





import math







def        __lowerCamelCase (							__a       :int   )		->    bool:






		"""simple docstring"""

		A__  				=       math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

		return exponent == int(__a   )







def        __lowerCamelCase (							__a       :float = 1 / 1_2_3_4_5   )		->    int:






		"""simple docstring"""

		A__  				=       0
		A__  				=       0

		A__  				=       3
		while True:
				A__  				=       (integer**2 - 1) / 4
				# if candidate is an integer, then there is a partition for k
				if partition_candidate == int(__a   ):
						A__  				=       int(__a   )
						total_partitions += 1
						if check_partition_perfect(__a   ):
								perfect_partitions += 1
				if perfect_partitions > 0:
						if perfect_partitions / total_partitions < max_proportion:
								return int(__a   )
				integer += 1


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










def        __lowerCamelCase (							__a       :float   ,					__a       :list[float]   )		->    float:






		"""simple docstring"""

		if discount_rate < 0:
				raise ValueError("""Discount rate cannot be negative"""   )
		if not cash_flows:
				raise ValueError("""Cash flows list cannot be empty"""   )
		A__  				=       sum(
		    cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(__a   )   )
		return round(__a   ,					ndigits=2   )


if __name__ == "__main__":
					import doctest

					doctest.testmod()



