


def     lowerCAmelCase_					( __lowerCamelCase = 1_0_0_0     ):
							__snake_case			,      __snake_case		:      int										=       1, 1
							__snake_case		:      Tuple										=       []
							for i in range(1							,     n + 1     ):
														__snake_case		:      List[str]										=       prev_numerator + 2 * prev_denominator
														__snake_case		:      Any										=       prev_numerator + prev_denominator
														if len(str(__lowerCamelCase     )     ) > len(str(__lowerCamelCase     )     ):
																					result.append(__lowerCamelCase     )
														__snake_case		:      List[Any]										=       numerator
														__snake_case		:      Union[str, Any]										=       denominator

							return len(__lowerCamelCase     )


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





def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase     ):
							return x if y == 0 else greatest_common_divisor(__lowerCamelCase							,     x % y     )







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase     ):
							return (x * y) // greatest_common_divisor(__lowerCamelCase							,     __lowerCamelCase     )







def     lowerCAmelCase_					( __lowerCamelCase = 2_0     ):
							__snake_case		:      Optional[Any]										=       1
							for i in range(1							,     n + 1     ):
														__snake_case		:      Any										=       lcm(__lowerCamelCase							,     __lowerCamelCase     )
							return g


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

