
'''simple docstring'''






from __future__ import annotations







def 		A_							(						_lowerCAmelCase :     list[int]					,						_lowerCAmelCase :     list[int]					,						_lowerCAmelCase :     list[int]					,						_lowerCAmelCase :     list[list[str]]					,						_lowerCAmelCase :     int					,						):



      """simple docstring"""




      _lowerCamelCase					: Any		    = 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 :     int				):



      """simple docstring"""




      _lowerCamelCase					: list[list[str]]		    = []
      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)






"""simple docstring"""






import os
import unicodedata
from shutil import copyfile
from typing import Any, Dict, List, Optional, Tuple

import sentencepiece as spm

from ...tokenization_utils import AddedToken, PreTrainedTokenizer
from ...utils import SPIECE_UNDERLINE, logging


__UpperCAmelCase						=			logging.get_logger(__name__)

__UpperCAmelCase						=			{'''vocab_file''': '''spiece.model'''}

__UpperCAmelCase						=			{
    '''vocab_file''': {
        '''TsinghuaAI/CPM-Generate''': '''https://huggingface.co/TsinghuaAI/CPM-Generate/resolve/main/spiece.model''',
    }
}



class 					__UpperCAmelCase							(						_UpperCamelCase  ):
				def __init__(		self    :			str	, a_    :			Dict	, a_    :			List[str]=False	, a_    :			Any=True	, a_    :			int=False	, a_    :			Union[str, Any]="<s>"	, a_    :			Optional[int]="</s>"	, a_    :			int="<unk>"	, a_    :			List[Any]="<sep>"	, a_    :			Dict="<pad>"	, a_    :			Any="<cls>"	, a_    :			Optional[Any]="<mask>"	, a_    :			int=["<eop>", "<eod>"]	, a_    :			Optional[Dict[str, Any]] = None	, **a_    :			int	, )	->	None:



							'''simple docstring'''



							a__  :	List[str]		 =			AddedToken(a_	, lstrip=a_	, rstrip=a_    ) if isinstance(a_	, a_    ) else mask_token

							a__  :	List[str]		 =			{} if sp_model_kwargs is None else sp_model_kwargs

							super().__init__(
							    do_lower_case=a_	, remove_space=a_	, keep_accents=a_	, bos_token=a_	, eos_token=a_	, unk_token=a_	, sep_token=a_	, pad_token=a_	, cls_token=a_	, mask_token=a_	, additional_special_tokens=a_	, sp_model_kwargs=self.sp_model_kwargs	, **a_	, )

							a__  :	Union[str, Any]		 =			3

							a__  :	Dict		 =			do_lower_case
							a__  :	Union[str, Any]		 =			remove_space
							a__  :	int		 =			keep_accents
							a__  :	str		 =			vocab_file

							a__  :	str		 =			spm.SentencePieceProcessor(**self.sp_model_kwargs    )
							self.sp_model.Load(a_    )

							try:
										import jieba
							except ModuleNotFoundError as error:
										raise error.__class__(
										    "You need to install jieba to use CpmTokenizer or CpmTokenizerFast. "
										    "See https://pypi.org/project/jieba/ for installation."    )
							a__  :	Optional[int]		 =			jieba
							a__  :	Optional[int]		 =			str.maketrans(" \n"	, "\u2582\u2583"    )
				@property
				# Copied from transformers.models.xlnet.tokenization_xlnet.XLNetTokenizer.vocab_size
				def       UpperCAmelCase      (		self    :			Union[str, Any]    )	->	str:



							'''simple docstring'''



							return len(self.sp_model    )
				def       UpperCAmelCase      (		self    :			Dict    )	->	Union[str, Any]:



							'''simple docstring'''



							a__  :	Optional[int]		 =			{self.convert_ids_to_tokens(a_    ): i for i in range(self.vocab_size    )}
							vocab.update(self.added_tokens_encoder    )
							return vocab
				def __getstate__(		self    :			Tuple    )	->	List[str]:



							'''simple docstring'''



							a__  :	Tuple		 =			self.__dict__.copy()
							a__  :	Union[str, Any]		 =			None
							return state
				def __setstate__(		self    :			Tuple	, a_    :			int    )	->	List[str]:



							'''simple docstring'''



							a__  :	Any		 =			d

							# for backward compatibility
							if not hasattr(self	, "sp_model_kwargs"    ):
										a__  :	str		 =			{}

							a__  :	List[str]		 =			spm.SentencePieceProcessor(**self.sp_model_kwargs    )
							self.sp_model.Load(self.vocab_file    )
				def       UpperCAmelCase      (		self    :			List[Any]	, a_    :			Optional[Any]    )	->	List[str]:



