





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

import torch_xla.distributed.xla_multiprocessing as xmp


def _A       (   ):
   lowercase__			       =  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=__magic_name__  , default=1  , help="Number of TPU cores to use (1 or 8)."	)

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

   return parser.parse_args()


def _A       (   ):
   lowercase__			       =  parse_args()

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

   # Patch sys.argv
   lowercase__			       =  [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()













import math


def _A       (   __magic_name__	):
   lowercase__			       =  math.loga(math.sqrt(4 * positive_integer + 1	) / 2 + 1 / 2	)

   return exponent == int(__magic_name__	)


def _A       (   __magic_name__ = 1 / 1_2345	):
   lowercase__			       =  0
   lowercase__			       =  0

   lowercase__			       =  3
   while True:
      lowercase__			       =  (integer**2 - 1) / 4
      # if candidate is an integer, then there is a partition for k
      if partition_candidate == int(__magic_name__	):
         lowercase__			       =  int(__magic_name__	)
         total_partitions += 1
         if check_partition_perfect(__magic_name__	):
            perfect_partitions += 1
      if perfect_partitions > 0:
         if perfect_partitions / total_partitions < max_proportion:
            return int(__magic_name__	)
      integer += 1


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






