
def  __snake_case							(	__magic_name__		,    __magic_name__						):







				'''simple docstring'''


				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
				lowercase         =      equationa
				lowercase         =      equationa

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




from math import isqrt




def       a_ (       SCREAMING_SNAKE_CASE__   : int	):
       '''simple docstring'''





       _lowerCamelCase			:						Optional[int]            =[True] * max_number
       for i in range(2						,     isqrt(max_number - 1	) + 1	):
              if is_prime[i]:
                     for j in range(i**2						,     SCREAMING_SNAKE_CASE__						,     SCREAMING_SNAKE_CASE__	):
                            _lowerCamelCase			:						str            =False

       return [i for i in range(2						,     SCREAMING_SNAKE_CASE__	) if is_prime[i]]




def       a_ (       SCREAMING_SNAKE_CASE__   : int = 10**8	):
       '''simple docstring'''





       _lowerCamelCase			:						Union[str, Any]            =calculate_prime_numbers(max_number // 2	)

       _lowerCamelCase			:						Dict            =0
       _lowerCamelCase			:						int            =0
       _lowerCamelCase			:						Optional[Any]            =len(SCREAMING_SNAKE_CASE__	) - 1
       while left <= right:
              while prime_numbers[left] * prime_numbers[right] >= max_number:
                     right -= 1
              semiprimes_count += right - left + 1
              left += 1

       return semiprimes_count


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


