


def 		lowercase_(  SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_     ):


  '''simple docstring'''

  if start == end:
    return start if lst[start] > item else start + 1
  if start > end:
    return start

  lowerCamelCase			: Tuple   =    (start + end) // 2
  if lst[mid] < item:
    return binary_search(SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_				,						mid + 1				,						SCREAMING_SNAKE_CASE_     )
  elif lst[mid] > item:
    return binary_search(SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_				,						mid - 1     )
  else:
    return mid






def 		lowercase_(  SCREAMING_SNAKE_CASE_     ):


  '''simple docstring'''

  lowerCamelCase			: int   =    len(SCREAMING_SNAKE_CASE_     )

  for index in range(1				,						SCREAMING_SNAKE_CASE_     ):
    lowerCamelCase			: List[Any]   =    lst[index]
    lowerCamelCase			: List[str]   =    binary_search(SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_				,						0				,						index - 1     )
    lowerCamelCase			: Union[str, Any]   =    lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]

  return lst






def 		lowercase_(  SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_     ):


  '''simple docstring'''

  if not left:
    return right

  if not right:
    return left

  if left[0] < right[0]:
    return [left[0], *merge(left[1:]				,						SCREAMING_SNAKE_CASE_     )]

  return [right[0], *merge(SCREAMING_SNAKE_CASE_				,						right[1:]     )]






def 		lowercase_(  SCREAMING_SNAKE_CASE_     ):


  '''simple docstring'''

  lowerCamelCase			: List[Any]   =    len(SCREAMING_SNAKE_CASE_     )
  lowerCamelCase   ,     lowerCamelCase			: List[str]   =    [], []
  lowerCamelCase			: Union[str, Any]   =    [lst[0]]
  lowerCamelCase			: Optional[Any]   =    []
  lowerCamelCase			: int   =    1
  while i < length:
    if lst[i] < lst[i - 1]:
      runs.append(SCREAMING_SNAKE_CASE_     )
      lowerCamelCase			: Any   =    [lst[i]]
    else:
      new_run.append(lst[i]     )
    i += 1
  runs.append(SCREAMING_SNAKE_CASE_     )

  for run in runs:
    sorted_runs.append(insertion_sort(SCREAMING_SNAKE_CASE_     )     )
  for run in sorted_runs:
    lowerCamelCase			: int   =    merge(SCREAMING_SNAKE_CASE_				,						SCREAMING_SNAKE_CASE_     )

  return sorted_array






def 		lowercase_(  ):


  '''simple docstring'''

  lowerCamelCase			: Tuple   =    [5, 9, 10, 3, -4, 5, 178, 92, 46, -18, 0, 7]
  lowerCamelCase			: List[Any]   =    tim_sort(SCREAMING_SNAKE_CASE_     )
  print(SCREAMING_SNAKE_CASE_     )


if __name__ == "__main__":
   main()







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

import torch_xla.distributed.xla_multiprocessing as xmp






def 		lowercase_(  ):


  '''simple docstring'''

  lowerCamelCase			: str   =    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=SCREAMING_SNAKE_CASE_				,						default=1				,						help="Number of TPU cores to use (1 or 8)."     )

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

  return parser.parse_args()






def 		lowercase_(  ):


  '''simple docstring'''

  lowerCamelCase			: Optional[Any]   =    parse_args()

  # Import training_script as a module.
  lowerCamelCase			: Tuple   =    Path(args.training_script     )
  sys.path.append(str(script_fpath.parent.resolve()     )     )
  lowerCamelCase			: int   =    script_fpath.stem
  lowerCamelCase			: Tuple   =    importlib.import_module(SCREAMING_SNAKE_CASE_     )

  # Patch sys.argv
  lowerCamelCase			: Union[str, Any]   =    [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()



