






from __future__ import annotations




def 				A		(					lowercase__  :  str ,		lowercase__  :  list[str] | None = None ,		lowercase__  :  dict[str, float] | None = None ,		lowercase__  :  bool = False ,		)		-> tuple[int, float, str]:
	UpperCamelCase__ :Dict						=      cipher_alphabet or [chr(lowercase__  ) for i in range(97 ,		123  )]

	# 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)
		UpperCamelCase__ :Optional[Any]						=      {
		    """a""": 0.08497,
		    """b""": 0.01492,
		    """c""": 0.02202,
		    """d""": 0.04253,
		    """e""": 0.11162,
		    """f""": 0.02228,
		    """g""": 0.02015,
		    """h""": 0.06094,
		    """i""": 0.07546,
		    """j""": 0.00153,
		    """k""": 0.01292,
		    """l""": 0.04025,
		    """m""": 0.02406,
		    """n""": 0.06749,
		    """o""": 0.07507,
		    """p""": 0.01929,
		    """q""": 0.00095,
		    """r""": 0.07587,
		    """s""": 0.06327,
		    """t""": 0.09356,
		    """u""": 0.02758,
		    """v""": 0.00978,
		    """w""": 0.02560,
		    """x""": 0.00150,
		    """y""": 0.01994,
		    """z""": 0.00077,
		}
	else:
		# Custom frequencies dictionary
		UpperCamelCase__ :Optional[int]						=      frequencies_dict

	if not case_sensitive:
		UpperCamelCase__ :int						=      ciphertext.lower()

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

	# cycle through all of the shifts
	for shift in range(len(lowercase__  )  ):
		UpperCamelCase__ :int						=      """"""

		# decrypt the message with the shift
		for letter in ciphertext:
			try:
				# Try to index the letter in the alphabet
				UpperCamelCase__ :int						=      (alphabet_letters.index(letter.lower()  ) - shift) % len(
				    lowercase__  )
				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

		UpperCamelCase__ :Optional[int]						=      0.0

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

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

					# Complete the chi squared statistic formula
					UpperCamelCase__ :Dict						=      ((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
					UpperCamelCase__ :List[str]						=      decrypted_with_shift.count(lowercase__  )

					# Get the excepcted amount of times the letter should appear based
					# on letter frequencies
					UpperCamelCase__ :Union[str, Any]						=      frequencies[letter] * occurrences

					# Complete the chi squared statistic formula
					UpperCamelCase__ :List[str]						=      ((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
		UpperCamelCase__ :Union[str, 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(lowercase__  :  int  ) -> tuple[float, str]:
		return chi_squared_statistic_values[key]

	UpperCamelCase__ :int						=      min(
	    lowercase__ ,		key=lowercase__ ,		)

	# Get all the data from the most likely cipher (key, decoded message)
	(
	    (
	    UpperCamelCase__
	)				,		(
	    UpperCamelCase__
	)				,		
	) :Tuple						=      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 collections.abc import Iterator, MutableMapping
from dataclasses import dataclass
from typing import Generic, TypeVar

__magic_name__  :  Any					=       TypeVar("""KEY""")
__magic_name__  :  Dict					=       TypeVar("""VAL""")





@dataclass(frozen=_a    ,					slots=_a			)
class     SCREAMING_SNAKE_CASE__		(Generic[KEY, VAL]			):
     lowercase_ :      KEY
     lowercase_ :      VAL





class     SCREAMING_SNAKE_CASE__		(_Item			):
     def __init__(						self	:		Tuple						):



       """simple docstring"""
       super().__init__(__lowerCamelCase       ,						__lowerCamelCase						)



     def __bool__(						self	:		Tuple						):



       """simple docstring"""
       return False



__magic_name__  :  str					=       _DeletedItem()





class     SCREAMING_SNAKE_CASE__		(MutableMapping[KEY, VAL]			):
     def __init__(						self	:		Any       ,						__lowerCamelCase	:		int = 8       ,						__lowerCamelCase	:		float = 0.75						):



       """simple docstring"""
       lowerCAmelCase__										=      initial_block_size
       lowerCAmelCase__										=      [None] * initial_block_size
       assert 0.0 < capacity_factor < 1.0
       lowerCAmelCase__										=      capacity_factor
       lowerCAmelCase__										=      0
     def        A__      (						self	:		Union[str, Any]       ,						__lowerCamelCase	:		KEY						):



