




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

import torch_xla.distributed.xla_multiprocessing as xmp


def 					_a							(					)->	Optional[int]:
		SCREAMING_SNAKE_CASE_					      =							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=lowerCAmelCase    ,						default=1    ,						help='Number of TPU cores to use (1 or 8).' )

		# positional
		parser.add_argument(
		    'training_script'    ,						type=lowerCAmelCase    ,						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=lowerCAmelCase )

		return parser.parse_args()


def 					_a							(					)->	Optional[Any]:
		SCREAMING_SNAKE_CASE_					      =							parse_args()

		# Import training_script as a module.
		SCREAMING_SNAKE_CASE_					      =							Path(args.training_script )
		sys.path.append(str(script_fpath.parent.resolve() ) )
		SCREAMING_SNAKE_CASE_					      =							script_fpath.stem
		SCREAMING_SNAKE_CASE_					      =							importlib.import_module(lowerCAmelCase )

		# Patch sys.argv
		SCREAMING_SNAKE_CASE_					      =							[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()





from __future__ import annotations

import math


def 					_a							(					lowerCAmelCase )->	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(lowerCAmelCase ) + 1 )    ,						6 ):
				if number % i == 0 or number % (i + 2) == 0:
						return False
		return True


SCREAMING_SNAKE_CASE:     List[str]									= [num for num in range(3, 1_0_0_0_0_1, 2) if not is_prime(num)]


def 					_a							(					lowerCAmelCase )->	list[int]:
		if not isinstance(lowerCAmelCase    ,						lowerCAmelCase ):
				raise ValueError('n must be an integer' )
		if n <= 0:
				raise ValueError('n must be >= 0' )

		SCREAMING_SNAKE_CASE_					      =							[]
		for num in range(len(lowerCAmelCase ) ):
				SCREAMING_SNAKE_CASE_					      =							0
				while 2 * i * i <= odd_composites[num]:
						SCREAMING_SNAKE_CASE_					      =							odd_composites[num] - 2 * i * i
						if is_prime(lowerCAmelCase ):
								break
						i += 1
				else:
						list_nums.append(odd_composites[num] )
						if len(lowerCAmelCase ) == n:
								return list_nums

		return []


def 					_a							(					)->	int:
		return compute_nums(1 )[0]


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