





"""simple docstring"""





def 							A_     (__a				):

					'''simple docstring'''





					A_				 =						min(__a				)  # min() finds the minimum value
					A_				 =						max(__a				)  # max() finds the maximum value

					A_				 =						max_val - min_val + 1  # size is difference of max and min values plus one

					# list of pigeonholes of size equal to the variable size
					A_				 =						[0] * size

					# Populate the pigeonholes.
					for x in a:
										assert isinstance(__a				,   __a				), "integers only please"
										holes[x - min_val] += 1

					# Putting the elements back into the array in an order.
					A_				 =						0
					for count in range(__a				):
										while holes[count] > 0:
															holes[count] -= 1
															A_				 =						count + min_val
															i += 1
def 							A_     ():

					'''simple docstring'''





					A_				 =						[8, 3, 2, 7, 4, 6, 8]
					pigeonhole_sort(__a				)
					print("Sorted order is:"				,   " ".join(__a				)				)


if __name__ == "__main__":
		main()






"""simple docstring"""





from __future__ import annotations
def 							A_     (__a				,   __a = None				,   __a = None				,   __a = False				,   ):

					'''simple docstring'''





					A_				 =						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)
										A_				 =						{
										    "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
										A_				 =						frequencies_dict

					if not case_sensitive:
										A_				 =						ciphertext.lower()

					# Chi squared statistic values
					A_				 =						{}

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

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

										A_				 =						0.0

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

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

																									# Complete the chi squared statistic formula
																									A_				 =						((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
																									A_				 =						decrypted_with_shift.count(__a				)

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

																									# Complete the chi squared statistic formula
																									A_				 =						((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
										A_				 =						(
										    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]

					A_				 =						min(
					    __a				,   key=__a				,   )

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




