





def       UpperCAmelCase							(     _lowerCamelCase      :  int     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				int   =					(1 + 24 * n) ** 0.5
						return ((1 + root) / 6) % 1 == 0







def       UpperCAmelCase							(     _lowerCamelCase      :  int = 5_000     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				List[Any]   =					[(i * (3 * i - 1)) // 2 for i in range(1			,   _lowerCamelCase     )]
						for i, pentagonal_i in enumerate(_lowerCamelCase     ):
												for j in range(_lowerCamelCase			,   len(_lowerCamelCase     )     ):
																		SCREAMING_SNAKE_CASE__     :				Any   =					pentagonal_nums[j]
																		SCREAMING_SNAKE_CASE__     :				int   =					pentagonal_i + pentagonal_j
																		SCREAMING_SNAKE_CASE__     :				Optional[Any]   =					pentagonal_j - pentagonal_i
																		if is_pentagonal(_lowerCamelCase     ) and is_pentagonal(_lowerCamelCase     ):
																								return b

						return -1


if __name__ == "__main__":
				print(f"{solution() = }")






from __future__ import annotations

from fractions import Fraction







def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  int     ):





						'''simple docstring'''


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







def       UpperCAmelCase							(     _lowerCamelCase      :  int     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				int   =					[]
						SCREAMING_SNAKE_CASE__     :				str   =					11
						SCREAMING_SNAKE_CASE__     :				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
												SCREAMING_SNAKE_CASE__     :				str   =					10
						return solutions







def       UpperCAmelCase							(     _lowerCamelCase      :  int = 2     ):





						'''simple docstring'''


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


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