



from __future__ import annotations

from fractions import Fraction




def 	UpperCAmelCase   (						_lowerCamelCase ,    _lowerCamelCase    ):
			return (
			    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
			)




def 	UpperCAmelCase   (						_lowerCamelCase    ):
			A							:					Union[str, Any]              =						[]
			A							:					List[Any]              =						11
			A							:					int              =						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
						A							:					Tuple              =						10
			return solutions




def 	UpperCAmelCase   (						_lowerCamelCase = 2    ):
			A							:					Optional[Any]              =						1.0
			for fraction in fraction_list(_lowerCamelCase    ):
						A							:					Dict              =						Fraction(_lowerCamelCase    )
						result *= frac.denominator / frac.numerator
			return int(_lowerCamelCase    )


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




import os


# All paths are set with the intent you should run this script from the root of the repo with the command
# python utils/check_doctest_list.py
__SCREAMING_SNAKE_CASE           =  """."""


if __name__ == "__main__":
							__SCREAMING_SNAKE_CASE           =  os.path.join(REPO_PATH, """utils/documentation_tests.txt""")
							__SCREAMING_SNAKE_CASE           =  []
							__SCREAMING_SNAKE_CASE           =  []
							with open(doctest_file_path) as fp:
														for line in fp:
																					__SCREAMING_SNAKE_CASE           =  line.strip()
																					__SCREAMING_SNAKE_CASE           =  os.path.join(REPO_PATH, line)
																					if not (os.path.isfile(path) or os.path.isdir(path)):
																												non_existent_paths.append(line)
																					all_paths.append(path)
							if len(non_existent_paths) > 0:
														__SCREAMING_SNAKE_CASE           =  """\n""".join(non_existent_paths)
														raise ValueError(F"""`utils/documentation_tests.txt` contains non-existent paths:\n{non_existent_paths}""")
							if all_paths != sorted(all_paths):
														raise ValueError("""Files in `utils/documentation_tests.txt` are not in alphabetical order.""")