




'''simple docstring'''



def   lowercase__(			__UpperCamelCase:					Any    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						0
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						len(__UpperCamelCase    )

      for i in range(n - 1    ):
            for j in range(i + 1      ,__UpperCamelCase    ):
                  if arr[i] > arr[j]:
                        num_inversions += 1

      return num_inversions




def   lowercase__(			__UpperCamelCase:					str    ):

      """simple docstring"""






      if len(__UpperCamelCase    ) <= 1:
            return arr, 0
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						len(__UpperCamelCase    ) // 2
      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						arr[0:mid]
      SCREAMING_SNAKE_CASE   :      Any    					=						arr[mid:]

      SCREAMING_SNAKE_CASE   :      List[Any]    					=						count_inversions_recursive(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Tuple    					=						count_inversions_recursive(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      str    					=						_count_cross_inversions(__UpperCamelCase      ,__UpperCamelCase    )

      SCREAMING_SNAKE_CASE   :      Tuple    					=						inversion_p + inversions_q + cross_inversions
      return c, num_inversions




def   lowercase__(			__UpperCamelCase:					int      ,__UpperCamelCase:					str    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      str    					=						[]
      SCREAMING_SNAKE_CASE   :      str    					=						0
      while i < len(__UpperCamelCase    ) and j < len(__UpperCamelCase    ):
            if p[i] > q[j]:
                  # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
                  # These are all inversions. The claim emerges from the
                  # property that P is sorted.
                  num_inversion += len(__UpperCamelCase    ) - i
                  r.append(q[j]    )
                  j += 1
            else:
                  r.append(p[i]    )
                  i += 1

      if i < len(__UpperCamelCase    ):
            r.extend(p[i:]    )
      else:
            r.extend(q[j:]    )

      return r, num_inversion




def   lowercase__(			):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Union[str, Any]    					=						[10, 2, 1, 5, 5, 2, 11]

      # this arr has 8 inversions:
      # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

      SCREAMING_SNAKE_CASE   :      Dict    					=						count_inversions_bf(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						count_inversions_recursive(__UpperCamelCase    )

      assert num_inversions_bf == num_inversions_recursive == 8

      print('number of inversions = '      ,__UpperCamelCase    )

      # testing an array with zero inversion (a sorted arr_1)

      arr_a.sort()
      SCREAMING_SNAKE_CASE   :      List[Any]    					=						count_inversions_bf(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      Any    					=						count_inversions_recursive(__UpperCamelCase    )

      assert num_inversions_bf == num_inversions_recursive == 0
      print('number of inversions = '      ,__UpperCamelCase    )

      # an empty list should also have zero inversions
      SCREAMING_SNAKE_CASE   :      str    					=						[]
      SCREAMING_SNAKE_CASE   :      str    					=						count_inversions_bf(__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      int    					=						count_inversions_recursive(__UpperCamelCase    )

      assert num_inversions_bf == num_inversions_recursive == 0
      print('number of inversions = '      ,__UpperCamelCase    )


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  __magic_name__  (				)				-> str:

							"""simple docstring"""



							lowercase_	:   Optional[int]  				=     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=lowercase				,       default=1				,       help="""Number of TPU cores to use (1 or 8)."""				)

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

							return parser.parse_args()





def  __magic_name__  (				)				-> List[Any]:

							"""simple docstring"""



							lowercase_	:   Union[str, Any]  				=     parse_args()

							# Import training_script as a module.
							lowercase_	:   List[Any]  				=     Path(args.training_script				)
							sys.path.append(str(script_fpath.parent.resolve()				)				)
							lowercase_	:   Tuple  				=     script_fpath.stem
							lowercase_	:   List[str]  				=     importlib.import_module(lowercase				)

							# Patch sys.argv
							lowercase_	:   Optional[int]  				=     [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()