'''simple docstring'''







from __future__ import annotations


def    lowerCamelCase       (			UpperCAmelCase__				:  str				,						UpperCAmelCase__				:  list[str] | None = None				,						UpperCAmelCase__				:  dict[str, float] | None = None				,						UpperCAmelCase__				:  bool = False				,						)			->	tuple[int, float, str]:


							'''simple docstring'''






							SCREAMING_SNAKE_CASE__     :Tuple						    = 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__     :Optional[Any]						    = {
														    '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__     :Union[str, Any]						    = frequencies_dict

							if not case_sensitive:
														SCREAMING_SNAKE_CASE__     :List[str]						    = ciphertext.lower()

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

							# cycle through all of the shifts
							for shift in range(len(UpperCAmelCase__		)		):
														SCREAMING_SNAKE_CASE__     :str						    = ''

														# decrypt the message with the shift
														for letter in ciphertext:
																					try:
																												# Try to index the letter in the alphabet
																												SCREAMING_SNAKE_CASE__     :int						    = (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__     :Optional[int]						    = 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__     :Any						    = letter.lower()
																												if letter in frequencies:
																																			# Get the amount of times the letter occurs in the message
																																			SCREAMING_SNAKE_CASE__     :List[Any]						    = decrypted_with_shift.lower().count(UpperCAmelCase__		)

																																			# Get the excepcted amount of times the letter should appear based
																																			# on letter frequencies
																																			SCREAMING_SNAKE_CASE__     :List[Any]						    = frequencies[letter] * occurrences

																																			# Complete the chi squared statistic formula
																																			SCREAMING_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
																																			SCREAMING_SNAKE_CASE__     :Dict						    = decrypted_with_shift.count(UpperCAmelCase__		)

																																			# Get the excepcted amount of times the letter should appear based
																																			# on letter frequencies
																																			SCREAMING_SNAKE_CASE__     :List[Any]						    = frequencies[letter] * occurrences

																																			# Complete the chi squared statistic formula
																																			SCREAMING_SNAKE_CASE__     :Optional[Any]						    = ((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__     :Dict						    = (
														    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__     :int						    = min(
							    UpperCAmelCase__				,						key=UpperCAmelCase__				,						)

							# Get all the data from the most likely cipher (key, decoded message)
							(
							    (
							    SCREAMING_SNAKE_CASE__
							)    ,      (
							    SCREAMING_SNAKE_CASE__
							)    ,      
							)     :Dict						    = 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,
							)







'''simple docstring'''







def    lowerCamelCase       (			UpperCAmelCase__				:  int		)			->	int:


							'''simple docstring'''






							assert (
							    isinstance(UpperCAmelCase__				,						UpperCAmelCase__		) and number_of_steps > 0
							), F'''number_of_steps needs to be positive integer, your input {number_of_steps}'''
							if number_of_steps == 1:
														return 1
							SCREAMING_SNAKE_CASE__    ,      SCREAMING_SNAKE_CASE__     :Dict						    = 1, 1
							for _ in range(number_of_steps - 1		):
														SCREAMING_SNAKE_CASE__    ,      SCREAMING_SNAKE_CASE__     :Union[str, Any]						    = current + previous, current
							return current


if __name__ == "__main__":
		import doctest

		doctest.testmod()






