
"""simple docstring"""

from __future__ import annotations

from fractions import Fraction
def 		UpperCAmelCase (		a_,						a_      ):





		'''simple docstring'''


		return (
		    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
		)
def 		UpperCAmelCase (		a_      ):





		'''simple docstring'''


		lowerCamelCase					:      List[str]          =   []
		lowerCamelCase					:      Tuple          =   11
		lowerCamelCase					:      Optional[int]          =   int('1' + '0' * digit_len      )
		for num in range(a_,						a_      ):
				while den <= 99:
						if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
								if is_digit_cancelling(a_,						a_      ):
										solutions.append(F"""{num}/{den}"""      )
						den += 1
				num += 1
				lowerCamelCase					:      Optional[Any]          =   10
		return solutions
def 		UpperCAmelCase (		a_ = 2      ):





		'''simple docstring'''


		lowerCamelCase					:      str          =   1.0
		for fraction in fraction_list(a_      ):
				lowerCamelCase					:      str          =   Fraction(a_      )
				result *= frac.denominator / frac.numerator
		return int(a_      )


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








"""simple docstring"""

import logging
import random

import ray

from transformers import RagConfig, RagRetriever, RagTokenizer
from transformers.models.rag.retrieval_rag import CustomHFIndex


_A						=			logging.getLogger(__name__)






class 	_lowercase       :




	def __init__(			self )		->							Tuple:
			lowerCamelCase					:      Dict          =   False




	def       _UpperCamelCase   (			self		,			UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_ )		->							Any:
			if not self.initialized:
					lowerCamelCase					:      Optional[int]          =   RagRetriever(
					    UpperCAmelCase_		,			question_encoder_tokenizer=UpperCAmelCase_		,			generator_tokenizer=UpperCAmelCase_		,			index=UpperCAmelCase_		,			init_retrieval=UpperCAmelCase_		,			)
					lowerCamelCase					:      Union[str, Any]          =   True




	def       _UpperCamelCase   (			self )		->							Union[str, Any]:
			self.retriever.index.init_index()




	def       _UpperCamelCase   (			self		,			UpperCAmelCase_		,			UpperCAmelCase_ )		->							str:
			lowerCamelCase     ,   lowerCamelCase					:      int          =   self.retriever._main_retrieve(UpperCAmelCase_		,			UpperCAmelCase_ )
			return doc_ids, retrieved_doc_embeds






class 	_lowercase       (    __UpperCAmelCase		):




	def __init__(			self		,			UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_=None )		->							Dict:
			if index is not None and index.is_initialized() and len(UpperCAmelCase_ ) > 0:
					raise ValueError(
					    'When using Ray for distributed fine-tuning, '
					    'you\'ll need to provide the paths instead, '
					    'as the dataset and the index are loaded '
					    'separately. More info in examples/rag/use_own_knowledge_dataset.py ' )
			super().__init__(
			    UpperCAmelCase_		,			question_encoder_tokenizer=UpperCAmelCase_		,			generator_tokenizer=UpperCAmelCase_		,			index=UpperCAmelCase_		,			init_retrieval=UpperCAmelCase_		,			)
			lowerCamelCase					:      List[str]          =   retrieval_workers
			if len(self.retrieval_workers ) > 0:
					ray.get(
					    [
					        worker.create_rag_retriever.remote(UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_ )
					        for worker in self.retrieval_workers
					    ] )




	def       _UpperCamelCase   (			self )		->							Dict:
			logger.info('initializing retrieval' )

			if len(self.retrieval_workers ) > 0:
					ray.get([worker.init_retrieval.remote() for worker in self.retrieval_workers] )
			else:
					# Non-distributed training. Load index into this same process.
					self.index.init_index()




	def       _UpperCamelCase   (			self		,			UpperCAmelCase_		,			UpperCAmelCase_ )		->							List[Any]:
			if len(self.retrieval_workers ) > 0:
					# Select a random retrieval actor.
					lowerCamelCase					:      Tuple          =   self.retrieval_workers[random.randint(0		,			len(self.retrieval_workers ) - 1 )]
					lowerCamelCase     ,   lowerCamelCase					:      Tuple          =   ray.get(random_worker.retrieve.remote(UpperCAmelCase_		,			UpperCAmelCase_ ) )
			else:
					lowerCamelCase     ,   lowerCamelCase					:      int          =   self._main_retrieve(UpperCAmelCase_		,			UpperCAmelCase_ )
			return retrieved_doc_embeds, doc_ids, self.index.get_doc_dicts(UpperCAmelCase_ )




	@classmethod
	def       _UpperCamelCase   (			cls		,			UpperCAmelCase_		,			UpperCAmelCase_=None		,			**UpperCAmelCase_ )		->							Dict:
			return super(UpperCAmelCase_		,			cls ).get_tokenizers(UpperCAmelCase_		,			UpperCAmelCase_		,			**UpperCAmelCase_ )




	@classmethod
	def       _UpperCamelCase   (			cls		,			UpperCAmelCase_		,			UpperCAmelCase_		,			UpperCAmelCase_=None		,			**UpperCAmelCase_ )		->							Dict:
			lowerCamelCase					:      str          =   kwargs.pop('config'		,			UpperCAmelCase_ ) or RagConfig.from_pretrained(UpperCAmelCase_		,			**UpperCAmelCase_ )
			lowerCamelCase					:      Any          =   RagTokenizer.from_pretrained(UpperCAmelCase_		,			config=UpperCAmelCase_ )
			lowerCamelCase					:      Any          =   rag_tokenizer.question_encoder
			lowerCamelCase					:      Union[str, Any]          =   rag_tokenizer.generator
			if indexed_dataset is not None:
					lowerCamelCase					:      int          =   'custom'
					lowerCamelCase					:      int          =   CustomHFIndex(config.retrieval_vector_size		,			UpperCAmelCase_ )
			else:
					lowerCamelCase					:      Optional[Any]          =   cls._build_index(UpperCAmelCase_ )
			return cls(
			    UpperCAmelCase_		,			question_encoder_tokenizer=UpperCAmelCase_		,			generator_tokenizer=UpperCAmelCase_		,			retrieval_workers=UpperCAmelCase_		,			index=UpperCAmelCase_		,			)






