





def 							SCREAMING_SNAKE_CASE__						(    __a   )     ->   Tuple:
	if not isinstance(__a   , __a   ) or number < 0:
		raise ValueError('Input must be a non-negative integer'   )

	snake_case_		:			Tuple											=	0
	while number:
		# This way we arrive at next set bit (next 1) instead of looping
		# through each bit and checking for 1s hence the
		# loop won't run 32 times it will only run the number of `1` times
		number &= number - 1
		count += 1
	return count


if __name__ == "__main__":
						import doctest

						doctest.testmod()








from __future__ import annotations


def 							SCREAMING_SNAKE_CASE__						(    __a   , __a = None   , __a = None   , __a = False   , ):
	snake_case_		:			int											=	cipher_alphabet or [chr(__a   ) 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_		:			Dict											=	{
		    '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
		snake_case_		:			int											=	frequencies_dict

	if not case_sensitive:
		snake_case_		:			Optional[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(__a   )   ):
		snake_case_		:			int											=	''

		# decrypt the message with the shift
		for letter in ciphertext:
			try:
				# Try to index the letter in the alphabet
				snake_case_		:			List[Any]											=	(alphabet_letters.index(letter.lower()   ) - shift) % len(
				    __a   )
				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[Any]											=	decrypted_with_shift.lower().count(__a   )

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

					# Complete the chi squared statistic formula
					snake_case_		:			Optional[int]											=	((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_		:			Any											=	decrypted_with_shift.count(__a   )

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

					# Complete the chi squared statistic formula
					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
		snake_case_		:			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(__a   ) -> tuple[float, str]:
		return chi_squared_statistic_values[key]

	snake_case_		:			int											=	min(
	    __a   , key=__a   , )

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

