



'''simple docstring'''





def 			a_	(				_lowerCAmelCase			,_lowerCAmelCase			) -> tuple[float, float]:

  # Check if the input is valid
  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			:			Union[str, Any]       			=					equationa
  __lowerCamelCase			,__lowerCamelCase			,__lowerCamelCase			:			Any       			=					equationa

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











'''simple docstring'''





def 			a_	(				_lowerCAmelCase			) -> int:

  if not isinstance(_lowerCAmelCase			,_lowerCAmelCase			):
    raise TypeError('only integers accepted as input'			)
  else:
    __lowerCamelCase			:			Any       			=					str(abs(_lowerCAmelCase			)			)
    __lowerCamelCase			:			Tuple       			=					[list(_lowerCAmelCase			) for char in range(len(_lowerCAmelCase			)			)]
    for index in range(len(_lowerCAmelCase			)			):
      num_transpositions[index].pop(_lowerCAmelCase			)
    return max(
        int(''.join(list(_lowerCAmelCase			)			)			) for transposition in num_transpositions			)


if __name__ == "__main__":
   __import__('doctest').testmod()






