






from __future__ import annotations
def      a_ (      _A      ,   _A = None      ,   _A = None      ,   _A = False      ,   )			->			tuple[int, float, str]:







				"""simple docstring"""
				snake_case__									=     cipher_alphabet or [chr(_A  ) 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)
								snake_case__									=     {
								    '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__									=     frequencies_dict

				if not case_sensitive:
								snake_case__									=     ciphertext.lower()

				# Chi squared statistic values
				snake_case__									=     {}

				# cycle through all of the shifts
				for shift in range(len(_A  )  ):
								snake_case__									=     ''

								# decrypt the message with the shift
								for letter in ciphertext:
												try:
																# Try to index the letter in the alphabet
																snake_case__									=     (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__									=     0.0

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

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

																				# Complete the chi squared statistic formula
																				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
																				snake_case__									=     decrypted_with_shift.count(_A  )

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

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

				snake_case__									=     min(
				    _A      ,   key=_A      ,   )

				# Get all the data from the most likely cipher (key, decoded message)
				(
				    (
				    snake_case__
				)							,						(
				    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,
				)












def      a_ (      _A      ,   _A  )			->			float:







				"""simple docstring"""
				if digit_amount > 0:
								return round(number - int(_A  )      ,   _A  )
				return number - int(_A  )


if __name__ == "__main__":
							print(decimal_isolate(1.5_3, 0))
							print(decimal_isolate(3_5.3_4_5, 1))
							print(decimal_isolate(3_5.3_4_5, 2))
							print(decimal_isolate(3_5.3_4_5, 3))
							print(decimal_isolate(-1_4.7_8_9, 3))
							print(decimal_isolate(0, 2))
							print(decimal_isolate(-1_4.1_2_3, 1))
							print(decimal_isolate(-1_4.1_2_3, 2))
							print(decimal_isolate(-1_4.1_2_3, 3))




