




from __future__ import annotations

from fractions import Fraction







def lowerCamelCase__  (     _lowercase					,		_lowercase ):

     '''simple docstring'''


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







def lowerCamelCase__  (     _lowercase ):

     '''simple docstring'''


     UpperCAmelCase_     :				Optional[int]  =     []
     UpperCAmelCase_     :				List[Any]  =     11
     UpperCAmelCase_     :				Union[str, Any]  =     int('''1''' + '''0''' * digit_len )
     for num in range(_lowercase					,		_lowercase ):
          while den <= 99:
               if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
                    if is_digit_cancelling(_lowercase					,		_lowercase ):
                         solutions.append(f'''{num}/{den}''' )
               den += 1
          num += 1
          UpperCAmelCase_     :				Dict  =     10
     return solutions







def lowerCamelCase__  (     _lowercase = 2 ):

     '''simple docstring'''


     UpperCAmelCase_     :				Tuple  =     1.0
     for fraction in fraction_list(_lowercase ):
          UpperCAmelCase_     :				List[str]  =     Fraction(_lowercase )
          result *= frac.denominator / frac.numerator
     return int(_lowercase )


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





import unittest

from transformers import is_torch_available, is_vision_available
from transformers.testing_utils import require_torch, require_vision, slow, torch_device


if is_torch_available():
     import torch

     from transformers import AutoModelForImageClassification

if is_vision_available():
     from transformers import AutoImageProcessor

@require_torch
@require_vision
class     __a(	unittest.TestCase  ):






    """simple docstring"""





    @slow
    def 				a__ ( self    )					->						List[str]:
         UpperCAmelCase_     :				Tuple  =     AutoImageProcessor.from_pretrained('''microsoft/dit-base-finetuned-rvlcdip'''    )
         UpperCAmelCase_     :				Union[str, Any]  =     AutoModelForImageClassification.from_pretrained('''microsoft/dit-base-finetuned-rvlcdip'''    )
         model.to(_SCREAMING_SNAKE_CASE    )

         from datasets import load_dataset

         UpperCAmelCase_     :				Optional[int]  =     load_dataset('''nielsr/rvlcdip-demo'''    )

         UpperCAmelCase_     :				Optional[Any]  =     dataset['''train'''][0]['''image'''].convert('''RGB'''    )

         UpperCAmelCase_     :				str  =     image_processor(_SCREAMING_SNAKE_CASE  ,return_tensors='''pt'''    ).to(_SCREAMING_SNAKE_CASE    )

         # forward pass
         with torch.no_grad():
              UpperCAmelCase_     :				Optional[int]  =     model(**_SCREAMING_SNAKE_CASE    )
              UpperCAmelCase_     :				List[Any]  =     outputs.logits

         UpperCAmelCase_     :				Tuple  =     torch.Size((1, 16)    )
         self.assertEqual(logits.shape  ,_SCREAMING_SNAKE_CASE    )

         UpperCAmelCase_     :				int  =     torch.tensor(
             [-0.41_58, -0.40_92, -0.43_47]  ,device=_SCREAMING_SNAKE_CASE  ,dtype=torch.float  ,)
         self.assertTrue(torch.allclose(logits[0, :3]  ,_SCREAMING_SNAKE_CASE  ,atol=1e-4    )    )