


'''simple docstring'''





import os
import sys
import unittest


UpperCAmelCase    =					os.path.abspath(os.path.dirname(os.path.dirname(os.path.dirname(__file__))))
sys.path.append(os.path.join(git_repo_path, """utils"""))

import check_dummies  # noqa: E402
from check_dummies import create_dummy_files, create_dummy_object, find_backend, read_init  # noqa: E402


# Align TRANSFORMERS_PATH in check_dummies with the current path
UpperCAmelCase    =					os.path.join(git_repo_path, """src""", """transformers""")

UpperCAmelCase    =					"""
{0} = None
"""

UpperCAmelCase    =					"""
class {0}(metaclass=DummyObject):
    _backends = {1}

    def __init__(self, *args, **kwargs):
        requires_backends(self, {1})
"""


UpperCAmelCase    =					"""
def {0}(*args, **kwargs):
    requires_backends({0}, {1})
"""







class lowerCAmelCase_		(				unittest.TestCase ):

 '''simple docstring'''

 def 		UpperCamelCase__  (			self      ):
       snake_case_ =   find_backend('''    _import_structure["models.albert"].append("AlbertTokenizerFast")'''      )
       self.assertIsNone(snake_case_      )

       snake_case_ =   find_backend('''    if not is_tokenizers_available():'''      )
       self.assertEqual(snake_case_	,   '''tokenizers'''      )

       snake_case_ =   find_backend('''    if not is_tensorflow_text_available():'''      )
       self.assertEqual(snake_case_	,   '''tensorflow_text'''      )

       snake_case_ =   find_backend('''    if not (is_sentencepiece_available() and is_tokenizers_available()):'''      )
       self.assertEqual(snake_case_	,   '''sentencepiece_and_tokenizers'''      )

       snake_case_ =   find_backend(
           '''    if not (is_sentencepiece_available() and is_tensorflow_text_available()):'''      )
       self.assertEqual(snake_case_	,   '''sentencepiece_and_tensorflow_text'''      )

       snake_case_ =   find_backend(
           '''    if not (is_sentencepiece_available() and is_tokenizers_available() and is_vision_available()):'''      )
       self.assertEqual(snake_case_	,   '''sentencepiece_and_tokenizers_and_vision'''      )



 def 		UpperCamelCase__  (			self      ):
       snake_case_ =   read_init()
       # We don't assert on the exact list of keys to allow for smooth grow of backend-specific objects
       self.assertIn('''torch'''	,   snake_case_      )
       self.assertIn('''tensorflow_text'''	,   snake_case_      )
       self.assertIn('''sentencepiece_and_tokenizers'''	,   snake_case_      )

       # Likewise, we can't assert on the exact content of a key
       self.assertIn('''BertModel'''	,   objects['''torch''']      )
       self.assertIn('''TFBertModel'''	,   objects['''tf''']      )
       self.assertIn('''FlaxBertModel'''	,   objects['''flax''']      )
       self.assertIn('''BertModel'''	,   objects['''torch''']      )
       self.assertIn('''TFBertTokenizer'''	,   objects['''tensorflow_text''']      )
       self.assertIn('''convert_slow_tokenizer'''	,   objects['''sentencepiece_and_tokenizers''']      )



 def 		UpperCamelCase__  (			self      ):
       snake_case_ =   create_dummy_object('''CONSTANT'''	,   '''\'torch\''''      )
       self.assertEqual(snake_case_	,   '''\nCONSTANT = None\n'''      )

       snake_case_ =   create_dummy_object('''function'''	,   '''\'torch\''''      )
       self.assertEqual(
           snake_case_	,   '''\ndef function(*args, **kwargs):\n    requires_backends(function, \'torch\')\n'''      )

       snake_case_ =   '''\nclass FakeClass(metaclass=DummyObject):\n    _backends = \'torch\'\n\n    def __init__(self, *args, **kwargs):\n        requires_backends(self, \'torch\')\n'''
       snake_case_ =   create_dummy_object('''FakeClass'''	,   '''\'torch\''''      )
       self.assertEqual(snake_case_	,   snake_case_      )





 def 		UpperCamelCase__  (			self      ):
       snake_case_ =   '''# This file is autogenerated by the command `make fix-copies`, do not edit.\nfrom ..utils import DummyObject, requires_backends\n\n\nCONSTANT = None\n\n\ndef function(*args, **kwargs):\n    requires_backends(function, ["torch"])\n\n\nclass FakeClass(metaclass=DummyObject):\n    _backends = ["torch"]\n\n    def __init__(self, *args, **kwargs):\n        requires_backends(self, ["torch"])\n'''
       snake_case_ =   create_dummy_files({'''torch''': ['''CONSTANT''', '''function''', '''FakeClass''']}      )
       self.assertEqual(dummy_files['''torch''']	,   snake_case_      )



def  __lowerCAmelCase					(SCREAMING_SNAKE_CASE = 3      ,      SCREAMING_SNAKE_CASE = 7      ,      SCREAMING_SNAKE_CASE = 100_0000      )->						int:




      """simple docstring"""

      snake_case_ =   0
      snake_case_ =   1

      for current_denominator in range(1      ,      limit + 1      ):
            snake_case_ =   current_denominator * numerator // denominator
            if current_denominator % denominator == 0:
                  current_numerator -= 1
            if current_numerator * max_denominator > current_denominator * max_numerator:
                  snake_case_ =   current_numerator
                  snake_case_ =   current_denominator
      return max_numerator


if __name__ == "__main__":
   print(solution(numerator=3, denominator=7, limit=100_0000))