





'''simple docstring'''




import math






def 			_lowerCAmelCase     (    __snake_case    :					int     )	->	bool:

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5					,				int(math.sqrt(__snake_case     ) + 1     )					,				6     ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True






def 			_lowerCAmelCase     (    __snake_case    :					float = 0.1     )	->	int:
     __A		:					Any						=			3
     __A		:					Optional[Any]						=			3

     while primes / (2 * j - 1) >= ratio:
          for i in range(j * j + j + 1					,				(j + 2) * (j + 2)					,				j + 1     ):
               primes += is_prime(__snake_case     )
          j += 2
     return j


if __name__ == "__main__":
  import doctest

  doctest.testmod()


import importlib
import sys
from argparse import REMAINDER, ArgumentParser
from pathlib import Path

import torch_xla.distributed.xla_multiprocessing as xmp
def 							__SCREAMING_SNAKE_CASE     (   )					->				Tuple:
	__A :			List[Any]		    =			ArgumentParser(
	    description=(
	        """PyTorch TPU distributed training launch helper utility that will spawn up multiple distributed processes"""
	    )       )

	# Optional arguments for the launch helper
	parser.add_argument("""--num_cores"""			,type=a__			,default=1			,help="""Number of TPU cores to use (1 or 8)."""       )

	# positional
	parser.add_argument(
	    """training_script"""			,type=a__			,help=(
	        """The full path to the single TPU training """
	        """program/script to be launched in parallel, """
	        """followed by all the arguments for the """
	        """training script"""
	    )			,)

	# rest from the training program
	parser.add_argument("""training_script_args"""			,nargs=a__       )

	return parser.parse_args()
def 							__SCREAMING_SNAKE_CASE     (   )					->				str:
	__A :			Union[str, Any]		    =			parse_args()

	# Import training_script as a module.
	__A :			List[Any]		    =			Path(args.training_script       )
	sys.path.append(str(script_fpath.parent.resolve()       )       )
	__A :			str		    =			script_fpath.stem
	__A :			int		    =			importlib.import_module(a__       )

	# Patch sys.argv
	__A :			List[str]		    =			[args.training_script] + args.training_script_args + ["""--tpu_num_cores""", str(args.num_cores       )]

	xmp.spawn(mod._mp_fn			,args=()			,nprocs=args.num_cores       )


if __name__ == "__main__":
			main()





