from __future__ import annotations







def 						A__  (					__A   , __A = None   , __A = None   , __A = False   , ):







				'''simple docstring'''
				_lowerCamelCase     :		Tuple 						=						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)
								_lowerCamelCase     :		Dict 						=						{
								    "a": 0.08_497,
								    "b": 0.01_492,
								    "c": 0.02_202,
								    "d": 0.04_253,
								    "e": 0.11_162,
								    "f": 0.02_228,
								    "g": 0.02_015,
								    "h": 0.06_094,
								    "i": 0.07_546,
								    "j": 0.00_153,
								    "k": 0.01_292,
								    "l": 0.04_025,
								    "m": 0.02_406,
								    "n": 0.06_749,
								    "o": 0.07_507,
								    "p": 0.01_929,
								    "q": 0.00_095,
								    "r": 0.07_587,
								    "s": 0.06_327,
								    "t": 0.09_356,
								    "u": 0.02_758,
								    "v": 0.00_978,
								    "w": 0.02_560,
								    "x": 0.00_150,
								    "y": 0.01_994,
								    "z": 0.00_077,
								}
				else:
								# Custom frequencies dictionary
								_lowerCamelCase     :		Optional[int] 						=						frequencies_dict

				if not case_sensitive:
								_lowerCamelCase     :		str 						=						ciphertext.lower()

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

				# cycle through all of the shifts
				for shift in range(len(_A	)	):
								_lowerCamelCase     :		Optional[Any] 						=						""

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

								_lowerCamelCase     :		str 						=						0.0

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

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

																				# Complete the chi squared statistic formula
																				_lowerCamelCase     :		str 						=						((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
																				_lowerCamelCase     :		Any 						=						decrypted_with_shift.count(_A	)

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

																				# Complete the chi squared statistic formula
																				_lowerCamelCase     :		int 						=						((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
								_lowerCamelCase     :		Optional[int] 						=						(
								    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]

				_lowerCamelCase     :		int 						=						min(
				    _A   , key=_A   , )

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

lowerCAmelCase			:							int     =[]







def 						A__  (					__A   , __A   , __A	):







    '''simple docstring'''
    for i in range(len(__A	)	):
        if board[row][i] == 1:
            return False
    for i in range(len(__A	)	):
        if board[i][column] == 1:
            return False
    for i, j in zip(range(__A   , -1   , -1	)   , range(__A   , -1   , -1	)	):
        if board[i][j] == 1:
            return False
    for i, j in zip(range(__A   , -1   , -1	)   , range(__A   , len(__A	)	)	):
        if board[i][j] == 1:
            return False
    return True







def 						A__  (					__A   , __A	):







    '''simple docstring'''
    if row >= len(__A	):
        solution.append(__A	)
        printboard(__A	)
        print()
        return True
    for i in range(len(__A	)	):
        if is_safe(__A   , __A   , __A	):
            _lowerCamelCase     :		int 						=						1
            solve(__A   , row + 1	)
            _lowerCamelCase     :		List[str] 						=						0
    return False







def 						A__  (					__A	):







    '''simple docstring'''
    for i in range(len(__A	)	):
        for j in range(len(__A	)	):
            if board[i][j] == 1:
                print("""Q"""   , end=""" """	)
            else:
                print("""."""   , end=""" """	)
        print()


# n=int(input("The no. of queens"))
lowerCAmelCase			:							int     =8
lowerCAmelCase			:							Union[str, Any]     =[[0 for i in range(n)] for j in range(n)]
solve(board, 0)
print("The total no. of solutions are :", len(solution))




