
"""simple docstring"""





from __future__ import annotations

from fractions import Fraction



def 						_lowerCAmelCase				(				UpperCamelCase_  ,				UpperCamelCase_				):
		return (
		    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
		)



def 						_lowerCAmelCase				(				UpperCamelCase_				):
		__SCREAMING_SNAKE_CASE            = []
		__SCREAMING_SNAKE_CASE            = 11
		__SCREAMING_SNAKE_CASE            = int("""1""" + """0""" * digit_len				)
		for num in range(UpperCamelCase_  ,				UpperCamelCase_				):
				while den <= 99:
						if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
								if is_digit_cancelling(UpperCamelCase_  ,				UpperCamelCase_				):
										solutions.append(f"{num}/{den}"				)
						den += 1
				num += 1
				__SCREAMING_SNAKE_CASE            = 10
		return solutions



def 						_lowerCAmelCase				(				UpperCamelCase_ = 2				):
		__SCREAMING_SNAKE_CASE            = 1.0
		for fraction in fraction_list(UpperCamelCase_				):
				__SCREAMING_SNAKE_CASE            = Fraction(UpperCamelCase_				)
				result *= frac.denominator / frac.numerator
		return int(UpperCamelCase_				)


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






"""simple docstring"""





def 						_lowerCAmelCase				(				UpperCamelCase_				):

		if isinstance(UpperCamelCase_  ,				UpperCamelCase_				):
				raise TypeError("""'float' object cannot be interpreted as an integer"""				)
		if isinstance(UpperCamelCase_  ,				UpperCamelCase_				):
				raise TypeError("""'str' object cannot be interpreted as an integer"""				)

		if num == 0:
				return "0b0"

		__SCREAMING_SNAKE_CASE            = False

		if num < 0:
				__SCREAMING_SNAKE_CASE            = True
				__SCREAMING_SNAKE_CASE            = -num

		__SCREAMING_SNAKE_CASE            = []
		while num > 0:
				binary.insert(0  ,				num % 2				)
				num >>= 1

		if negative:
				return "-0b" + "".join(str(UpperCamelCase_				) for e in binary				)

		return "0b" + "".join(str(UpperCamelCase_				) for e in binary				)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