       """simple docstring"""
       return hash(__lowerCamelCase						) % len(self._buckets						)
     def        A__      (						self	:		Tuple       ,						__lowerCamelCase	:		int						):



       """simple docstring"""
       return (ind + 1) % len(self._buckets						)
     def        A__      (						self	:		Dict       ,						__lowerCamelCase	:		int       ,						__lowerCamelCase	:		KEY       ,						__lowerCamelCase	:		VAL						):



       """simple docstring"""
       lowerCAmelCase__										=      self._buckets[ind]
       if not stored:
         lowerCAmelCase__										=      _Item(__lowerCamelCase       ,						__lowerCamelCase						)
         self._len += 1
         return True
       elif stored.key == key:
         lowerCAmelCase__										=      _Item(__lowerCamelCase       ,						__lowerCamelCase						)
         return True
       else:
         return False
     def        A__      (						self	:		Any						):



       """simple docstring"""
       lowerCAmelCase__										=      len(self._buckets						) * self._capacity_factor
       return len(self						) >= int(__lowerCamelCase						)
     def        A__      (						self	:		Tuple						):



       """simple docstring"""
       if len(self._buckets						) <= self._initial_block_size:
         return False
       lowerCAmelCase__										=      len(self._buckets						) * self._capacity_factor / 2
       return len(self						) < limit
     def        A__      (						self	:		List[Any]       ,						__lowerCamelCase	:		int						):



       """simple docstring"""
       lowerCAmelCase__										=      self._buckets
       lowerCAmelCase__										=      [None] * new_size
       lowerCAmelCase__										=      0
       for item in old_buckets:
         if item:
           self._add_item(item.key       ,						item.val						)
     def        A__      (						self	:		Any						):



       """simple docstring"""
       self._resize(len(self._buckets						) * 2						)
     def        A__      (						self	:		Dict						):



       """simple docstring"""
       self._resize(len(self._buckets						) // 2						)
     def        A__      (						self	:		List[str]       ,						__lowerCamelCase	:		KEY						):



       """simple docstring"""
       lowerCAmelCase__										=      self._get_bucket_index(__lowerCamelCase						)
       for _ in range(len(self._buckets						)						):
         yield ind
         lowerCAmelCase__										=      self._get_next_ind(__lowerCamelCase						)
     def        A__      (						self	:		Dict       ,						__lowerCamelCase	:		KEY       ,						__lowerCamelCase	:		VAL						):



       """simple docstring"""
       for ind in self._iterate_buckets(__lowerCamelCase						):
         if self._try_set(__lowerCamelCase       ,						__lowerCamelCase       ,						__lowerCamelCase						):
           break
     def __setitem__(						self	:		str       ,						__lowerCamelCase	:		KEY       ,						__lowerCamelCase	:		VAL						):



       """simple docstring"""
       if self._is_full():
         self._size_up()

       self._add_item(__lowerCamelCase       ,						__lowerCamelCase						)
     def __delitem__(						self	:		Tuple       ,						__lowerCamelCase	:		KEY						):



       """simple docstring"""
       for ind in self._iterate_buckets(__lowerCamelCase						):
         lowerCAmelCase__										=      self._buckets[ind]
         if item is None:
           raise KeyError(__lowerCamelCase						)
         if item is _deleted:
           continue
         if item.key == key:
           lowerCAmelCase__										=      _deleted
           self._len -= 1
           break
       if self._is_sparse():
         self._size_down()
     def __getitem__(						self	:		Optional[int]       ,						__lowerCamelCase	:		KEY						):



       """simple docstring"""
       for ind in self._iterate_buckets(__lowerCamelCase						):
         lowerCAmelCase__										=      self._buckets[ind]
         if item is None:
           break
         if item is _deleted:
           continue
         if item.key == key:
           return item.val
       raise KeyError(__lowerCamelCase						)
     def __len__(						self	:		int						):



       """simple docstring"""
       return self._len
     def __iter__(						self	:		Union[str, Any]						):



       """simple docstring"""
       yield from (item.key for item in self._buckets if item)



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



       """simple docstring"""
       lowerCAmelCase__										=      ''' ,'''.join(
           F"""{item.key}: {item.val}""" for item in self._buckets if item						)
       return F"""HashMap({val_string})"""

