
import math



def 						lowercase_      (       A__		)							->							Tuple:
				"""simple docstring"""

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

				return exponent == int(__lowerCamelCase		)



def 						lowercase_      (       A__ = 1 / 1_2345		)							->							Any:
				"""simple docstring"""

				snake_case								= 0
				snake_case								= 0

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


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



def 						lowercase_      (       A__ = 1000		)							->							int:
    """simple docstring"""

    return sum(2 * a * ((a - 1) // 2) for a in range(3			,		n + 1		)		)


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

