



'''simple docstring'''






def    lowerCamelCase__ (		_A       ):

  if not grid or not grid[0]:
    raise TypeError('The grid does not contain the appropriate information'       )

  for cell_n in range(1				,    len(grid[0]       )       ):
    grid[0][cell_n] += grid[0][cell_n - 1]
  a		:      Any       =  grid[0]

  for row_n in range(1				,    len(_A       )       ):
    a		:      Optional[int]       =  grid[row_n]
    a		:      Dict       =  fill_row(_A				,    _A       )
    a		:      Any       =  grid[row_n]

  return grid[-1][-1]
def    lowerCamelCase__ (		_A				,    _A       ):
  current_row[0] += row_above[0]
  for cell_n in range(1				,    len(_A       )       ):
    current_row[cell_n] += min(current_row[cell_n - 1]				,    row_above[cell_n]       )

  return current_row


if __name__ == "__main__":
     import doctest

     doctest.testmod()










'''simple docstring'''






from math import factorial, pi
def    lowerCamelCase__ (		_A				,    _A = 30       ):

  if not isinstance(_A				,    (int, float)       ):
    raise ValueError('maclaurin_sin() requires either an int or float for theta'       )

  if not isinstance(_A				,    _A       ) or accuracy <= 0:
    raise ValueError('maclaurin_sin() requires a positive int for accuracy'       )

  a		:      List[Any]       =  float(_A       )
  a		:      Optional[int]       =  theta // (2 * pi)
  theta -= 2 * div * pi
  return sum(
      (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1       ) for r in range(_A       )       )
def    lowerCamelCase__ (		_A				,    _A = 30       ):

  if not isinstance(_A				,    (int, float)       ):
    raise ValueError('maclaurin_cos() requires either an int or float for theta'       )

  if not isinstance(_A				,    _A       ) or accuracy <= 0:
    raise ValueError('maclaurin_cos() requires a positive int for accuracy'       )

  a		:      List[str]       =  float(_A       )
  a		:      List[str]       =  theta // (2 * pi)
  theta -= 2 * div * pi
  return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r       ) for r in range(_A       )       )


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     print(maclaurin_sin(1_0))
     print(maclaurin_sin(-1_0))
     print(maclaurin_sin(1_0, 1_5))
     print(maclaurin_sin(-1_0, 1_5))

     print(maclaurin_cos(5))
     print(maclaurin_cos(-5))
     print(maclaurin_cos(1_0, 1_5))
     print(maclaurin_cos(-1_0, 1_5))