





from __future__ import annotations


def     lowerCamelCase_	(      lowerCAmelCase:	str    ,							lowerCAmelCase:	list[str] | None = None    ,							lowerCAmelCase:	dict[str, float] | None = None    ,							lowerCAmelCase:	bool = False    ,							)->		tuple[int, float, str]:
  _snake_case   :				Any														=	cipher_alphabet or [chr(lowerCAmelCase				) for i in range(97    ,							1_23				)]

  # If the argument is None or the user provided an empty dictionary
  if not frequencies_dict:
    # Frequencies of letters in the english language (how much they show up)
    _snake_case   :				Optional[Any]														=	{
        'a': 0.0_8_4_9_7,
        'b': 0.0_1_4_9_2,
        'c': 0.0_2_2_0_2,
        'd': 0.0_4_2_5_3,
        'e': 0.1_1_1_6_2,
        'f': 0.0_2_2_2_8,
        'g': 0.0_2_0_1_5,
        'h': 0.0_6_0_9_4,
        'i': 0.0_7_5_4_6,
        'j': 0.0_0_1_5_3,
        'k': 0.0_1_2_9_2,
        'l': 0.0_4_0_2_5,
        'm': 0.0_2_4_0_6,
        'n': 0.0_6_7_4_9,
        'o': 0.0_7_5_0_7,
        'p': 0.0_1_9_2_9,
        'q': 0.0_0_0_9_5,
        'r': 0.0_7_5_8_7,
        's': 0.0_6_3_2_7,
        't': 0.0_9_3_5_6,
        'u': 0.0_2_7_5_8,
        'v': 0.0_0_9_7_8,
        'w': 0.0_2_5_6_0,
        'x': 0.0_0_1_5_0,
        'y': 0.0_1_9_9_4,
        'z': 0.0_0_0_7_7,
    }
  else:
    # Custom frequencies dictionary
    _snake_case   :				List[Any]														=	frequencies_dict

  if not case_sensitive:
    _snake_case   :				List[Any]														=	ciphertext.lower()

  # Chi squared statistic values
  _snake_case   :				dict[int, tuple[float, str]]														=	{}

  # cycle through all of the shifts
  for shift in range(len(lowerCAmelCase				)				):
    _snake_case   :				List[Any]														=	''

    # decrypt the message with the shift
    for letter in ciphertext:
      try:
        # Try to index the letter in the alphabet
        _snake_case   :				Tuple														=	(alphabet_letters.index(letter.lower()				) - shift) % len(
            lowerCAmelCase				)
        decrypted_with_shift += (
            alphabet_letters[new_key].upper()
            if case_sensitive and letter.isupper()
            else alphabet_letters[new_key]
        )
      except ValueError:
        # Append the character if it isn't in the alphabet
        decrypted_with_shift += letter

    _snake_case   :				Union[str, Any]														=	0.0

    # Loop through each letter in the decoded message with the shift
    for letter in decrypted_with_shift:
      if case_sensitive:
        _snake_case   :				List[Any]														=	letter.lower()
        if letter in frequencies:
          # Get the amount of times the letter occurs in the message
          _snake_case   :				Optional[int]														=	decrypted_with_shift.lower().count(lowerCAmelCase				)

          # Get the excepcted amount of times the letter should appear based
          # on letter frequencies
          _snake_case   :				int														=	frequencies[letter] * occurrences

          # Complete the chi squared statistic formula
          _snake_case   :				Union[str, Any]														=	((occurrences - expected) ** 2) / expected

          # Add the margin of error to the total chi squared statistic
          chi_squared_statistic += chi_letter_value
      else:
        if letter.lower() in frequencies:
          # Get the amount of times the letter occurs in the message
          _snake_case   :				str														=	decrypted_with_shift.count(lowerCAmelCase				)

          # Get the excepcted amount of times the letter should appear based
          # on letter frequencies
          _snake_case   :				int														=	frequencies[letter] * occurrences

          # Complete the chi squared statistic formula
          _snake_case   :				int														=	((occurrences - expected) ** 2) / expected

          # Add the margin of error to the total chi squared statistic
          chi_squared_statistic += chi_letter_value

        # Add the data to the chi_squared_statistic_values dictionary
    _snake_case   :				List[Any]														=	(
        chi_squared_statistic,
        decrypted_with_shift,
    )

  # Get the most likely cipher by finding the cipher with the smallest chi squared
  # statistic
  def chi_squared_statistic_values_sorting_key(lowerCAmelCase:	int				) -> tuple[float, str]:
    return chi_squared_statistic_values[key]

  _snake_case   :				int														=	min(
      lowerCAmelCase    ,							key=lowerCAmelCase    ,							)

  # Get all the data from the most likely cipher (key, decoded message)
  (
      (
      _snake_case
  )							,					(
      _snake_case
  )							,					
  )   :				Optional[int]														=	chi_squared_statistic_values[most_likely_cipher]

  # Return the data on the most likely shift
  return (
      most_likely_cipher,
      most_likely_cipher_chi_squared_value,
      decoded_most_likely_cipher,
  )











from functools import reduce

lowerCAmelCase_						   =    (
    """73167176531330624919225119674426574742355349194934"""
    """96983520312774506326239578318016984801869478851843"""
    """85861560789112949495459501737958331952853208805511"""
    """12540698747158523863050715693290963295227443043557"""
    """66896648950445244523161731856403098711121722383113"""
    """62229893423380308135336276614282806444486645238749"""
    """30358907296290491560440772390713810515859307960866"""
    """70172427121883998797908792274921901699720888093776"""
    """65727333001053367881220235421809751254540594752243"""
    """52584907711670556013604839586446706324415722155397"""
    """53697817977846174064955149290862569321978468622482"""
    """83972241375657056057490261407972968652414535100474"""
    """82166370484403199890008895243450658541227588666881"""
    """16427171479924442928230863465674813919123162824586"""
    """17866458359124566529476545682848912883142607690042"""
    """24219022671055626321111109370544217506941658960408"""
    """07198403850962455444362981230987879927244284909188"""
    """84580156166097919133875499200524063689912560717606"""
    """05886116467109405077541002256983155200055935729725"""
    """71636269561882670428252483600823257530420752963450"""
)


def     lowerCamelCase_	(      lowerCAmelCase:	str = N				)->		int:
  return max(
      # mypy cannot properly interpret reduce
      int(reduce(lambda lowerCAmelCase    ,							lowerCAmelCase				: str(int(lowerCAmelCase				) * int(lowerCAmelCase				)				)    ,							n[i : i + 13]				)				)
      for i in range(len(lowerCAmelCase				) - 12				)				)


if __name__ == "__main__":
      print(F"""{solution() = }""")




