


'''simple docstring'''






def       _snake_case     (  A = 10**12 )		->					int:
							lowerCAmelCase__      =			1
							lowerCAmelCase__      =			0

							lowerCAmelCase__      =			1
							lowerCAmelCase__      =			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       _snake_case     (  A )		->					bool:
							if not isinstance(A				,					A ):
														raise ValueError('''Input series is not valid, valid series - [2, 4, 6]''' )
							if len(A ) == 0:
														raise ValueError('''Input list must be a non empty list''' )
							if len(A ) == 1:
														return True
							lowerCAmelCase__      =			series[1] - series[0]
							for index in range(len(A ) - 1 ):
														if series[index + 1] - series[index] != common_diff:
																					return False
							return True


def       _snake_case     (  A )		->					float:
							if not isinstance(A				,					A ):
														raise ValueError('''Input series is not valid, valid series - [2, 4, 6]''' )
							if len(A ) == 0:
														raise ValueError('''Input list must be a non empty list''' )
							lowerCAmelCase__      =			0
							for val in series:
														answer += val
							return answer / len(A )


if __name__ == "__main__":
		import doctest

		doctest.testmod()