

'''simple docstring'''




_a				: Tuple 							=						[chr(i) for i in range(32, 126)]
_a				: Tuple 							=						list(range(len(alphabets)))
_a				: int 							=						list(range(len(alphabets)))
_a				: Tuple 							=						list(range(len(alphabets)))
_a				: List[str] 							=						list(reversed(range(len(alphabets))))
_a				: str 							=						[]
_a				: int 							=						0


def       lowerCamelCase__		(						):
  global gear_one_pos
  global gear_two_pos
  global gear_three_pos
  UpperCAmelCase													=	gear_one[0]
  gear_one.append(SCREAMING_SNAKE_CASE						)
  del gear_one[0]
  gear_one_pos += 1
  if gear_one_pos % int(len(SCREAMING_SNAKE_CASE						)						) == 0:
    UpperCAmelCase													=	gear_two[0]
    gear_two.append(SCREAMING_SNAKE_CASE						)
    del gear_two[0]
    gear_two_pos += 1
    if gear_two_pos % int(len(SCREAMING_SNAKE_CASE						)						) == 0:
      UpperCAmelCase													=	gear_three[0]
      gear_three.append(SCREAMING_SNAKE_CASE						)
      del gear_three[0]
      gear_three_pos += 1


def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   Optional[Any]						):
  UpperCAmelCase													=	alphabets.index(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	gear_one[target]
  UpperCAmelCase													=	gear_two[target]
  UpperCAmelCase													=	gear_three[target]
  UpperCAmelCase													=	reflector[target]
  UpperCAmelCase													=	gear_three.index(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	gear_two.index(SCREAMING_SNAKE_CASE						)
  UpperCAmelCase													=	gear_one.index(SCREAMING_SNAKE_CASE						)
  code.append(alphabets[target]						)
  rotator()


if __name__ == "__main__":
  _a				: Dict 							=						list(input('Type your message:\n'))
  while True:
    try:
      _a				: List[str] 							=						int(input('Please set token:(must be only digits)\n'))
      break
    except Exception as error:
      print(error)
  for _ in range(token):
    rotator()
  for j in decode:
    engine(j)
  print('\n' + ''.join(code))
  print(
      F'''\nYour Token is {token} please write it down.\nIf you want to decode '''
      'this message again you should input same digits as token!'
  )





'''simple docstring'''




def       lowerCamelCase__		(						SCREAMING_SNAKE_CASE      :   list[list[int]]						):
  if len(SCREAMING_SNAKE_CASE						) == 0 or not all(len(SCREAMING_SNAKE_CASE						) == 2 for pair in coordinates						):
    raise ValueError('The program cannot work out a fitting polynomial.'						)

  if len({tuple(SCREAMING_SNAKE_CASE						) for pair in coordinates}						) != len(SCREAMING_SNAKE_CASE						):
    raise ValueError('The program cannot work out a fitting polynomial.'						)

  UpperCAmelCase													=	{x for x, _ in coordinates}
  if len(SCREAMING_SNAKE_CASE						) == 1:
    return f'''x={coordinates[0][0]}'''

  if len(SCREAMING_SNAKE_CASE						) != len(SCREAMING_SNAKE_CASE						):
    raise ValueError('The program cannot work out a fitting polynomial.'						)

  UpperCAmelCase													=	len(SCREAMING_SNAKE_CASE						)

  UpperCAmelCase													=	0
  UpperCAmelCase													=	[]
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    UpperCAmelCase													=	0
    UpperCAmelCase													=	coordinates[count_of_line][0]
    UpperCAmelCase													=	[]
    while count_in_line < x:
      count_line.append(a ** (x - (count_in_line + 1))						)
      count_in_line += 1
    matrix.append(SCREAMING_SNAKE_CASE						)
    count_of_line += 1

  UpperCAmelCase													=	0
  # put the y values into a vector
  UpperCAmelCase													=	[]
  while count_of_line < x:
    vector.append(coordinates[count_of_line][1]						)
    count_of_line += 1

  UpperCAmelCase													=	0

  while count < x:
    UpperCAmelCase													=	0
    while zahlen < x:
      if count == zahlen:
        zahlen += 1
      if zahlen == x:
        break
      UpperCAmelCase													=	matrix[zahlen][count] / matrix[count][count]
      for counting_columns, item in enumerate(matrix[count]						):
        # manipulating all the values in the matrix
        matrix[zahlen][counting_columns] -= item * bruch
      # manipulating the values in the vector
      vector[zahlen] -= vector[count] * bruch
      zahlen += 1
    count += 1

  UpperCAmelCase													=	0
  # make solutions
  UpperCAmelCase													=	[]
  while count < x:
    solution.append(str(vector[count] / matrix[count][count]						)						)
    count += 1

  UpperCAmelCase													=	0
  UpperCAmelCase													=	'f(x)='

  while count < x:
    UpperCAmelCase													=	solution[count].split('E'						)
    if len(SCREAMING_SNAKE_CASE						) > 1:
      UpperCAmelCase													=	f'''{remove_e[0]}*10^{remove_e[1]}'''
    solved += f'''x^{x - (count + 1)}*{solution[count]}'''
    if count + 1 != x:
      solved += "+"
    count += 1

  return solved


if __name__ == "__main__":
  print(points_to_polynomial([]))
  print(points_to_polynomial([[]]))
  print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
  print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
  print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
  print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
  print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
  print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
  print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
  print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))


