


import math


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







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

			return exponent == int(_UpperCamelCase  )


def 		lowercase_  (     _UpperCamelCase = 1 / 1_23_45  ):


			'''simple docstring'''







			__lowercase 					=   0
			__lowercase 					=   0

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


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






from ..utils import DummyObject, requires_backends
class 	lowerCamelCase_       (				metaclass=lowerCAmelCase__				):



					'''simple docstring'''







					__UpperCAmelCase            =				["onnx"]






					def __init__(				self ,       *snake_case_ ,       **snake_case_						)   ->			List[Any]:







								'''simple docstring'''

								requires_backends(self ,       ['''onnx''']						)






					@classmethod
					def A      (				cls ,       *snake_case_ ,       **snake_case_						)   ->			int:







								'''simple docstring'''

								requires_backends(cls ,       ['''onnx''']						)






					@classmethod
					def A      (				cls ,       *snake_case_ ,       **snake_case_						)   ->			List[str]:







								'''simple docstring'''

								requires_backends(cls ,       ['''onnx''']						)


