
from collections.abc import Generator
from math import sin


def 							__A(lowerCAmelCase )		->				bytes:

		"""simple docstring"""






		if len(lowerCAmelCase ) != 3_2:
				raise ValueError("""Input must be of length 32""" )

		_UpperCamelCase						    =	b""""""
		for i in [3, 2, 1, 0]:
				little_endian += string_aa[8 * i : 8 * i + 8]
		return little_endian


def 							__A(lowerCAmelCase )		->				bytes:

		"""simple docstring"""






		if i < 0:
				raise ValueError("""Input must be non-negative""" )

		_UpperCamelCase						    =	format(lowerCAmelCase						,  """08x""" )[-8:]
		_UpperCamelCase						    =	b""""""
		for i in [3, 2, 1, 0]:
				little_endian_hex += hex_rep[2 * i : 2 * i + 2].encode("""utf-8""" )
		return little_endian_hex


def 							__A(lowerCAmelCase )		->				bytes:

		"""simple docstring"""






		_UpperCamelCase						    =	b""""""
		for char in message:
				bit_string += format(lowerCAmelCase						,  """08b""" ).encode("""utf-8""" )
		_UpperCamelCase						    =	format(len(lowerCAmelCase )						,  """064b""" ).encode("""utf-8""" )

		# Pad bit_string to a multiple of 512 chars
		bit_string += b"1"
		while len(lowerCAmelCase ) % 5_1_2 != 4_4_8:
				bit_string += b"0"
		bit_string += to_little_endian(start_len[3_2:] ) + to_little_endian(start_len[:3_2] )

		return bit_string


def 							__A(lowerCAmelCase )		->				Generator[list[int], None, None]:

		"""simple docstring"""






		if len(lowerCAmelCase ) % 5_1_2 != 0:
				raise ValueError("""Input must have length that's a multiple of 512""" )

		for pos in range(0						,  len(lowerCAmelCase )						,  5_1_2 ):
				_UpperCamelCase						    =	bit_string[pos : pos + 5_1_2]
				_UpperCamelCase						    =	[]
				for i in range(0						,  5_1_2						,  3_2 ):
						block_words.append(int(to_little_endian(block[i : i + 3_2] )						,  2 ) )
				yield block_words


def 							__A(lowerCAmelCase )		->				int:

		"""simple docstring"""






		if i < 0:
				raise ValueError("""Input must be non-negative""" )

		_UpperCamelCase						    =	format(lowerCAmelCase						,  """032b""" )
		_UpperCamelCase						    =	""""""
		for c in i_str:
				new_str += "1" if c == "0" else "0"
		return int(lowerCAmelCase						,  2 )


def 							__A(lowerCAmelCase						,  lowerCAmelCase )		->				int:

		"""simple docstring"""






		return (a + b) % 2**3_2


def 							__A(lowerCAmelCase						,  lowerCAmelCase )		->				int:

		"""simple docstring"""






		if i < 0:
				raise ValueError("""Input must be non-negative""" )
		if shift < 0:
				raise ValueError("""Shift must be non-negative""" )
		return ((i << shift) ^ (i >> (3_2 - shift))) % 2**3_2


def 							__A(lowerCAmelCase )		->				bytes:

		"""simple docstring"""






		_UpperCamelCase						    =	preprocess(lowerCAmelCase )

		_UpperCamelCase						    =	[int(2**3_2 * abs(sin(i + 1 ) ) ) for i in range(6_4 )]

		# Starting states
		_UpperCamelCase						    =	0x67452301
		_UpperCamelCase						    =	0xefcdab89
		_UpperCamelCase						    =	0x98badcfe
		_UpperCamelCase						    =	0x10325476

		_UpperCamelCase						    =	[
		    7,
		    1_2,
		    1_7,
		    2_2,
		    7,
		    1_2,
		    1_7,
		    2_2,
		    7,
		    1_2,
		    1_7,
		    2_2,
		    7,
		    1_2,
		    1_7,
		    2_2,
		    5,
		    9,
		    1_4,
		    2_0,
		    5,
		    9,
		    1_4,
		    2_0,
		    5,
		    9,
		    1_4,
		    2_0,
		    5,
		    9,
		    1_4,
		    2_0,
		    4,
		    1_1,
		    1_6,
		    2_3,
		    4,
		    1_1,
		    1_6,
		    2_3,
		    4,
		    1_1,
		    1_6,
		    2_3,
		    4,
		    1_1,
		    1_6,
		    2_3,
		    6,
		    1_0,
		    1_5,
		    2_1,
		    6,
		    1_0,
		    1_5,
		    2_1,
		    6,
		    1_0,
		    1_5,
		    2_1,
		    6,
		    1_0,
		    1_5,
		    2_1,
		]

