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

import torch_xla.distributed.xla_multiprocessing as xmp


def 							SCREAMING_SNAKE_CASE_      (			):
      UpperCamelCase__    :   List[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=__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 							SCREAMING_SNAKE_CASE_      (			):
      UpperCamelCase__    :   List[str]					=				parse_args()

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

      # Patch sys.argv
      UpperCamelCase__    :   Tuple					=				[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 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__		):
      UpperCamelCase__    :   List[str]					=				math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

      return exponent == int(UpperCamelCase__		)


def 							SCREAMING_SNAKE_CASE_      (			UpperCamelCase__ = 1 / 1_2_3_4_5		):
      UpperCamelCase__    :   Dict					=				0
      UpperCamelCase__    :   Tuple					=				0

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


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


