from __future__ import annotations





def 		__lowerCamelCase							(UpperCAmelCase__       :							str ,	UpperCAmelCase__       :							list[str] | None = None ,	UpperCAmelCase__       :							dict[str, float] | None = None ,	UpperCAmelCase__       :							bool = False ,	):
					SCREAMING_SNAKE_CASE           =    cipher_alphabet or [chr(UpperCAmelCase__					) for i in range(9_7 ,	1_2_3					)]

					# 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)
										SCREAMING_SNAKE_CASE           =    {
										    "a": 0.0_8497,
										    "b": 0.0_1492,
										    "c": 0.0_2202,
										    "d": 0.0_4253,
										    "e": 0.1_1162,
										    "f": 0.0_2228,
										    "g": 0.0_2015,
										    "h": 0.0_6094,
										    "i": 0.0_7546,
										    "j": 0.0_0153,
										    "k": 0.0_1292,
										    "l": 0.0_4025,
										    "m": 0.0_2406,
										    "n": 0.0_6749,
										    "o": 0.0_7507,
										    "p": 0.0_1929,
										    "q": 0.0_0095,
										    "r": 0.0_7587,
										    "s": 0.0_6327,
										    "t": 0.0_9356,
										    "u": 0.0_2758,
										    "v": 0.0_0978,
										    "w": 0.0_2560,
										    "x": 0.0_0150,
										    "y": 0.0_1994,
										    "z": 0.0_0077,
										}
					else:
										# Custom frequencies dictionary
										SCREAMING_SNAKE_CASE           =    frequencies_dict

					if not case_sensitive:
										SCREAMING_SNAKE_CASE           =    ciphertext.lower()

					# Chi squared statistic values
					SCREAMING_SNAKE_CASE           =    {}

					# cycle through all of the shifts
					for shift in range(len(UpperCAmelCase__					)					):
										SCREAMING_SNAKE_CASE           =    ""

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

										SCREAMING_SNAKE_CASE           =    0.0

										# Loop through each letter in the decoded message with the shift
										for letter in decrypted_with_shift:
															if case_sensitive:
																				SCREAMING_SNAKE_CASE           =    letter.lower()
																				if letter in frequencies:
																									# Get the amount of times the letter occurs in the message
																									SCREAMING_SNAKE_CASE           =    decrypted_with_shift.lower().count(UpperCAmelCase__					)

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

																									# Complete the chi squared statistic formula
																									SCREAMING_SNAKE_CASE           =    ((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
																									SCREAMING_SNAKE_CASE           =    decrypted_with_shift.count(UpperCAmelCase__					)

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

																									# Complete the chi squared statistic formula
																									SCREAMING_SNAKE_CASE           =    ((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
										SCREAMING_SNAKE_CASE           =    (
										    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(UpperCAmelCase__       :							int					) -> tuple[float, str]:
										return chi_squared_statistic_values[key]

					SCREAMING_SNAKE_CASE           =    min(
					    UpperCAmelCase__ ,	key=UpperCAmelCase__ ,	)

					# Get all the data from the most likely cipher (key, decoded message)
					(
					    (
					    SCREAMING_SNAKE_CASE
					)     ,				(
					    SCREAMING_SNAKE_CASE
					)     ,				
					)           =    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 __future__ import annotations

from collections.abc import Iterator


class   lowercase      :




							def __init__(  self				:   str		,							_UpperCamelCase				:   int )   ->			None:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    value
												SCREAMING_SNAKE_CASE           =    None
												SCREAMING_SNAKE_CASE           =    None



class   lowercase      :




							def __init__(  self				:   str		,							_UpperCamelCase				:   Node )   ->			None:



												'''simple docstring'''

												SCREAMING_SNAKE_CASE           =    tree




							def 		__snake_case(  self				:   int		,							_UpperCamelCase				:   Node | None )   ->			int:



												'''simple docstring'''

												if node is None:
																	return 0
												return node.value + (
												    self.depth_first_search(node.left ) + self.depth_first_search(node.right )
												)





							def __iter__(  self				:   List[Any] )   ->			Iterator[int]:



												'''simple docstring'''

												yield self.depth_first_search(self.tree )


if __name__ == "__main__":
							import doctest

							doctest.testmod()




