






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"""



						_UpperCAmelCase									=			[]
						_UpperCAmelCase									=			11
						_UpperCAmelCase									=			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
												_UpperCAmelCase									=			10
						return solutions


def __A    (      __lowerCAmelCase = 2	)->  int:





						"""simple docstring"""



						_UpperCAmelCase									=			1.0
						for fraction in fraction_list(__lowerCAmelCase	):
												_UpperCAmelCase									=			Fraction(__lowerCAmelCase	)
												result *= frac.denominator / frac.numerator
						return int(__lowerCAmelCase	)


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








from __future__ import annotations


def __A    (      __lowerCAmelCase	)->  list[int]:





						"""simple docstring"""



						_UpperCAmelCase									=			2
						_UpperCAmelCase									=			[]
						while i * i <= n:
												if n % i:
																		i += 1
												else:
																		n //= i
																		factors.append(__lowerCAmelCase	)
						if n > 1:
												factors.append(__lowerCAmelCase	)
						return factors


if __name__ == "__main__":
		import doctest

		doctest.testmod()
