


import math
import unittest

def       lowercase_		(		_A			:    List[Any]						):

      """simple docstring"""




      assert isinstance(_snake_case    ,					_snake_case						) and (
          number >= 0
      ), "'number' must been an int and positive"

      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







class 			_lowercase (							unittest.TestCase):


       """simple docstring"""




       def 						lowerCAmelCase     (   self							:			Any       ):


             '''simple docstring'''



             self.assertTrue(is_prime(2       )       )
             self.assertTrue(is_prime(3       )       )
             self.assertTrue(is_prime(5       )       )
             self.assertTrue(is_prime(7       )       )
             self.assertTrue(is_prime(11       )       )
             self.assertTrue(is_prime(13       )       )
             self.assertTrue(is_prime(17       )       )
             self.assertTrue(is_prime(19       )       )
             self.assertTrue(is_prime(23       )       )
             self.assertTrue(is_prime(29       )       )





       def 						lowerCAmelCase     (   self							:			Dict       ):


             '''simple docstring'''



             with self.assertRaises(SCREAMING_SNAKE_CASE__       ):
                   is_prime(-19       )
             self.assertFalse(
                 is_prime(0       )					,      "Zero doesn't have any positive factors, primes must have exactly two."					,      )
             self.assertFalse(
                 is_prime(1       )					,      "One only has 1 positive factor, primes must have exactly two."					,      )
             self.assertFalse(is_prime(2 * 2       )       )
             self.assertFalse(is_prime(2 * 3       )       )
             self.assertFalse(is_prime(3 * 3       )       )
             self.assertFalse(is_prime(3 * 5       )       )
             self.assertFalse(is_prime(3 * 5 * 7       )       )


if __name__ == "__main__":
    unittest.main()




"""simple docstring"""




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

import torch_xla.distributed.xla_multiprocessing as xmp

def lowercase_  (   ):
							SCREAMING_SNAKE_CASE__						:       Optional[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=_snake_case   ,default=1   ,help="""Number of TPU cores to use (1 or 8)."""						)

							# positional
							parser.add_argument(
							    """training_script"""   ,type=_snake_case   ,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=_snake_case						)

							return parser.parse_args()

def lowercase_  (   ):
							SCREAMING_SNAKE_CASE__						:       int           =   parse_args()

							# Import training_script as a module.
							SCREAMING_SNAKE_CASE__						:       Dict           =   Path(args.training_script						)
							sys.path.append(str(script_fpath.parent.resolve()						)						)
							SCREAMING_SNAKE_CASE__						:       int           =   script_fpath.stem
							SCREAMING_SNAKE_CASE__						:       Optional[Any]           =   importlib.import_module(_snake_case						)

							# Patch sys.argv
							SCREAMING_SNAKE_CASE__						:       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()




