


from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar




class  A_ (			__A  ):







 """simple docstring"""





 @abstractmethod
 def __lt__(      self       :			Any							,     _a       :			Tuple					)     ->      bool:
      pass
 @abstractmethod
 def __gt__(      self       :			List[str]							,     _a       :			int					)     ->      bool:
      pass

 @abstractmethod
 def __eq__(      self       :			str							,     _a       :			Optional[int]					)     ->      bool:
      pass
_snake_case				=			TypeVar("T", bound=Comparable)




class  A_ (			Generic[T]  ):







 """simple docstring"""





 def __init__(      self       :			int					)     ->      None:
      UpperCAmelCase    :					list[T]			=      []
      UpperCAmelCase    :					int			=      0
 def __repr__(      self       :			str					)     ->      str:
      return str(self.h					)
 def 	_UpperCamelCase     (      self       :			Dict							,     _a       :			Tuple					)     ->      int | None:

      if child_idx > 0:
           return (child_idx - 1) // 2
      return None
 def 	_UpperCamelCase     (      self       :			Tuple							,     _a       :			Dict					)     ->      int | None:
      UpperCAmelCase    :					str			=      2 * parent_idx + 1
      if left_child_index < self.heap_size:
           return left_child_index
      return None
 def 	_UpperCamelCase     (      self       :			Any							,     _a       :			Dict					)     ->      int | None:
      UpperCAmelCase    :					List[Any]			=      2 * parent_idx + 2
      if right_child_index < self.heap_size:
           return right_child_index
      return None
 def 	_UpperCamelCase     (      self       :			int							,     _a       :			Dict					)     ->      None:

      if index < self.heap_size:
           UpperCAmelCase    :					int			=      index
           UpperCAmelCase    :					int			=      self.left_child_idx(__snake_case					)
           UpperCAmelCase    :					List[str]			=      self.right_child_idx(__snake_case					)
           # check which child is larger than its parent
           if left_child is not None and self.h[left_child] > self.h[violation]:
                UpperCAmelCase    :					int			=      left_child
           if right_child is not None and self.h[right_child] > self.h[violation]:
                UpperCAmelCase    :					List[Any]			=      right_child
           # if violation indeed exists
           if violation != index:
                # swap to fix the violation
                UpperCAmelCase    :					List[str]			=      self.h[index], self.h[violation]
                # fix the subsequent violation recursively if any
                self.max_heapify(__snake_case					)
 def 	_UpperCamelCase     (      self       :			List[Any]							,     _a       :			Tuple					)     ->      None:
      UpperCAmelCase    :					Dict			=      list(__snake_case					)
      UpperCAmelCase    :					List[Any]			=      len(self.h					)
      if self.heap_size > 1:
           # max_heapify from right to left but exclude leaves (last level)
           for i in range(self.heap_size // 2 - 1							,     -1							,     -1					):
                self.max_heapify(__snake_case					)
 def 	_UpperCamelCase     (      self       :			Union[str, Any]					)     ->      T:

      if self.heap_size >= 2:
           UpperCAmelCase    :					Dict			=      self.h[0]
           UpperCAmelCase    :					int			=      self.h.pop(-1					)
           self.heap_size -= 1
           self.max_heapify(0					)
           return me
      elif self.heap_size == 1:
           self.heap_size -= 1
           return self.h.pop(-1					)
      else:
           raise Exception("Empty heap"					)
 def 	_UpperCamelCase     (      self       :			List[Any]							,     _a       :			str					)     ->      None:
      self.h.append(__snake_case					)
      UpperCAmelCase    :					Tuple			=      (self.heap_size - 1) // 2
      self.heap_size += 1
      while idx >= 0:
           self.max_heapify(__snake_case					)
           UpperCAmelCase    :					Any			=      (idx - 1) // 2

 def 	_UpperCamelCase     (      self       :			Optional[Any]					)     ->      None:
      UpperCAmelCase    :					Any			=      self.heap_size
      for j in range(size - 1							,     0							,     -1					):
           UpperCAmelCase    :					Optional[Any]			=      self.h[j], self.h[0]
           self.heap_size -= 1
           self.max_heapify(0					)
      UpperCAmelCase    :					List[Any]			=      size


if __name__ == "__main__":
      import doctest

      # run doc test
      doctest.testmod()

      # demo
      for unsorted in [
          [0],
          [2],
          [3, 5],
          [5, 3],
          [5, 5],
          [0, 0, 0, 0],
          [1, 1, 1, 1],
          [2, 2, 3, 5],
          [0, 2, 2, 3, 5],
          [2, 5, 3, 0, 2, 3, 0, 3],
          [6, 1, 2, 7, 9, 3, 4, 5, 1_0, 8],
          [1_0_3, 9, 1, 7, 1_1, 1_5, 2_5, 2_0_1, 2_0_9, 1_0_7, 5],
          [-4_5, -2, -5],
      ]:
            print(f'''unsorted array: {unsorted}''')

            _snake_case				=			Heap()
            heap.build_max_heap(unsorted)
            print(f'''after build heap: {heap}''')

            print(f'''max value: {heap.extract_max()}''')
            print(f'''after max value removed: {heap}''')

            heap.insert(1_0_0)
            print(f'''after new value 100 inserted: {heap}''')

            heap.heap_sort()
            print(f'''heap-sorted array: {heap}\n''')










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

import torch_xla.distributed.xla_multiprocessing as xmp







def  A					(				):
					_snake_case							:       Optional[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  A					(				):
					_snake_case							:       Any												= parse_args()

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

					# Patch sys.argv
					_snake_case							:       str												= [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()