




"""simple docstring"""


from __future__ import annotations

from fractions import Fraction




def       snake_case  (A_				:int     ,      A_				:int				):







  '''simple docstring'''

  return (
      num != den and num % 1_0 == den // 1_0 and (num // 1_0) / (den % 1_0) == num / den
  )




def       snake_case  (A_				:int				):







  '''simple docstring'''

  a					:      Dict    =       []
  a					:      str    =       1_1
  a					:      Tuple    =       int('1' + '0' * digit_len				)
  for num in range(A_     ,      A_				):
    while den <= 9_9:
      if (num != den) and (num % 1_0 == den // 1_0) and (den % 1_0 != 0):
        if is_digit_cancelling(A_     ,      A_				):
          solutions.append(f'''{num}/{den}'''				)
      den += 1
    num += 1
    a					:      List[str]    =       1_0
  return solutions




def       snake_case  (A_				:int = 2				):







  '''simple docstring'''

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


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












"""simple docstring"""


import unittest

from transformers import SPIECE_UNDERLINE, XLNetTokenizer, XLNetTokenizerFast
from transformers.testing_utils import get_tests_dir, require_sentencepiece, require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin


_UpperCamelCase    :   List[str]   			=						get_tests_dir('fixtures/test_sentencepiece.model')






@require_sentencepiece
@require_tokenizers
class 						snake_case  (  UpperCAmelCase       ,			unittest.TestCase	):
    __magic_name__   					=					XLNetTokenizer
    __magic_name__   					=					XLNetTokenizerFast
    __magic_name__   					=					True
    __magic_name__   					=					True





    def     lowerCamelCase__				(							self     : List[Any]      ):


      '''simple docstring'''




      super().setUp()

      # We have a SentencePiece fixture for testing
      a					:      Tuple    =       XLNetTokenizer(A    ,		keep_accents=A      )
      tokenizer.sanitize_special_tokens()
      tokenizer.save_pretrained(self.tmpdirname      )





    def     lowerCamelCase__				(							self     : Optional[int]      ):


      '''simple docstring'''




      a					:      Optional[int]    =       '<s>'
      a					:      int    =       1

      self.assertEqual(self.get_tokenizer()._convert_token_to_id(A      )    ,		A      )
      self.assertEqual(self.get_tokenizer()._convert_id_to_token(A      )    ,		A      )





    def     lowerCamelCase__				(							self     : Tuple      ):


      '''simple docstring'''




      a					:      str    =       list(self.get_tokenizer().get_vocab().keys()      )

      self.assertEqual(vocab_keys[0]    ,		'<unk>'      )
      self.assertEqual(vocab_keys[1]    ,		'<s>'      )
      self.assertEqual(vocab_keys[-1]    ,		'<eod>'      )
      self.assertEqual(len(A      )    ,		1_0_0_6      )





    def     lowerCamelCase__				(							self     : Any      ):


      '''simple docstring'''




      self.assertEqual(self.get_tokenizer().vocab_size    ,		1_0_0_0      )





    def     lowerCamelCase__				(							self     : Optional[int]      ):


      '''simple docstring'''




      a					:      Optional[Any]    =       XLNetTokenizer(A    ,		keep_accents=A      )

      a					:      List[str]    =       tokenizer.tokenize('This is a test'      )
      self.assertListEqual(A    ,		['▁This', '▁is', '▁a', '▁t', 'est']      )

      self.assertListEqual(tokenizer.convert_tokens_to_ids(A      )    ,		[2_8_5, 4_6, 1_0, 1_7_0, 3_8_2]      )

