


def 				UpperCAmelCase_					(							__snake_case     ,						__snake_case						)     ->			tuple[float, float]:







 """simple docstring"""


 if not len(__snake_case						) == len(__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      ,    _lowercase      ,    _lowercase							      =equationa
 _lowercase      ,    _lowercase      ,    _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 				UpperCAmelCase_					(							__snake_case						)     ->			list[int]:







 """simple docstring"""


 _lowercase							      =[True] * max_number
 for i in range(2     ,						isqrt(max_number - 1						) + 1						):
  if is_prime[i]:
   for j in range(i**2     ,						__snake_case     ,						__snake_case						):
    _lowercase							      =False

 return [i for i in range(2     ,						__snake_case						) if is_prime[i]]
def 				UpperCAmelCase_					(							__snake_case = 10**8						)     ->			int:







 """simple docstring"""


 _lowercase							      =calculate_prime_numbers(max_number // 2						)

 _lowercase							      =0
 _lowercase							      =0
 _lowercase							      =len(__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() = }''')

