



'''simple docstring'''



from __future__ import annotations

lowerCamelCase	 =       []



def   _A       (   _lowerCAmelCase  ,   _lowerCAmelCase  ,   _lowerCAmelCase					):



							"""simple docstring"""



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



def   _A       (   _lowerCAmelCase  ,   _lowerCAmelCase					):



							"""simple docstring"""



							if row >= len(lowerCamelCase_					):
														solution.append(lowerCamelCase_					)
														printboard(lowerCamelCase_					)
														print()
														return True
							for i in range(len(lowerCamelCase_					)					):
														if is_safe(lowerCamelCase_  ,   lowerCamelCase_  ,   lowerCamelCase_					):
																					__lowercase       	=1
																					solve(lowerCamelCase_  ,   row + 1					)
																					__lowercase       	=0
							return False



def   _A       (   _lowerCAmelCase					):



							"""simple docstring"""



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


# n=int(input("The no. of queens"))
lowerCamelCase	 =       8
lowerCamelCase	 =       [[0 for i in range(n)] for j in range(n)]
solve(board, 0)


print("""The total no. of solutions are :""", len(solution))









'''simple docstring'''



from __future__ import annotations



def   _A       (   _lowerCAmelCase  ,   _lowerCAmelCase = None  ,   _lowerCAmelCase = None  ,   _lowerCAmelCase = False  ,   ):



							"""simple docstring"""



							__lowercase       	=cipher_alphabet or [chr(_lowerCAmelCase					) 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)
														__lowercase       	={
														    'a': 0.0_84_97,
														    'b': 0.0_14_92,
														    'c': 0.0_22_02,
														    'd': 0.0_42_53,
														    'e': 0.1_11_62,
														    'f': 0.0_22_28,
														    'g': 0.0_20_15,
														    'h': 0.0_60_94,
														    'i': 0.0_75_46,
														    'j': 0.0_01_53,
														    'k': 0.0_12_92,
														    'l': 0.0_40_25,
														    'm': 0.0_24_06,
														    'n': 0.0_67_49,
														    'o': 0.0_75_07,
														    'p': 0.0_19_29,
														    'q': 0.0_00_95,
														    'r': 0.0_75_87,
														    's': 0.0_63_27,
														    't': 0.0_93_56,
														    'u': 0.0_27_58,
														    'v': 0.0_09_78,
														    'w': 0.0_25_60,
														    'x': 0.0_01_50,
														    'y': 0.0_19_94,
														    'z': 0.0_00_77,
														}
							else:
														# Custom frequencies dictionary
														__lowercase       	=frequencies_dict

							if not case_sensitive:
														__lowercase       	=ciphertext.lower()

							# Chi squared statistic values
							__lowercase       	={}

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

														# decrypt the message with the shift
														for letter in ciphertext:
																					try:
																												# Try to index the letter in the alphabet
																												__lowercase       	=(alphabet_letters.index(letter.lower()					) - shift) % len(
																												    _lowerCAmelCase					)
																												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

														__lowercase       	=0.0

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

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

																																			# Complete the chi squared statistic formula
																																			__lowercase       	=((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
																																			__lowercase       	=decrypted_with_shift.count(_lowerCAmelCase					)

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

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

							__lowercase       	=min(
							    _lowerCAmelCase  ,   key=_lowerCAmelCase  ,   )

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



