
from __future__ import annotations



class 		UpperCamelCase__  :
   def __init__(self :					Any					,				snake_case_ :					int   ):
    __a :  Tuple						=  order

    # a_{0} ... a_{k}
    __a :  Dict						=  [1.0] + [0.0] * order
    # b_{0} ... b_{k}
    __a :  Tuple						=  [1.0] + [0.0] * order

    # x[n-1] ... x[n-k]
    __a :  Optional[int]						=  [0.0] * self.order
    # y[n-1] ... y[n-k]
    __a :  List[Any]						=  [0.0] * self.order
   def       lowerCAmelCase			(self :					Dict					,				snake_case_ :					list[float]					,				snake_case_ :					list[float]   ):
    if len(snake_case_   ) < self.order:
     __a :  Any						=  [1.0, *a_coeffs]

    if len(snake_case_   ) != self.order + 1:
     __a :  str						=  (
         f"Expected a_coeffs to have {self.order + 1} elements "
         f"for {self.order}-order filter, got {len(snake_case_   )}"
     )
     raise ValueError(snake_case_   )

    if len(snake_case_   ) != self.order + 1:
     __a :  int						=  (
         f"Expected b_coeffs to have {self.order + 1} elements "
         f"for {self.order}-order filter, got {len(snake_case_   )}"
     )
     raise ValueError(snake_case_   )

    __a :  str						=  a_coeffs
    __a :  List[Any]						=  b_coeffs







   def       lowerCAmelCase			(self :					Any					,				snake_case_ :					float   ):
    __a :  Optional[Any]						=  0.0

    # Start at index 1 and do index 0 at the end.
    for i in range(1					,				self.order + 1   ):
     result += (
         self.b_coeffs[i] * self.input_history[i - 1]
         - self.a_coeffs[i] * self.output_history[i - 1]
     )

    __a :  List[Any]						=  (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

    __a :  Optional[int]						=  self.input_history[:-1]
    __a :  Tuple						=  self.output_history[:-1]

    __a :  Optional[int]						=  sample
    __a :  Dict						=  result

    return result


import string

# frequency taken from https://en.wikipedia.org/wiki/Letter_frequency
lowercase__       ={
    'E': 12.70,
    'T': 9.06,
    'A': 8.17,
    'O': 7.51,
    'I': 6.97,
    'N': 6.75,
    'S': 6.33,
    'H': 6.09,
    'R': 5.99,
    'D': 4.25,
    'L': 4.03,
    'C': 2.78,
    'U': 2.76,
    'M': 2.41,
    'W': 2.36,
    'F': 2.23,
    'G': 2.02,
    'Y': 1.97,
    'P': 1.93,
    'B': 1.29,
    'V': 0.98,
    'K': 0.77,
    'J': 0.15,
    'X': 0.15,
    'Q': 0.10,
    'Z': 0.07,
}
lowercase__       ='ETAOINSHRDLCUMWFGYPBVKJXQZ'
lowercase__       ='ABCDEFGHIJKLMNOPQRSTUVWXYZ'




def    __UpperCamelCase     (				lowerCAmelCase__							:				str  ):
 __a :  List[Any]						=  {letter: 0 for letter in string.ascii_uppercase}
 for letter in message.upper():
  if letter in LETTERS:
   letter_count[letter] += 1

 return letter_count




def    __UpperCamelCase     (				lowerCAmelCase__							:				tuple  ):
 return x[0]




def    __UpperCamelCase     (				lowerCAmelCase__							:				str  ):
 __a :  Optional[Any]						=  get_letter_count(lowerCAmelCase__  )
 __a :  dict[int, list[str]]						=  {
     freq: [] for letter, freq in letter_to_freq.items()
 }
 for letter in LETTERS:
  freq_to_letter[letter_to_freq[letter]].append(lowerCAmelCase__  )

 __a :  dict[int, str]						=  {}

 for freq in freq_to_letter:
  freq_to_letter[freq].sort(key=ETAOIN.find  ,   reverse=lowerCAmelCase__  )
  __a :  int						=  ''''''.join(freq_to_letter[freq]  )

 __a :  Any						=  list(freq_to_letter_str.items()  )
 freq_pairs.sort(key=lowerCAmelCase__  ,   reverse=lowerCAmelCase__  )

 __a :  list[str]						=  [freq_pair[1] for freq_pair in freq_pairs]

 return "".join(lowerCAmelCase__  )




def    __UpperCamelCase     (				lowerCAmelCase__							:				str  ):
 __a :  int						=  get_frequency_order(lowerCAmelCase__  )
 __a :  str						=  0
 for common_letter in ETAOIN[:6]:
  if common_letter in freq_order[:6]:
   match_score += 1

 for uncommon_letter in ETAOIN[-6:]:
  if uncommon_letter in freq_order[-6:]:
   match_score += 1

 return match_score


if __name__ == "__main__":
      import doctest

      doctest.testmod()