							'''simple docstring'''



							if self.remove_space:
										a__  :	Union[str, Any]		 =			" ".join(inputs.strip().split()    )
							else:
										a__  :	Optional[Any]		 =			inputs
							a__  :	List[str]		 =			outputs.replace("``"	, "\""    ).replace("''"	, "\""    )

							if not self.keep_accents:
										a__  :	Union[str, Any]		 =			unicodedata.normalize("NFKD"	, a_    )
										a__  :	Union[str, Any]		 =			"".join([c for c in outputs if not unicodedata.combining(a_    )]    )
							if self.do_lower_case:
										a__  :	List[Any]		 =			outputs.lower()

							return outputs
				def       UpperCAmelCase      (		self    :			Any	, a_    :			str    )	->	List[str]:



							'''simple docstring'''



							a__  :	Optional[Any]		 =			self.preprocess_text(a_    )
							a__  :	Dict		 =			self.sp_model.encode(a_	, out_type=a_    )
							a__  :	Optional[Any]		 =			[]
							for piece in pieces:
										if len(a_    ) > 1 and piece[-1] == str(","    ) and piece[-2].isdigit():
													a__  :	Optional[Any]		 =			self.sp_model.EncodeAsPieces(piece[:-1].replace(a_	, ""    )    )
													if piece[0] != SPIECE_UNDERLINE and cur_pieces[0][0] == SPIECE_UNDERLINE:
																if len(cur_pieces[0]    ) == 1:
																			a__  :	List[str]		 =			cur_pieces[1:]
																else:
																			a__  :	List[str]		 =			cur_pieces[0][1:]
													cur_pieces.append(piece[-1]    )
													new_pieces.extend(a_    )
										else:
													new_pieces.append(a_    )

							return new_pieces
				def       UpperCAmelCase      (		self    :			int	, a_    :			Dict    )	->	int:



							'''simple docstring'''



							return self.sp_model.PieceToId(a_    )
				def       UpperCAmelCase      (		self    :			Dict	, a_    :			Tuple    )	->	List[Any]:



							'''simple docstring'''



							return self.sp_model.IdToPiece(a_    )
				def       UpperCAmelCase      (		self    :			Union[str, Any]	, a_    :			List[Any]    )	->	str:



							'''simple docstring'''



							a__  :	Optional[Any]		 =			"".join(a_    ).replace(a_	, " "    ).strip()
							return out_string
				def       UpperCAmelCase      (		self    :			str	, a_    :			List[int]	, a_    :			Optional[List[int]] = None    )	->	List[int]:



							'''simple docstring'''



							a__  :	List[Any]		 =			[self.sep_token_id]
							a__  :	int		 =			[self.cls_token_id]
							if token_ids_a is None:
										return token_ids_a + sep + cls
							return token_ids_a + sep + token_ids_a + sep + cls
				def       UpperCAmelCase      (		self    :			int	, a_    :			List[int]	, a_    :			Optional[List[int]] = None	, a_    :			bool = False    )	->	List[int]:



							'''simple docstring'''



							if already_has_special_tokens:
										return super().get_special_tokens_mask(
										    token_ids_a=a_	, token_ids_a=a_	, already_has_special_tokens=a_    )

							if token_ids_a is not None:
										return ([0] * len(a_    )) + [1] + ([0] * len(a_    )) + [1, 1]
							return ([0] * len(a_    )) + [1, 1]
				def       UpperCAmelCase      (		self    :			List[Any]	, a_    :			List[int]	, a_    :			Optional[List[int]] = None    )	->	List[int]:



							'''simple docstring'''



							a__  :	List[str]		 =			[self.sep_token_id]
							a__  :	Tuple		 =			[2]

							if token_ids_a is None:
										return len(token_ids_a + sep    ) * [0] + cls_segment_id
							return len(token_ids_a + sep    ) * [0] + len(token_ids_a + sep    ) * [1] + cls_segment_id
				def       UpperCAmelCase      (		self    :			Dict	, a_    :			str	, a_    :			Optional[str] = None    )	->	Tuple[str]:



							'''simple docstring'''



							if not os.path.isdir(a_    ):
										logger.error(F"Vocabulary path ({save_directory}) should be a directory"    )
										return
							a__  :	Optional[int]		 =			os.path.join(
							    a_	, (filename_prefix + "-" if filename_prefix else "") + VOCAB_FILES_NAMES["vocab_file"]    )

							if os.path.abspath(self.vocab_file    ) != os.path.abspath(a_    ) and os.path.isfile(self.vocab_file    ):
										copyfile(self.vocab_file	, a_    )
							elif not os.path.isfile(self.vocab_file    ):
										with open(a_	, "wb"    ) as fi:
													a__  :	int		 =			self.sp_model.serialized_model_proto()
													fi.write(a_    )

							return (out_vocab_file,)






				def       UpperCAmelCase      (		self    :			str	, *a_    :			Union[str, Any]	, **a_    :			Any    )	->	int:



							'''simple docstring'''



							a__  :	Optional[int]		 =			super()._decode(*a_	, **a_    )
							a__  :	Tuple		 =			text.replace(" "	, ""    ).replace("\u2582"	, " "    ).replace("\u2583"	, "\n"    )
							return text