






from __future__ import annotations

from collections.abc import MutableSequence





class 					A__     :

     '''simple docstring'''






     def __init__( self      :    Dict   ,						_SCREAMING_SNAKE_CASE      :    int   ,						_SCREAMING_SNAKE_CASE      :    MutableSequence[float] ):






           """simple docstring"""




           if len(_SCREAMING_SNAKE_CASE ) != degree + 1:
                 raise ValueError(
                     'The number of coefficients should be equal to the degree + 1.' )

           UpperCamelCase					       =  list(_SCREAMING_SNAKE_CASE )
           UpperCamelCase					       =  degree







     def __add__( self      :    Any   ,						_SCREAMING_SNAKE_CASE      :    Polynomial ):






           """simple docstring"""




           if self.degree > polynomial_a.degree:
                 UpperCamelCase					       =  self.coefficients[:]
                 for i in range(polynomial_a.degree + 1 ):
                       coefficients[i] += polynomial_a.coefficients[i]
                 return Polynomial(self.degree   ,						_SCREAMING_SNAKE_CASE )
           else:
                 UpperCamelCase					       =  polynomial_a.coefficients[:]
                 for i in range(self.degree + 1 ):
                       coefficients[i] += self.coefficients[i]
                 return Polynomial(polynomial_a.degree   ,						_SCREAMING_SNAKE_CASE )







     def __sub__( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    Polynomial ):






           """simple docstring"""




           return self + polynomial_a * Polynomial(0   ,						[-1] )







     def __neg__( self      :    Any ):






           """simple docstring"""




           return Polynomial(self.degree   ,						[-c for c in self.coefficients] )







     def __mul__( self      :    Union[str, Any]   ,						_SCREAMING_SNAKE_CASE      :    Polynomial ):






           """simple docstring"""




           UpperCamelCase					       =  [0] * (self.degree + polynomial_a.degree + 1)
           for i in range(self.degree + 1 ):
                 for j in range(polynomial_a.degree + 1 ):
                       coefficients[i + j] += (
                           self.coefficients[i] * polynomial_a.coefficients[j]
                       )

           return Polynomial(self.degree + polynomial_a.degree   ,						_SCREAMING_SNAKE_CASE )







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    int | float ):






           """simple docstring"""




           UpperCamelCase					       =  0
           for i in range(self.degree + 1 ):
                 result += self.coefficients[i] * (substitution**i)
           return result







     def __str__( self      :    Union[str, Any] ):






           """simple docstring"""




           UpperCamelCase					       =  ''
           for i in range(self.degree   ,						-1   ,						-1 ):
                 if self.coefficients[i] == 0:
                       continue
                 elif self.coefficients[i] > 0:
                       if polynomial:
                             polynomial += " + "
                 else:
                       polynomial += " - "

                 if i == 0:
                       polynomial += str(abs(self.coefficients[i] ) )
                 elif i == 1:
                       polynomial += str(abs(self.coefficients[i] ) ) + "x"
                 else:
                       polynomial += str(abs(self.coefficients[i] ) ) + "x^" + str(_SCREAMING_SNAKE_CASE )

           return polynomial







     def __repr__( self      :    str ):






           """simple docstring"""




           return self.__str__()







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[Any] ):






           """simple docstring"""




           UpperCamelCase					       =  [0] * self.degree
           for i in range(self.degree ):
                 UpperCamelCase					       =  self.coefficients[i + 1] * (i + 1)
           return Polynomial(self.degree - 1   ,						_SCREAMING_SNAKE_CASE )







     def   _SCREAMING_SNAKE_CASE     ( self      :    Optional[int]   ,						_SCREAMING_SNAKE_CASE      :    int | float = 0 ):






           """simple docstring"""




           UpperCamelCase					       =  [0] * (self.degree + 2)
           UpperCamelCase					       =  constant
           for i in range(self.degree + 1 ):
                 UpperCamelCase					       =  self.coefficients[i] / (i + 1)
           return Polynomial(self.degree + 1   ,						_SCREAMING_SNAKE_CASE )







     def __eq__( self      :    Any   ,						_SCREAMING_SNAKE_CASE      :    object ):






           """simple docstring"""




           if not isinstance(_SCREAMING_SNAKE_CASE   ,						_SCREAMING_SNAKE_CASE ):
                 return False

           if self.degree != polynomial_a.degree:
                 return False

           for i in range(self.degree + 1 ):
                 if self.coefficients[i] != polynomial_a.coefficients[i]:
                       return False

           return True







     def __ne__( self      :    str   ,						_SCREAMING_SNAKE_CASE      :    object ):






           """simple docstring"""




           return not self.__eq__(_SCREAMING_SNAKE_CASE )











__magic_name__   :  Optional[Any]        =							0  # The first color of the flag.
__magic_name__   :  List[str]        =							1  # The second color of the flag.
__magic_name__   :  Dict        =							2  # The third color of the flag.
__magic_name__   :  Union[str, Any]        =							(red, white, blue)
def 		lowercase__  (				_UpperCamelCase) ->			list:
      """simple docstring"""

      if not sequence:
            return []
      if len(_UpperCamelCase) == 1:
            return list(_UpperCamelCase)
      UpperCamelCase					       =  0
      UpperCamelCase					       =  len(_UpperCamelCase) - 1
      UpperCamelCase					       =  0
      while mid <= high:
            if sequence[mid] == colors[0]:
                  UpperCamelCase       ,  UpperCamelCase					       =  sequence[mid], sequence[low]
                  low += 1
                  mid += 1
            elif sequence[mid] == colors[1]:
                  mid += 1
            elif sequence[mid] == colors[2]:
                  UpperCamelCase       ,  UpperCamelCase					       =  sequence[high], sequence[mid]
                  high -= 1
            else:
                  UpperCamelCase					       =  F'The elements inside the sequence must contains only {colors} values'
                  raise ValueError(_UpperCamelCase)
      return sequence


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       __magic_name__   :  str        =							input('''Enter numbers separated by commas:\n''').strip()
       __magic_name__   :  Union[str, Any]        =							[int(item.strip()) for item in user_input.split(''',''')]
       print(F'{dutch_national_flag_sort(unsorted)}')



