




'''simple docstring'''
def 			lowerCamelCase(							SCREAMING_SNAKE_CASE_ = 5000_0000     )		->		int:
			A_									= set()
			A_									= int((limit - 24) ** (1 / 2)     )

			A_									= 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       ,SCREAMING_SNAKE_CASE_     )     )     )

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

			return len(SCREAMING_SNAKE_CASE_     )


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










'''simple docstring'''
def 			lowerCamelCase(							SCREAMING_SNAKE_CASE_       ,SCREAMING_SNAKE_CASE_     )		->		tuple[float, float]:

			# Check if the input is valid
			if not len(SCREAMING_SNAKE_CASE_     ) == len(SCREAMING_SNAKE_CASE_     ) == 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
			A_		, A_		, A_									= equationa
			A_		, A_		, A_									= equationa

			# Calculate the determinants of the matrices
			A_									= aa * ba - aa * ba
			A_									= ca * ba - ca * ba
			A_									= 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:
									A_									= determinant_x / determinant
									A_									= determinant_y / determinant
									# Non-Trivial Solution (Consistent system)
									return (x, y)