		# Process bit string in chunks, each with 16 32-char words
		for block_words in get_block_words(lowerCAmelCase ):
				_UpperCamelCase						    =	aa
				_UpperCamelCase						    =	ba
				_UpperCamelCase						    =	ca
				_UpperCamelCase						    =	da

				# Hash current chunk
				for i in range(6_4 ):
						if i <= 1_5:
								# f = (b & c) | (not_32(b) & d)     # Alternate definition for f
								_UpperCamelCase						    =	d ^ (b & (c ^ d))
								_UpperCamelCase						    =	i
						elif i <= 3_1:
								# f = (d & b) | (not_32(d) & c)     # Alternate definition for f
								_UpperCamelCase						    =	c ^ (d & (b ^ c))
								_UpperCamelCase						    =	(5 * i + 1) % 1_6
						elif i <= 4_7:
								_UpperCamelCase						    =	b ^ c ^ d
								_UpperCamelCase						    =	(3 * i + 5) % 1_6
						else:
								_UpperCamelCase						    =	c ^ (b | not_aa(lowerCAmelCase ))
								_UpperCamelCase						    =	(7 * i) % 1_6
						_UpperCamelCase						    =	(f + a + added_consts[i] + block_words[g]) % 2**3_2
						_UpperCamelCase						    =	d
						_UpperCamelCase						    =	c
						_UpperCamelCase						    =	b
						_UpperCamelCase						    =	sum_aa(lowerCAmelCase						,  left_rotate_aa(lowerCAmelCase						,  shift_amounts[i] ) )

				# Add hashed chunk to running total
				_UpperCamelCase						    =	sum_aa(lowerCAmelCase						,  lowerCAmelCase )
				_UpperCamelCase						    =	sum_aa(lowerCAmelCase						,  lowerCAmelCase )
				_UpperCamelCase						    =	sum_aa(lowerCAmelCase						,  lowerCAmelCase )
				_UpperCamelCase						    =	sum_aa(lowerCAmelCase						,  lowerCAmelCase )

		_UpperCamelCase						    =	reformat_hex(lowerCAmelCase ) + reformat_hex(lowerCAmelCase ) + reformat_hex(lowerCAmelCase ) + reformat_hex(lowerCAmelCase )
		return digest


if __name__ == "__main__":
		import doctest

		doctest.testmod()





from __future__ import annotations


def 							__A(lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase						,  )		->				None:

		"""simple docstring"""






		_UpperCamelCase						    =	len(lowerCAmelCase )

		# If row is equal to the size of the board it means there are a queen in each row in
		# the current board (possible_board)
		if row == n:
				# We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
				# this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
				boards.append([""". """ * i + """Q """ + """. """ * (n - 1 - i) for i in possible_board] )
				return

		# We iterate each column in the row to find all possible results in each row
		for col in range(lowerCAmelCase ):
				# We apply that we learned previously. First we check that in the current board
				# (possible_board) there are not other same value because if there is it means
				# that there are a collision in vertical. Then we apply the two formulas we
				# learned before:
				#
				# 45º: y - x = b or 45: row - col = b
				# 135º: y + x = b or row + col = b.
				#
				# And we verify if the results of this two formulas not exist in their variables
				# respectively.  (diagonal_right_collisions, diagonal_left_collisions)
				#
				# If any or these are True it means there is a collision so we continue to the
				# next value in the for loop.
				if (
				    col in possible_board
				    or row - col in diagonal_right_collisions
				    or row + col in diagonal_left_collisions
				):
						continue

				# If it is False we call dfs function again and we update the inputs
				depth_first_search(
				    [*possible_board, col]						,  [*diagonal_right_collisions, row - col]						,  [*diagonal_left_collisions, row + col]						,  lowerCAmelCase						,  lowerCAmelCase						,  )


def 							__A(lowerCAmelCase )		->				None:

		"""simple docstring"""






		_UpperCamelCase						    =	[]
		depth_first_search([]						,  []						,  []						,  lowerCAmelCase						,  lowerCAmelCase )

		# Print all the boards
		for board in boards:
				for column in board:
						print(lowerCAmelCase )
				print("""""" )

		print(len(lowerCAmelCase )						,  """solutions were found.""" )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		n_queens_solution(4)



