





'''simple docstring'''






from __future__ import annotations

from fractions import Fraction







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase ) ->				bool:



			"""simple docstring"""


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







def 					_a						(       _lowerCamelCase ) ->				list[str]:



			"""simple docstring"""


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







def 					_a						(       _lowerCamelCase = 2 ) ->				int:



			"""simple docstring"""


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


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







SCREAMING_SNAKE_CASE__   			=   '''
# Transformers installation
! pip install transformers datasets
# To install from source instead of the last release, comment the command above and uncomment the following one.
# ! pip install git+https://github.com/huggingface/transformers.git
'''

SCREAMING_SNAKE_CASE__   			=   [{'''type''': '''code''', '''content''': INSTALL_CONTENT}]
SCREAMING_SNAKE_CASE__   			=   {
    '''{processor_class}''': '''FakeProcessorClass''',
    '''{model_class}''': '''FakeModelClass''',
    '''{object_class}''': '''FakeObjectClass''',
}




