



"""simple docstring"""






from __future__ import annotations

from fractions import Fraction






def 			snake_case_    ( A_   :						int,							A_   :						int		):


       '''simple docstring'''





       return (
           num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
       )






def 			snake_case_    ( A_   :						int		):


       '''simple docstring'''





       _lowerCamelCase		:							Optional[int]            =					[]
       _lowerCamelCase		:							int            =					11
       _lowerCamelCase		:							Any            =					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		:							Dict            =					10
       return solutions






def 			snake_case_    ( A_   :						int = 2		):


       '''simple docstring'''





       _lowerCamelCase		:							List[str]            =					1.0
       for fraction in fraction_list(A_		):
              _lowerCamelCase		:							List[Any]            =					Fraction(A_		)
              result *= frac.denominator / frac.numerator
       return int(A_		)


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









'''simple docstring'''




import unittest

import numpy as np

from transformers import RobertaConfig, is_flax_available
from transformers.testing_utils import require_flax, slow

from ...test_modeling_flax_common import FlaxModelTesterMixin, floats_tensor, ids_tensor, random_attention_mask


if is_flax_available():
			from transformers.models.roberta.modeling_flax_roberta import (
			    FlaxRobertaForCausalLM,
			    FlaxRobertaForMaskedLM,
			    FlaxRobertaForMultipleChoice,
			    FlaxRobertaForQuestionAnswering,
			    FlaxRobertaForSequenceClassification,
			    FlaxRobertaForTokenClassification,
			    FlaxRobertaModel,
			)






class 				__snake_case     (					unittest.TestCase							):





	def __init__(		self      ,       UpperCamelCase_      ,       UpperCamelCase_=13      ,       UpperCamelCase_=7      ,       UpperCamelCase_=True      ,       UpperCamelCase_=True      ,       UpperCamelCase_=True      ,       UpperCamelCase_=True      ,       UpperCamelCase_=99      ,       UpperCamelCase_=32      ,       UpperCamelCase_=5      ,       UpperCamelCase_=4      ,       UpperCamelCase_=37      ,       UpperCamelCase_="gelu"      ,       UpperCamelCase_=0.1      ,       UpperCamelCase_=0.1      ,       UpperCamelCase_=512      ,       UpperCamelCase_=16      ,       UpperCamelCase_=2      ,       UpperCamelCase_=0.0_2      ,       UpperCamelCase_=4      ,       )      ->		List[Any]:
		snake_case__	       =   parent
		snake_case__	       =   batch_size
		snake_case__	       =   seq_length
		snake_case__	       =   is_training
		snake_case__	       =   use_attention_mask
		snake_case__	       =   use_token_type_ids
		snake_case__	       =   use_labels
		snake_case__	       =   vocab_size
		snake_case__	       =   hidden_size
		snake_case__	       =   num_hidden_layers
		snake_case__	       =   num_attention_heads
		snake_case__	       =   intermediate_size
		snake_case__	       =   hidden_act
		snake_case__	       =   hidden_dropout_prob
		snake_case__	       =   attention_probs_dropout_prob
		snake_case__	       =   max_position_embeddings
		snake_case__	       =   type_vocab_size
		snake_case__	       =   type_sequence_label_size
		snake_case__	       =   initializer_range
		snake_case__	       =   num_choices





	def   _snake_case   (		self		)      ->		Any:
		snake_case__	       =   ids_tensor([self.batch_size, self.seq_length]      ,       self.vocab_size		)

		snake_case__	       =   None
		if self.use_attention_mask:
			snake_case__	       =   random_attention_mask([self.batch_size, self.seq_length]		)

		snake_case__	       =   None
		if self.use_token_type_ids:
			snake_case__	       =   ids_tensor([self.batch_size, self.seq_length]      ,       self.type_vocab_size		)

		snake_case__	       =   RobertaConfig(
		    vocab_size=self.vocab_size      ,       hidden_size=self.hidden_size      ,       num_hidden_layers=self.num_hidden_layers      ,       num_attention_heads=self.num_attention_heads      ,       intermediate_size=self.intermediate_size      ,       hidden_act=self.hidden_act      ,       hidden_dropout_prob=self.hidden_dropout_prob      ,       attention_probs_dropout_prob=self.attention_probs_dropout_prob      ,       max_position_embeddings=self.max_position_embeddings      ,       type_vocab_size=self.type_vocab_size      ,       is_decoder=UpperCamelCase_      ,       initializer_range=self.initializer_range      ,       )

		return config, input_ids, token_type_ids, attention_mask





	def   _snake_case   (		self		)      ->		Tuple:
		snake_case__	       =   self.prepare_config_and_inputs()
		snake_case__       ,  snake_case__       ,  snake_case__       ,  snake_case__	       =   config_and_inputs
		snake_case__	       =   {'input_ids': input_ids, 'token_type_ids': token_type_ids, 'attention_mask': attention_mask}
		return config, inputs_dict





	def   _snake_case   (		self		)      ->		Union[str, Any]:
		snake_case__	       =   self.prepare_config_and_inputs()
		snake_case__       ,  snake_case__       ,  snake_case__       ,  snake_case__	       =   config_and_inputs

		snake_case__	       =   True
		snake_case__	       =   floats_tensor([self.batch_size, self.seq_length, self.hidden_size]		)
		snake_case__	       =   ids_tensor([self.batch_size, self.seq_length]      ,       vocab_size=2		)

		return (
		    config,
		    input_ids,
		    token_type_ids,
		    encoder_hidden_states,
		    encoder_attention_mask,
		)






@require_flax
class 				__snake_case     (					__magic_name__       ,       unittest.TestCase							):
	__lowerCAmelCase       						=  True

	__lowerCAmelCase       						=  (
	    (
	        FlaxRobertaModel,
	        FlaxRobertaForCausalLM,
	        FlaxRobertaForMaskedLM,
	        FlaxRobertaForSequenceClassification,
	        FlaxRobertaForTokenClassification,
	        FlaxRobertaForMultipleChoice,
	        FlaxRobertaForQuestionAnswering,
	    )
	    if is_flax_available()
	    else ()
	)





	def   _snake_case   (		self		)      ->		List[Any]:
		snake_case__	       =   FlaxRobertaModelTester(self		)





	@slow
	def   _snake_case   (		self		)      ->		Tuple:
		for model_class_name in self.all_model_classes:
			snake_case__	       =   model_class_name.from_pretrained('roberta-base'      ,       from_pt=UpperCamelCase_		)
			snake_case__	       =   model(np.ones((1, 1)		)		)
			self.assertIsNotNone(UpperCamelCase_		)



