


'''simple docstring'''




from typing import List

from .keymap import KEYMAP, get_character


def    UpperCAmelCase_  (       A      ):
   '''simple docstring'''





   def decorator(A      ):
      _a					:  str						=  getattr(A		,	'handle_key'		,	[]      )
      handle += [key]
      setattr(A		,	'handle_key'		,	A      )
      return func

   return decorator


def    UpperCAmelCase_  (       *A      ):
   '''simple docstring'''





   def decorator(A      ):
      _a					:  Union[str, Any]						=  getattr(A		,	'handle_key'		,	[]      )
      handle += keys
      setattr(A		,	'handle_key'		,	A      )
      return func

   return decorator







class 					a			(				snake_case__  ):
 '''simple docstring'''




 def __new__(    cls		,      lowerCamelCase_		,      lowerCamelCase_		,      lowerCamelCase_      )      ->    int:
    _a					:  int						=  super().__new__(cls		,      lowerCamelCase_		,      lowerCamelCase_		,      lowerCamelCase_      )
    if not hasattr(lowerCamelCase_		,      'key_handler'      ):
       setattr(lowerCamelCase_		,      'key_handler'		,      {}      )
    setattr(lowerCamelCase_		,      'handle_input'		,      KeyHandler.handle_input      )

    for value in attrs.values():
       _a					:  Optional[int]						=  getattr(lowerCamelCase_		,      'handle_key'		,      []      )
       for key in handled_keys:
          _a					:  Union[str, Any]						=  value
    return new_cls




 @staticmethod
 def   __UpperCamelCase   (    cls      )      ->    str:
    _a					:  Optional[Any]						=  get_character()
    if char != KEYMAP["undefined"]:
       _a					:  List[Any]						=  ord(lowerCamelCase_      )
    _a					:  Optional[Any]						=  cls.key_handler.get(lowerCamelCase_      )
    if handler:
       _a					:  List[str]						=  char
       return handler(cls      )
    else:
       return None





def    UpperCAmelCase_  (       cls      ):
   '''simple docstring'''





   return KeyHandler(cls.__name__		,	cls.__bases__		,	cls.__dict__.copy()      )






'''simple docstring'''




import mpmath  # for roots of unity
import numpy as np







class 					a			:
 '''simple docstring'''




 def __init__(    self		,      lowerCamelCase_=None		,      lowerCamelCase_=None      )      ->    Tuple:
    # Input as list
    _a					:  Optional[int]						=  list(poly_a or [0]      )[:]
    _a					:  List[str]						=  list(poly_b or [0]      )[:]

    # Remove leading zero coefficients
    while self.polyA[-1] == 0:
       self.polyA.pop()
    _a					:  str						=  len(self.polyA      )

    while self.polyB[-1] == 0:
       self.polyB.pop()
    _a					:  Optional[int]						=  len(self.polyB      )

    # Add 0 to make lengths equal a power of 2
    _a					:  str						=  int(
        2 ** np.ceil(np.loga(len(self.polyA      ) + len(self.polyB      ) - 1      )      )      )

    while len(self.polyA      ) < self.c_max_length:
       self.polyA.append(0      )
    while len(self.polyB      ) < self.c_max_length:
       self.polyB.append(0      )
    # A complex root used for the fourier transform
    _a					:  Optional[int]						=  complex(mpmath.root(x=1		,      n=self.c_max_length		,      k=1      )      )

    # The product
    _a					:  Union[str, Any]						=  self.__multiply()




 def   __UpperCamelCase   (    self		,      lowerCamelCase_      )      ->    Dict:
    _a					:  Dict						=  [[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
    # Corner case
    if len(lowerCamelCase_      ) <= 1:
       return dft[0]
    #
    _a					:  List[str]						=  self.c_max_length // 2
    while next_ncol > 0:
       _a					:  Tuple						=  [[] for i in range(lowerCamelCase_      )]
       _a					:  Tuple						=  self.root**next_ncol

       # First half of next step
       _a					:  Optional[Any]						=  1
       for j in range(self.c_max_length // (next_ncol * 2)      ):
          for i in range(lowerCamelCase_      ):
             new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]      )
          current_root *= root
       # Second half of next step
       _a					:  int						=  1
       for j in range(self.c_max_length // (next_ncol * 2)      ):
          for i in range(lowerCamelCase_      ):
             new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]      )
          current_root *= root
       # Update
       _a					:  Union[str, Any]						=  new_dft
       _a					:  List[Any]						=  next_ncol // 2
    return dft[0]




 def   __UpperCamelCase   (    self      )      ->    List[Any]:
    _a					:  Tuple						=  self.__dft('A'      )
    _a					:  Union[str, Any]						=  self.__dft('B'      )
    _a					:  List[Any]						=  [[dft_a[i] * dft_b[i] for i in range(self.c_max_length      )]]
    del dft_a
    del dft_b

    # Corner Case
    if len(inverce_c[0]      ) <= 1:
       return inverce_c[0]
    # Inverse DFT
    _a					:  Optional[Any]						=  2
    while next_ncol <= self.c_max_length:
       _a					:  Optional[int]						=  [[] for i in range(lowerCamelCase_      )]
       _a					:  List[str]						=  self.root ** (next_ncol // 2)
       _a					:  int						=  1
       # First half of next step
       for j in range(self.c_max_length // next_ncol      ):
          for i in range(next_ncol // 2      ):
             # Even positions
             new_inverse_c[i].append(
                 (
                     inverce_c[i][j]
                     + inverce_c[i][j + self.c_max_length // next_ncol]
                 )
                 / 2      )
             # Odd positions
             new_inverse_c[i + next_ncol // 2].append(
                 (
                     inverce_c[i][j]
                     - inverce_c[i][j + self.c_max_length // next_ncol]
                 )
                 / (2 * current_root)      )
          current_root *= root
       # Update
       _a					:  Dict						=  new_inverse_c
       next_ncol *= 2
    # Unpack
    _a					:  Union[str, Any]						=  [round(x[0].real		,      8      ) + round(x[0].imag		,      8      ) * 1J for x in inverce_c]

    # Remove leading 0's
    while inverce_c[-1] == 0:
       inverce_c.pop()
    return inverce_c




 def __str__(    self      )      ->    Dict:
    _a					:  Optional[int]						=  'A = ' + ' + '.join(
        F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyA[: self.len_A]      )      )
    _a					:  Dict						=  'B = ' + ' + '.join(
        F'''{coef}*x^{i}''' for coef, i in enumerate(self.polyB[: self.len_B]      )      )
    _a					:  Tuple						=  'A*B = ' + ' + '.join(
        F'''{coef}*x^{i}''' for coef, i in enumerate(self.product      )      )

    return F'''{a}\n{b}\n{c}'''


# Unit tests
if __name__ == "__main__":
 import doctest

 doctest.testmod()


