
"""simple docstring"""


def  lowercase						(	lowerCAmelCase__ = 50_000_000						):
			lowerCamelCase_					=  set()
			lowerCamelCase_					=  int((limit - 24) ** (1 / 2)						)

			lowerCamelCase_					=  set(range(3	,prime_square_limit + 1	,2						)						)
			primes.add(2						)
			for p in range(3	,prime_square_limit + 1	,2						):
						if p not in primes:
									continue
						primes.difference_update(set(range(p * p	,prime_square_limit + 1	,lowerCAmelCase__						)						)						)

			for primea in primes:
						lowerCamelCase_					=  primea * primea
						for primea in primes:
									lowerCamelCase_					=  primea * primea * primea
									if square + cube >= limit - 16:
												break
									for primea in primes:
												lowerCamelCase_					=  primea * primea * primea * primea
												lowerCamelCase_					=  square + cube + tetr
												if total >= limit:
															break
												ret.add(lowerCAmelCase__						)

			return len(lowerCAmelCase__						)


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





def 		UpperCamelCase     (       _UpperCAmelCase  :   list[int] ,			_UpperCAmelCase  :   list[int]  )   ->			tuple[float, float]:






						'''simple docstring'''

						if not len(_UpperCAmelCase  ) == len(_UpperCAmelCase  ) == 3:
												raise ValueError("Please enter a valid equation."  )
						if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
												raise ValueError("Both a & b of two equations can't be zero."  )

						# Extract the coefficients
						_lowercase      ,    _lowercase      ,    _lowercase       :	List[str]           =   equationa
						_lowercase      ,    _lowercase      ,    _lowercase       :	List[str]           =   equationa

						# Calculate the determinants of the matrices
						_lowercase       :	List[Any]           =   aa * ba - aa * ba
						_lowercase       :	Tuple           =   ca * ba - ca * ba
						_lowercase       :	Union[str, Any]           =   aa * ca - aa * ca

						# Check if the system of linear equations has a solution (using Cramer's rule)
						if determinant == 0:
												if determinant_x == determinant_y == 0:
																		raise ValueError("Infinite solutions. (Consistent system)"  )
												else:
																		raise ValueError("No solution. (Inconsistent system)"  )
						else:
												if determinant_x == determinant_y == 0:
																		# Trivial solution (Inconsistent system)
																		return (0.0, 0.0)
												else:
																		_lowercase       :	str           =   determinant_x / determinant
																		_lowercase       :	Union[str, Any]           =   determinant_y / determinant
																		# Non-Trivial Solution (Consistent system)
																		return (x, y)




