





"""simple docstring"""
from __future__ import annotations

from collections.abc import MutableSequence
class lowerCamelCase__	:



   def __init__(							self   , snake_case   , snake_case						)			->     Tuple:







      """simple docstring"""






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

      lowercase     :      int	=							list(snake_case__						)
      lowercase     :      Optional[int]	=							degree



   def __add__(							self   , snake_case						)			->     str:







      """simple docstring"""






      if self.degree > polynomial_a.degree:
         lowercase     :      Any	=							self.coefficients[:]
         for i in range(polynomial_a.degree + 1						):
            coefficients[i] += polynomial_a.coefficients[i]
         return Polynomial(self.degree   , snake_case__						)
      else:
         lowercase     :      Optional[int]	=							polynomial_a.coefficients[:]
         for i in range(self.degree + 1						):
            coefficients[i] += self.coefficients[i]
         return Polynomial(polynomial_a.degree   , snake_case__						)



   def __sub__(							self   , snake_case						)			->     Optional[Any]:







      """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   , snake_case						)			->     Dict:







      """simple docstring"""
      lowercase     :      Tuple	=							[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   , snake_case__						)



   def  _UpperCAmelCase						(							self   , snake_case						)			->     List[str]:







      """simple docstring"""
      lowercase     :      str	=							0
      for i in range(self.degree + 1						):
         result += self.coefficients[i] * (substitution**i)
      return result



   def __str__(							self						)			->     Any:







      """simple docstring"""
      lowercase     :      List[str]	=							""""""
      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(snake_case__						)

      return polynomial



   def __repr__(							self						)			->     Dict:







      """simple docstring"""
      return self.__str__()



   def  _UpperCAmelCase						(							self						)			->     Union[str, Any]:







      """simple docstring"""
      lowercase     :      List[Any]	=							[0] * self.degree
      for i in range(self.degree						):
         lowercase     :      Tuple	=							self.coefficients[i + 1] * (i + 1)
      return Polynomial(self.degree - 1   , snake_case__						)



   def  _UpperCAmelCase						(							self   , snake_case = 0						)			->     int:







      """simple docstring"""
      lowercase     :      List[Any]	=							[0] * (self.degree + 2)
      lowercase     :      Union[str, Any]	=							constant
      for i in range(self.degree + 1						):
         lowercase     :      Optional[Any]	=							self.coefficients[i] / (i + 1)
      return Polynomial(self.degree + 1   , snake_case__						)



   def __eq__(							self   , snake_case						)			->     Tuple:







      """simple docstring"""






      if not isinstance(snake_case__   , 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   , snake_case						)			->     Union[str, Any]:







      """simple docstring"""
      return not self.__eq__(snake_case__						)





import string


def 							__lowerCAmelCase     (							_UpperCamelCase		:	str						)		->				str:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      ''
 for i in sequence:
  SCREAMING_SNAKE_CASE		    =      ord(_UpperCamelCase						)
  if 65 <= extract <= 90:
   output += chr(1_55 - extract						)
  elif 97 <= extract <= 1_22:
   output += chr(2_19 - extract						)
  else:
   output += i
 return output


def 							__lowerCAmelCase     (							_UpperCamelCase		:	str						)		->				str:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      string.ascii_letters
 SCREAMING_SNAKE_CASE		    =      string.ascii_lowercase[::-1] + string.ascii_uppercase[::-1]
 return "".join(
     letters_reversed[letters.index(_UpperCamelCase						)] if c in letters else c for c in sequence						)


def 							__lowerCAmelCase     (							)		->				None:
 '''simple docstring'''


 from timeit import timeit

 print('Running performance benchmarks...'						)
 SCREAMING_SNAKE_CASE		    =      'from string import printable ; from __main__ import atbash, atbash_slow'
 print(f"""> atbash_slow(): {timeit('atbash_slow(printable)'		,				setup=_UpperCamelCase						)} seconds"""						)
 print(f""">      atbash(): {timeit('atbash(printable)'		,				setup=_UpperCamelCase						)} seconds"""						)


if __name__ == "__main__":
      for example in ("ABCDEFGH", "123GGjj", "testStringtest", "with space"):
            print(F"""{example} encrypted in atbash: {atbash(example)}""")
      benchmark()

