


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

import torch_xla.distributed.xla_multiprocessing as xmp





def __UpperCAmelCase							(		)    ->       Dict:



       '''simple docstring'''





       UpperCAmelCase__					    =  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=__UpperCamelCase			,    default=1			,    help="Number of TPU cores to use (1 or 8)."      )

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

       return parser.parse_args()





def __UpperCAmelCase							(		)    ->       Optional[Any]:



       '''simple docstring'''





       UpperCAmelCase__					    =  parse_args()

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

       # Patch sys.argv
       UpperCAmelCase__					    =  [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()











'''simple docstring'''



def   lowercase__(			__UpperCamelCase:					int = 1_00_00_00    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Tuple    					=						[i - 1 for i in range(limit + 1    )]

      for i in range(2      ,limit + 1    ):
            if phi[i] == i - 1:
                  for j in range(2 * i      ,limit + 1      ,__UpperCamelCase    ):
                        phi[j] -= phi[j] // i

      return sum(phi[2 : limit + 1]    )


if __name__ == "__main__":
      print(solution())


