





def      _lowercase					(						_UpperCAmelCase				)						->  Optional[int]:
				lowerCamelCase	 =0
				lowerCamelCase	 =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				)						->  Union[str, Any]:
				if len(_UpperCAmelCase				) <= 1:
								return arr, 0
				lowerCamelCase	 =len(_UpperCAmelCase				) // 2
				lowerCamelCase	 =arr[0:mid]
				lowerCamelCase	 =arr[mid:]

				lowerCamelCase ,  lowerCamelCase	 =count_inversions_recursive(_UpperCAmelCase				)
				lowerCamelCase ,  lowerCamelCase	 =count_inversions_recursive(_UpperCAmelCase				)
				lowerCamelCase ,  lowerCamelCase	 =_count_cross_inversions(_UpperCAmelCase			,      _UpperCAmelCase				)

				lowerCamelCase	 =inversion_p + inversions_q + cross_inversions
				return c, num_inversions





def      _lowercase					(						_UpperCAmelCase			,      _UpperCAmelCase				)						->  Optional[int]:
				lowerCamelCase	 =[]
				lowerCamelCase	 =lowerCamelCase	 =lowerCamelCase	 =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					(						)						->  int:
				lowerCamelCase	 =[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	 =count_inversions_bf(_UpperCAmelCase				)
				lowerCamelCase ,  lowerCamelCase	 =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()
				lowerCamelCase	 =count_inversions_bf(_UpperCAmelCase				)
				lowerCamelCase ,  lowerCamelCase	 =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
				lowerCamelCase	 =[]
				lowerCamelCase	 =count_inversions_bf(_UpperCAmelCase				)
				lowerCamelCase ,  lowerCamelCase	 =count_inversions_recursive(_UpperCAmelCase				)

				assert num_inversions_bf == num_inversions_recursive == 0
				print("""number of inversions = """			,      _UpperCAmelCase				)


if __name__ == "__main__":
							main()












from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase__						:			str									={'''configuration_fnet''': ['''FNET_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''FNetConfig''']}

try:
							if not is_sentencepiece_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase__						:			List[Any]									=['''FNetTokenizer''']

try:
							if not is_tokenizers_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase__						:			Any									=['''FNetTokenizerFast''']

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							UpperCAmelCase__						:			Dict									=[
							    '''FNET_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''FNetForMaskedLM''',
							    '''FNetForMultipleChoice''',
							    '''FNetForNextSentencePrediction''',
							    '''FNetForPreTraining''',
							    '''FNetForQuestionAnswering''',
							    '''FNetForSequenceClassification''',
							    '''FNetForTokenClassification''',
							    '''FNetLayer''',
							    '''FNetModel''',
							    '''FNetPreTrainedModel''',
							]


if TYPE_CHECKING:
							from .configuration_fnet import FNET_PRETRAINED_CONFIG_ARCHIVE_MAP, FNetConfig

							try:
														if not is_sentencepiece_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_fnet import FNetTokenizer

							try:
														if not is_tokenizers_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_fnet_fast import FNetTokenizerFast

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_fnet import (
														    FNET_PRETRAINED_MODEL_ARCHIVE_LIST,
														    FNetForMaskedLM,
														    FNetForMultipleChoice,
														    FNetForNextSentencePrediction,
														    FNetForPreTraining,
														    FNetForQuestionAnswering,
														    FNetForSequenceClassification,
														    FNetForTokenClassification,
														    FNetLayer,
														    FNetModel,
														    FNetPreTrainedModel,
														)


else:
							import sys

							UpperCAmelCase__						:			Optional[int]									=_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)





