


from typing import TYPE_CHECKING

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


A       :		Optional[int]    =   {"configuration_fnet": ["FNET_PRETRAINED_CONFIG_ARCHIVE_MAP", "FNetConfig"]}

try:
	if not is_sentencepiece_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	A       :		Optional[int]    =   ["FNetTokenizer"]

try:
	if not is_tokenizers_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	A       :		Tuple    =   ["FNetTokenizerFast"]

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	A       :		List[str]    =   [
	    "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

	A       :		List[Any]    =   _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)



from __future__ import annotations

from fractions import Fraction




def  __magic_name__ (   __lowerCAmelCase	:						int		,  __lowerCAmelCase	:						int							)			->   bool:
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)




def  __magic_name__ (   __lowerCAmelCase	:						int							)			->   list[str]:
				__lowerCamelCase    					=	[]
				__lowerCamelCase    					=	11
				__lowerCamelCase    					=	int('''1''' + '''0''' * digit_len							)
				for num in range(__lowerCAmelCase		,  __lowerCAmelCase							):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(__lowerCAmelCase		,  __lowerCAmelCase							):
																				solutions.append(f'''{num}/{den}'''							)
												den += 1
								num += 1
								__lowerCamelCase    					=	10
				return solutions




def  __magic_name__ (   __lowerCAmelCase	:						int = 2							)			->   int:
				__lowerCamelCase    					=	1.0
				for fraction in fraction_list(__lowerCAmelCase							):
								__lowerCamelCase    					=	Fraction(__lowerCAmelCase							)
								result *= frac.denominator / frac.numerator
				return int(__lowerCAmelCase							)


if __name__ == "__main__":
					print(solution())



