






'''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		(     )			->		int:

      '''simple docstring'''


      _A     	=      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    __lowercase		(     )			->		str:

      '''simple docstring'''


      _A     	=      parse_args()

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

      # Patch sys.argv
      _A     	=      [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 math import isqrt, loga







def 						lowerCamelCase__      ( __A    :int		):


       """simple docstring"""




       __snake_case       	=							[True] * max_number
       for i in range(2	,isqrt(max_number - 1		) + 1		):
              if is_prime[i]:
                     for j in range(i**2	,__A	,__A		):
                            __snake_case       	=							False

       return [i for i in range(2	,__A		) if is_prime[i]]







def 						lowerCamelCase__      ( __A    :int = 8_0_0_8_0_0	,__A    :int = 8_0_0_8_0_0		):


       """simple docstring"""




       __snake_case       	=							degree * loga(__A		)
       __snake_case       	=							int(__A		)
       __snake_case       	=							calculate_prime_numbers(__A		)

       __snake_case       	=							0
       __snake_case       	=							0
       __snake_case       	=							len(__A		) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left]		)
                  + prime_numbers[left] * loga(prime_numbers[right]		)
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


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

