
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		Optional[int]:
			lowerCAmelCase__      :      str         =		0
			lowerCAmelCase__      :      Union[str, Any]         =		len(__lowerCAmelCase     )

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

			return num_inversions
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		Union[str, Any]:
			if len(__lowerCAmelCase     ) <= 1:
						return arr, 0
			lowerCAmelCase__      :      Any         =		len(__lowerCAmelCase     ) // 2
			lowerCAmelCase__      :      Union[str, Any]         =		arr[0:mid]
			lowerCAmelCase__      :      Any         =		arr[mid:]

			lowerCAmelCase__      :      List[str]         =		count_inversions_recursive(__lowerCAmelCase     )
			lowerCAmelCase__      :      List[Any]         =		count_inversions_recursive(__lowerCAmelCase     )
			lowerCAmelCase__      :      Optional[int]         =		_count_cross_inversions(__lowerCAmelCase       ,							__lowerCAmelCase     )

			lowerCAmelCase__      :      List[str]         =		inversion_p + inversions_q + cross_inversions
			return c, num_inversions
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     )				->		Optional[int]:
			lowerCAmelCase__      :      str         =		[]
			lowerCAmelCase__      :      Any         =		0
			while i < len(__lowerCAmelCase     ) and j < len(__lowerCAmelCase     ):
						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(__lowerCAmelCase     ) - i
									r.append(q[j]     )
									j += 1
						else:
									r.append(p[i]     )
									i += 1

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

			return r, num_inversion
def  lowerCAmelCase__			(  )				->		str:
			lowerCAmelCase__      :      int         =		[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)

			lowerCAmelCase__      :      List[str]         =		count_inversions_bf(__lowerCAmelCase     )
			lowerCAmelCase__      :      Dict         =		count_inversions_recursive(__lowerCAmelCase     )

			assert num_inversions_bf == num_inversions_recursive == 8

			print('number of inversions = '       ,							__lowerCAmelCase     )

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

			arr_a.sort()
			lowerCAmelCase__      :      Dict         =		count_inversions_bf(__lowerCAmelCase     )
			lowerCAmelCase__      :      str         =		count_inversions_recursive(__lowerCAmelCase     )

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

			# an empty list should also have zero inversions
			lowerCAmelCase__      :      Dict         =		[]
			lowerCAmelCase__      :      Tuple         =		count_inversions_bf(__lowerCAmelCase     )
			lowerCAmelCase__      :      str         =		count_inversions_recursive(__lowerCAmelCase     )

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


if __name__ == "__main__":
					main()







from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCamelCase	:							Tuple				={
    '''configuration_luke''': ['''LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''LukeConfig'''],
    '''tokenization_luke''': ['''LukeTokenizer'''],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 lowerCamelCase	:							Union[str, Any]				=[
     '''LUKE_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''LukeForEntityClassification''',
     '''LukeForEntityPairClassification''',
     '''LukeForEntitySpanClassification''',
     '''LukeForMultipleChoice''',
     '''LukeForQuestionAnswering''',
     '''LukeForSequenceClassification''',
     '''LukeForTokenClassification''',
     '''LukeForMaskedLM''',
     '''LukeModel''',
     '''LukePreTrainedModel''',
 ]


if TYPE_CHECKING:
 from .configuration_luke import LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP, LukeConfig
 from .tokenization_luke import LukeTokenizer

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_luke import (
      LUKE_PRETRAINED_MODEL_ARCHIVE_LIST,
      LukeForEntityClassification,
      LukeForEntityPairClassification,
      LukeForEntitySpanClassification,
      LukeForMaskedLM,
      LukeForMultipleChoice,
      LukeForQuestionAnswering,
      LukeForSequenceClassification,
      LukeForTokenClassification,
      LukeModel,
      LukePreTrainedModel,
  )

else:
 import sys

 lowerCamelCase	:							Dict				=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)