      a					:      List[str]    =       tokenizer.tokenize('I was born in 92000, and this is falsé.'      )
      self.assertListEqual(
          A    ,		[
              SPIECE_UNDERLINE + 'I',
              SPIECE_UNDERLINE + 'was',
              SPIECE_UNDERLINE + 'b',
              'or',
              'n',
              SPIECE_UNDERLINE + 'in',
              SPIECE_UNDERLINE + '',
              '9',
              '2',
              '0',
              '0',
              '0',
              ',',
              SPIECE_UNDERLINE + 'and',
              SPIECE_UNDERLINE + 'this',
              SPIECE_UNDERLINE + 'is',
              SPIECE_UNDERLINE + 'f',
              'al',
              's',
              'é',
              '.',
          ]    ,		)
      a					:      Union[str, Any]    =       tokenizer.convert_tokens_to_ids(A      )
      self.assertListEqual(A    ,		[8, 2_1, 8_4, 5_5, 2_4, 1_9, 7, 0, 6_0_2, 3_4_7, 3_4_7, 3_4_7, 3, 1_2, 6_6, 4_6, 7_2, 8_0, 6, 0, 4]      )

      a					:      Tuple    =       tokenizer.convert_ids_to_tokens(A      )
      self.assertListEqual(
          A    ,		[
              SPIECE_UNDERLINE + 'I',
              SPIECE_UNDERLINE + 'was',
              SPIECE_UNDERLINE + 'b',
              'or',
              'n',
              SPIECE_UNDERLINE + 'in',
              SPIECE_UNDERLINE + '',
              '<unk>',
              '2',
              '0',
              '0',
              '0',
              ',',
              SPIECE_UNDERLINE + 'and',
              SPIECE_UNDERLINE + 'this',
              SPIECE_UNDERLINE + 'is',
              SPIECE_UNDERLINE + 'f',
              'al',
              's',
              '<unk>',
              '.',
          ]    ,		)





    def     lowerCamelCase__				(							self     : Union[str, Any]      ):


      '''simple docstring'''




      a					:      Optional[int]    =       XLNetTokenizer(A    ,		do_lower_case=A      )
      a					:      Any    =       tokenizer.tokenize('I was born in 92000, and this is falsé.'      )
      self.assertListEqual(
          A    ,		[
              SPIECE_UNDERLINE + '',
              'i',
              SPIECE_UNDERLINE + 'was',
              SPIECE_UNDERLINE + 'b',
              'or',
              'n',
              SPIECE_UNDERLINE + 'in',
              SPIECE_UNDERLINE + '',
              '9',
              '2',
              '0',
              '0',
              '0',
              ',',
              SPIECE_UNDERLINE + 'and',
              SPIECE_UNDERLINE + 'this',
              SPIECE_UNDERLINE + 'is',
              SPIECE_UNDERLINE + 'f',
              'al',
              'se',
              '.',
          ]    ,		)
      self.assertListEqual(tokenizer.tokenize('H\u00E9llo'      )    ,		['▁he', 'll', 'o']      )





    def     lowerCamelCase__				(							self     : int      ):


      '''simple docstring'''




      a					:      str    =       XLNetTokenizer(A    ,		do_lower_case=A      )
      a					:      List[Any]    =       tokenizer.tokenize('I was born in 92000, and this is falsé.'      )
      self.assertListEqual(
          A    ,		[
              SPIECE_UNDERLINE + 'I',
              SPIECE_UNDERLINE + 'was',
              SPIECE_UNDERLINE + 'b',
              'or',
              'n',
              SPIECE_UNDERLINE + 'in',
              SPIECE_UNDERLINE + '',
              '9',
              '2',
              '0',
              '0',
              '0',
              ',',
              SPIECE_UNDERLINE + 'and',
              SPIECE_UNDERLINE + 'this',
              SPIECE_UNDERLINE + 'is',
              SPIECE_UNDERLINE + 'f',
              'al',
              'se',
              '.',
          ]    ,		)





    @slow
    def     lowerCamelCase__				(							self     : Optional[int]      ):


