






"""simple docstring"""




def 			lowerCAmelCase__     (     UpperCamelCase__     ,   UpperCamelCase__				):



  '''simple docstring'''
  if not isinstance(UpperCamelCase__     ,   UpperCamelCase__				):
    raise ValueError("""iterations must be defined as integers"""				)
  if not isinstance(UpperCamelCase__     ,   UpperCamelCase__				) or not number >= 1:
    raise ValueError(
        """starting number must be
                         and integer and be more than 0"""				)
  if not iterations >= 1:
    raise ValueError("""Iterations must be done more than 0 times to play FizzBuzz"""				)

  _a  :       Optional[int]             =	""""""
  while number <= iterations:
    if number % 3 == 0:
      out += "Fizz"
    if number % 5 == 0:
      out += "Buzz"
    if 0 not in (number % 3, number % 5):
      out += str(UpperCamelCase__				)

    # print(out)
    number += 1
    out += " "
  return out


if __name__ == "__main__":
 import doctest

 doctest.testmod()









"""simple docstring"""




def 			lowerCAmelCase__     (     UpperCamelCase__     ,   UpperCamelCase__				):



  '''simple docstring'''

  # Check if the input is valid
  if not len(UpperCamelCase__				) == len(UpperCamelCase__				) == 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  :       Any             =	equationa
  _a      ,  _a      ,  _a  :       Tuple             =	equationa

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

