


'''simple docstring'''

from __future__ import annotations

from fractions import Fraction





def __snake_case					(      UpperCAmelCase_						:						int					,				UpperCAmelCase_						:						int		):
 return (
     num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
 )





def __snake_case					(      UpperCAmelCase_						:						int		):
 lowerCamelCase_      =  []
 lowerCamelCase_      =  11
 lowerCamelCase_      =  int("1" + "0" * digit_len		)
 for num in range(UpperCAmelCase_					,				UpperCAmelCase_		):
  while den <= 99:
   if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
    if is_digit_cancelling(UpperCAmelCase_					,				UpperCAmelCase_		):
     solutions.append(F'''{num}/{den}'''		)
   den += 1
  num += 1
  lowerCamelCase_      =  10
 return solutions





def __snake_case					(      UpperCAmelCase_						:						int = 2		):
 lowerCamelCase_      =  1.0
 for fraction in fraction_list(UpperCAmelCase_		):
  lowerCamelCase_      =  Fraction(UpperCAmelCase_		)
  result *= frac.denominator / frac.numerator
 return int(UpperCAmelCase_		)


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










'''simple docstring'''
from typing import List, Optional, Union

from ...image_utils import ImageInput
from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType

class      snake_case     (    __lowerCamelCase       ):




 """simple docstring"""



 SCREAMING_SNAKE_CASE_	:					Any					=["image_processor", "tokenizer"]
 SCREAMING_SNAKE_CASE_	:					List[Any]					="BlipImageProcessor"
 SCREAMING_SNAKE_CASE_	:					Optional[int]					=("BertTokenizer", "BertTokenizerFast")






 def __init__(       self       :							Dict							,	__A       :							Optional[int]							,	__A       :							List[Any]	):
        __UpperCamelCase       =  False
        super().__init__(__A							,	__A	)
        __UpperCamelCase       =  self.image_processor






 def __call__(       self       :							List[Any]							,	__A       :							ImageInput = None							,	__A       :							Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None							,	__A       :							bool = True							,	__A       :							Union[bool, str, PaddingStrategy] = False							,	__A       :							Union[bool, str, TruncationStrategy] = None							,	__A       :							Optional[int] = None							,	__A       :							int = 0							,	__A       :							Optional[int] = None							,	__A       :							Optional[bool] = None							,	__A       :							bool = False							,	__A       :							bool = False							,	__A       :							bool = False							,	__A       :							bool = False							,	__A       :							bool = False							,	__A       :							bool = True							,	__A       :							Optional[Union[str, TensorType]] = None							,	**__A       :							List[Any]							,	):
        if images is None and text is None:
               raise ValueError('You have to specify either images or text.'	)

        # Get only text
        if images is None:
               __UpperCamelCase       =  self.tokenizer
               __UpperCamelCase       =  self.tokenizer(
                   text=__A							,	add_special_tokens=__A							,	padding=__A							,	truncation=__A							,	max_length=__A							,	stride=__A							,	pad_to_multiple_of=__A							,	return_attention_mask=__A							,	return_overflowing_tokens=__A							,	return_special_tokens_mask=__A							,	return_offsets_mapping=__A							,	return_token_type_ids=__A							,	return_length=__A							,	verbose=__A							,	return_tensors=__A							,	**__A							,	)
               return text_encoding

        # add pixel_values
        __UpperCamelCase       =  self.image_processor(__A							,	return_tensors=__A	)

        if text is not None:
               __UpperCamelCase       =  self.tokenizer(
                   text=__A							,	add_special_tokens=__A							,	padding=__A							,	truncation=__A							,	max_length=__A							,	stride=__A							,	pad_to_multiple_of=__A							,	return_attention_mask=__A							,	return_overflowing_tokens=__A							,	return_special_tokens_mask=__A							,	return_offsets_mapping=__A							,	return_token_type_ids=__A							,	return_length=__A							,	verbose=__A							,	return_tensors=__A							,	**__A							,	)
        else:
               __UpperCamelCase       =  None

        if text_encoding is not None:
               encoding_image_processor.update(__A	)

        return encoding_image_processor






 def        _lowerCamelCase					(       self       :							List[Any]							,	*__A       :							Dict							,	**__A       :							Optional[int]	):
        return self.tokenizer.batch_decode(*__A							,	**__A	)






 def        _lowerCamelCase					(       self       :							List[Any]							,	*__A       :							List[str]							,	**__A       :							Dict	):
        return self.tokenizer.decode(*__A							,	**__A	)






 @property
 def        _lowerCamelCase					(       self       :							Tuple	):
        __UpperCamelCase       =  self.tokenizer.model_input_names
        __UpperCamelCase       =  self.image_processor.model_input_names
        return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names	)	)
