ValueError('Invalid input' )
		SCREAMING_SNAKE_CASE_					      =							10**n
		SCREAMING_SNAKE_CASE_					      =							28433 * (pow(2    ,						7830457    ,						UpperCamelCase_ )) + 1
		return str(number % modulus )


if __name__ == "__main__":
						from doctest import testmod

						testmod()
						print(f"""{solution(1_0) = }""")



'''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


__lowerCamelCase												=						logging.get_logger(__name__)


def        a__     (					):
   # Get the sagemaker specific mp parameters from smp_options variable.
   UpperCAmelCase__	:Any      =      os.getenv('''SM_HP_MP_PARAMETERS''',   '''{}'''						)
   try:
      # Parse it and check the field "partitions" is included, it is required for model parallel.
      UpperCAmelCase__	:Any      =      json.loads(UpperCamelCase_						)
      if "partitions" not in smp_options:
         return False
   except json.JSONDecodeError:
      return False

   # Get the sagemaker specific framework parameters from mpi_options variable.
   UpperCAmelCase__	:Optional[Any]      =      os.getenv('''SM_FRAMEWORK_PARAMS''',   '''{}'''						)
   try:
      # Parse it and check the field "sagemaker_distributed_dataparallel_enabled".
      UpperCAmelCase__	:str      =      json.loads(UpperCamelCase_						)
      if not mpi_options.get('''sagemaker_mpi_enabled''',   UpperCamelCase_						):
         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			(			_snake_case						):
 UpperCAmelCase				=					field(
     default=""						, metadata={"help": "Used by the SageMaker launcher to send mp-specific args. Ignored in SageMakerTrainer"}						, )


 def        __SCREAMING_SNAKE_CASE					(      self							:	List[Any] ):
    super().__post_init__()
    warnings.warn(
        '''`SageMakerTrainingArguments` is deprecated and will be removed in v5 of Transformers. You can use '''
        '''`TrainingArguments` instead.'''			,       __lowerCamelCase			,       )


 @cached_property
 def        __SCREAMING_SNAKE_CASE					(      self							:	List[Any] ):
    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:
       UpperCAmelCase__	:Union[str, Any]      =      torch.device('''cpu''' )
       UpperCAmelCase__	:Dict      =      0
    elif is_sagemaker_model_parallel_available():
       UpperCAmelCase__	:Dict      =      smp.local_rank()
       UpperCAmelCase__	:List[str]      =      torch.device('''cuda'''			,       __lowerCamelCase )
       UpperCAmelCase__	: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 )
       UpperCAmelCase__	:int      =      int(os.getenv('''SMDATAPARALLEL_LOCAL_RANK''' ) )
       UpperCAmelCase__	:int      =      torch.device('''cuda'''			,       self.local_rank )
       UpperCAmelCase__	:Union[str, 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
       UpperCAmelCase__	:str      =      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.
       UpperCAmelCase__	:str      =      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 )
       UpperCAmelCase__	:str      =      torch.device('''cuda'''			,       self.local_rank )
       UpperCAmelCase__	:Union[str, Any]      =      1

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

    return device


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	List[str] ):
    if is_sagemaker_model_parallel_available():
       return smp.dp_size()

    return super().world_size


 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	Dict ):
    return not is_sagemaker_model_parallel_available()





 @property
 def        __SCREAMING_SNAKE_CASE					(      self							:	int ):
    return False



