



"""simple docstring"""







def 				UpperCamelCase_    (    lowerCAmelCase__      :				list[int]    ,   lowerCAmelCase__      :				list[int]						)						->   tuple[float, float]:

  """simple docstring"""




  if not len(lowerCAmelCase__						) == len(lowerCAmelCase__						) == 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
  lowerCAmelCase_						,lowerCAmelCase_						,lowerCAmelCase_   :				Dict								= equationa
  lowerCAmelCase_						,lowerCAmelCase_						,lowerCAmelCase_   :				List[Any]								= equationa

  # Calculate the determinants of the matrices
  lowerCAmelCase_   :				List[str]								= aa * ba - aa * ba
  lowerCAmelCase_   :				str								= ca * ba - ca * ba
  lowerCAmelCase_   :				str								= 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:
      lowerCAmelCase_   :				Optional[int]								= determinant_x / determinant
      lowerCAmelCase_   :				Union[str, Any]								= determinant_y / determinant
      # Non-Trivial Solution (Consistent system)
      return (x, y)










"""simple docstring"""







def 				UpperCamelCase_    (    lowerCAmelCase__      :				int = 100						)						->   int:

  """simple docstring"""




  lowerCAmelCase_   :				Any								= (n * (n + 1) // 2) ** 2
  lowerCAmelCase_   :				Optional[int]								= n * (n + 1) * (2 * n + 1) // 6
  return sum_cubes - sum_squares


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