      '''simple docstring'''




      a					:      Dict    =       XLNetTokenizer.from_pretrained('xlnet-base-cased'      )

      a					:      int    =       tokenizer.encode('sequence builders'    ,		add_special_tokens=A      )
      a					:      List[Any]    =       tokenizer.encode('multi-sequence build'    ,		add_special_tokens=A      )

      a					:      Optional[int]    =       tokenizer.build_inputs_with_special_tokens(A      )
      a					:      Optional[Any]    =       tokenizer.build_inputs_with_special_tokens(A    ,		A      )

      assert encoded_sentence == text + [4, 3]
      assert encoded_pair == text + [4] + text_a + [4, 3]





    @slow
    def     lowerCamelCase__				(							self     : Any      ):


      '''simple docstring'''




      a					:      Union[str, Any]    =       {'input_ids': [[1_7, 2_1_4_4_2, 2_7_0, 1_7, 1_0, 1_4_6_4_5, 3_1_8, 3_4, 1_7, 4_5_4_6, 3_1_4_5, 7_8_7, 1_3, 7_7_5_2, 2_2_0_1_8, 2_3, 2_1, 1_7, 4_5_4_6, 3_1_4_5, 7_8_7, 1_3, 3_3_5_2, 1_4_4_3_1, 1_3, 5_5_0_0, 1_1, 1_1_7_6, 5_8_0, 1_3, 1_6_8_1_9, 4_7_9_7, 2_3, 1_7, 1_0, 1_7_1_3_5, 6_5_8, 1_9, 4_5_7, 7_9_3_2, 1_3, 1_8_4, 1_9, 3_1_5_4, 1_7_1_3_5, 6_4_6_8, 1_9, 1_4_0_4, 1_2_2_6_9, 1_9, 4_2_2_9, 5_3_5_6, 1_6_2_6_4, 4_6, 1_9, 1_7, 2_0_5_4_5, 1_0_3_9_5, 9, 9, 9, 1_1, 2_8, 6_4_2_1, 9_5_3_1, 2_0_7_2_9, 1_7, 1_0, 3_5_3, 1_7_0_2_2, 1_1, 2_1, 6_4_2_1, 9_5_3_1, 1_6_9_4_9, 1_7, 1_0, 1_1_5_0_9, 7_5_3, 1_1, 3_3, 9_5, 2_4_2_1, 7_3_8_5, 9_5_6, 1_4_4_3_1, 2_6_2_6, 2_5, 8_4_2, 7_3_8_5, 4_8_3_6, 2_1, 1_4_2_9, 2_2_7_2, 9_8_5_5, 3_1_2_0, 1_6_1, 2_4_7_3_8, 1_9, 1_3_2_0_3, 6_5_8, 2_1_8, 7_8_7, 2_1, 4_3_0, 1_8_4_8_2, 8_4_7, 2_6_3_7, 9, 4, 3], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3_2_2, 2_2_1_7_8, 2_7, 1_0_6_4, 2_2, 9_5_6, 1_3, 1_1_1_0_1, 1_4_2_9, 5_8_5_4, 2_4_3_1_3, 1_8_9_5_3, 4_0, 4_2_2, 2_4_3_6_6, 6_8, 1_7_5_8, 3_7, 1_0_4_8_3, 1_4_2_5_7, 3_1, 2_0_7, 2_6_3, 2_1, 2_0_3, 3_7_7_3, 2_5, 7_1, 9_7_3_5, 9, 4, 3], [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3_2, 2_0_4_9, 3_4_4_2, 1_7, 1_3_8_9_4, 3_3_8_0, 2_3, 9_5, 1_8, 1_7_6_3_4, 2_2_8_8, 9, 4, 3]], 'token_type_ids': [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], [3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2]], 'attention_mask': [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]}  # noqa: E501
      # fmt: on

      self.tokenizer_integration_test_util(
          expected_encoding=A    ,		model_name='xlnet-base-cased'    ,		revision='c841166438c31ec7ca9a106dee7bb312b73ae511'    ,		)




