






'''simple docstring'''




def 	__UpperCAmelCase       ( __magic_name__ = 10**12						)->    int:



			"""simple docstring"""



			snake_case_				:					Dict   =       1
			snake_case_				:					str   =       0

			snake_case_				:					Dict   =       1
			snake_case_				:					Union[str, Any]   =       1

			while numerator <= 2 * min_total - 1:
						prev_numerator += 2 * numerator
						numerator += 2 * prev_numerator

						prev_denominator += 2 * denominator
						denominator += 2 * prev_denominator

			return (denominator + 1) // 2


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












'''simple docstring'''




def 	__UpperCAmelCase       ( __magic_name__						)->    list[int]:



			"""simple docstring"""



			if length <= 0 or not isinstance(__magic_name__     ,__magic_name__						):
						raise ValueError("Length must be a positive integer."						)
			return [n * (2 * n - 1) for n in range(__magic_name__						)]


if __name__ == "__main__":
		print(hexagonal_numbers(length=5))
		print(hexagonal_numbers(length=10))




