





from maths.prime_factors import prime_factors







def        __lowerCamelCase (							__a       :int   )		->    int:






		"""simple docstring"""

		if not isinstance(__a   ,					__a   ):
				A__  				=       F'Input value of [number={number}] must be an integer'
				raise TypeError(__a   )
		if number < 1:
				raise ValueError("""Input must be a positive integer"""   )
		return -1 if len(prime_factors(__a   )   ) % 2 else 1


if __name__ == "__main__":
					import doctest

					doctest.testmod()










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() = }''')



