





from __future__ import annotations

from fractions import Fraction







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







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







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


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






def    A				(							UpperCAmelCase				):
					return str(UpperCAmelCase				) == str(UpperCAmelCase				)[::-1]







def    A				(							UpperCAmelCase				):
					return int(UpperCAmelCase				) + int(str(UpperCAmelCase				)[::-1]				)







def    A				(							UpperCAmelCase = 10_000				):
					_snake_case       :					Optional[int]				       =   []
					for num in range(1  ,  UpperCAmelCase				):
										_snake_case       :					Optional[Any]				       =   0
										_snake_case       :					Optional[int]				       =   num
										while iterations < 50:
															_snake_case       :					Optional[Any]				       =   sum_reverse(UpperCAmelCase				)
															iterations += 1
															if is_palindrome(UpperCAmelCase				):
																				break
										else:
															lychrel_nums.append(UpperCAmelCase				)
					return len(UpperCAmelCase				)


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