






"""simple docstring"""



def 						lowercase    (				__snake_case				: Optional[int]	):
		lowercase_ : int							       =   0
		lowercase_ : Optional[Any]							       =   len(__snake_case	)

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

		return num_inversions



def 						lowercase    (				__snake_case				: str	):
		if len(__snake_case	) <= 1:
				return arr, 0
		lowercase_ : Optional[Any]							       =   len(__snake_case	) // 2
		lowercase_ : List[Any]							       =   arr[0:mid]
		lowercase_ : Union[str, Any]							       =   arr[mid:]

		lowercase_       ,					lowercase_ : Tuple							       =   count_inversions_recursive(__snake_case	)
		lowercase_       ,					lowercase_ : List[Any]							       =   count_inversions_recursive(__snake_case	)
		lowercase_       ,					lowercase_ : List[Any]							       =   _count_cross_inversions(__snake_case		,					__snake_case	)

		lowercase_ : List[Any]							       =   inversion_p + inversions_q + cross_inversions
		return c, num_inversions



def 						lowercase    (				__snake_case				: str		,					__snake_case				: Optional[int]	):
		lowercase_ : Optional[Any]							       =   []
		lowercase_ : Any							       =   0
		while i < len(__snake_case	) and j < len(__snake_case	):
				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(__snake_case	) - i
						r.append(q[j]	)
						j += 1
				else:
						r.append(p[i]	)
						i += 1

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

		return r, num_inversion



def 						lowercase    (				):
		lowercase_ : Union[str, Any]							       =   [1_0, 2, 1, 5, 5, 2, 1_1]

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

		lowercase_ : int							       =   count_inversions_bf(__snake_case	)
		lowercase_       ,					lowercase_ : Dict							       =   count_inversions_recursive(__snake_case	)

		assert num_inversions_bf == num_inversions_recursive == 8

		print('''number of inversions = '''		,					__snake_case	)

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

		arr_a.sort()
		lowercase_ : Dict							       =   count_inversions_bf(__snake_case	)
		lowercase_       ,					lowercase_ : Dict							       =   count_inversions_recursive(__snake_case	)

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

		# an empty list should also have zero inversions
		lowercase_ : List[Any]							       =   []
		lowercase_ : Any							       =   count_inversions_bf(__snake_case	)
		lowercase_       ,					lowercase_ : List[str]							       =   count_inversions_recursive(__snake_case	)

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


if __name__ == "__main__":
						main()





from typing import TYPE_CHECKING

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


__A				={'''configuration_xglm''': ['''XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''XGLMConfig''']}

try:
			if not is_sentencepiece_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__A				=['''XGLMTokenizer''']

try:
			if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__A				=['''XGLMTokenizerFast''']

try:
			if not is_torch_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__A				=[
			    '''XGLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''XGLMForCausalLM''',
			    '''XGLMModel''',
			    '''XGLMPreTrainedModel''',
			]


try:
			if not is_flax_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__A				=[
			    '''FlaxXGLMForCausalLM''',
			    '''FlaxXGLMModel''',
			    '''FlaxXGLMPreTrainedModel''',
			]


try:
			if not is_tf_available():
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			pass
else:
			__A				=[
			    '''TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
			    '''TFXGLMForCausalLM''',
			    '''TFXGLMModel''',
			    '''TFXGLMPreTrainedModel''',
			]


if TYPE_CHECKING:
			from .configuration_xglm import XGLM_PRETRAINED_CONFIG_ARCHIVE_MAP, XGLMConfig

			try:
						if not is_sentencepiece_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .tokenization_xglm import XGLMTokenizer

			try:
						if not is_tokenizers_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .tokenization_xglm_fast import XGLMTokenizerFast

			try:
						if not is_torch_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_xglm import XGLM_PRETRAINED_MODEL_ARCHIVE_LIST, XGLMForCausalLM, XGLMModel, XGLMPreTrainedModel

			try:
						if not is_flax_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_flax_xglm import FlaxXGLMForCausalLM, FlaxXGLMModel, FlaxXGLMPreTrainedModel

			try:
						if not is_tf_available():
									raise OptionalDependencyNotAvailable()
			except OptionalDependencyNotAvailable:
						pass
			else:
						from .modeling_tf_xglm import (
						    TF_XGLM_PRETRAINED_MODEL_ARCHIVE_LIST,
						    TFXGLMForCausalLM,
						    TFXGLMModel,
						    TFXGLMPreTrainedModel,
						)


else:
			import sys

			__A				=_LazyModule(__name__, globals()['''__file__'''], _import_structure)


