




'''simple docstring'''



from __future__ import annotations




def   lowercase__(			__UpperCamelCase:					list[int]      ,__UpperCamelCase:					list[int]      ,__UpperCamelCase:					list[int]      ,__UpperCamelCase:					list[list[str]]      ,__UpperCamelCase:					int      ,):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Tuple    					=						len(__UpperCamelCase    )

      # 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(__UpperCamelCase    ):
            # 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]      ,__UpperCamelCase      ,__UpperCamelCase      ,)




def   lowercase__(			__UpperCamelCase:					int    ):

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      list[list[str]]    					=						[]
      depth_first_search([]      ,[]      ,[]      ,__UpperCamelCase      ,__UpperCamelCase    )

      # Print all the boards
      for board in boards:
            for column in board:
                  print(__UpperCamelCase    )
            print(''    )

      print(len(__UpperCamelCase    )      ,'solutions were found.'    )


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      n_queens_solution(4)






from transformers import BertTokenizer, EncoderDecoderModel, SeqaSeqTrainer, SeqaSeqTrainingArguments
from transformers.testing_utils import TestCasePlus, require_torch, slow
from transformers.utils import is_datasets_available


if is_datasets_available():
	import datasets



class 				A       (			UpperCAmelCase__				):
					'''simple docstring'''






					@slow
					@require_torch
					def     lowerCamelCase__	(self       :		int						)		->  Tuple:




							"""simple docstring"""


							lowercase__	     =						EncoderDecoderModel.from_encoder_decoder_pretrained("""prajjwal1/bert-tiny""" ,   """prajjwal1/bert-tiny"""						)
							lowercase__	     =						BertTokenizer.from_pretrained("""bert-base-uncased"""						)

							lowercase__	     =						bertabert.config.encoder.vocab_size
							lowercase__	     =						tokenizer.sep_token_id
							lowercase__	     =						tokenizer.cls_token_id
							lowercase__	     =						128

							lowercase__	     =						datasets.load_dataset("""cnn_dailymail""" ,   """3.0.0""" ,   split="""train[:1%]"""						)
							lowercase__	     =						datasets.load_dataset("""cnn_dailymail""" ,   """3.0.0""" ,   split="""validation[:1%]"""						)

							lowercase__	     =						train_dataset.select(range(32						)						)
							lowercase__	     =						val_dataset.select(range(16						)						)

							lowercase__	     =						4

							def _map_to_encoder_decoder_inputs(_UpperCAmelCase       :		Any						):
									# Tokenizer will automatically set [BOS] <text> [EOS]
									lowercase__	     =						tokenizer(batch["""article"""] ,   padding="""max_length""" ,   truncation=_UpperCAmelCase ,   max_length=512						)
									lowercase__	     =						tokenizer(batch["""highlights"""] ,   padding="""max_length""" ,   truncation=_UpperCAmelCase ,   max_length=128						)
									lowercase__	     =						inputs.input_ids
									lowercase__	     =						inputs.attention_mask

									lowercase__	     =						outputs.input_ids
									lowercase__	     =						outputs.input_ids.copy()
									lowercase__	     =						[
									    [-100 if token == tokenizer.pad_token_id else token for token in labels] for labels in batch["""labels"""]
									]
									lowercase__	     =						outputs.attention_mask

									assert all(len(_UpperCAmelCase						) == 512 for x in inputs.input_ids						)
									assert all(len(_UpperCAmelCase						) == 128 for x in outputs.input_ids						)

									return batch

							def _compute_metrics(_UpperCAmelCase       :		List[Any]						):
									lowercase__	     =						pred.label_ids
									lowercase__	     =						pred.predictions

									# all unnecessary tokens are removed
									lowercase__	     =						tokenizer.batch_decode(_UpperCAmelCase ,   skip_special_tokens=_UpperCAmelCase						)
									lowercase__	     =						tokenizer.batch_decode(_UpperCAmelCase ,   skip_special_tokens=_UpperCAmelCase						)

									lowercase__	     =						sum([int(pred_str[i] == label_str[i]						) for i in range(len(_UpperCAmelCase						)						)]						) / len(_UpperCAmelCase						)

									return {"accuracy": accuracy}

							# map train dataset
							lowercase__	     =						train_dataset.map(
							    _map_to_encoder_decoder_inputs ,   batched=_UpperCAmelCase ,   batch_size=_UpperCAmelCase ,   remove_columns=["""article""", """highlights"""] ,   )
							train_dataset.set_format(
							    type="""torch""" ,   columns=["""input_ids""", """attention_mask""", """decoder_input_ids""", """decoder_attention_mask""", """labels"""] ,   )

							# same for validation dataset
							lowercase__	     =						val_dataset.map(
							    _map_to_encoder_decoder_inputs ,   batched=_UpperCAmelCase ,   batch_size=_UpperCAmelCase ,   remove_columns=["""article""", """highlights"""] ,   )
							val_dataset.set_format(
							    type="""torch""" ,   columns=["""input_ids""", """attention_mask""", """decoder_input_ids""", """decoder_attention_mask""", """labels"""] ,   )

							lowercase__	     =						self.get_auto_remove_tmp_dir()

							lowercase__	     =						SeqaSeqTrainingArguments(
							    output_dir=_UpperCAmelCase ,   per_device_train_batch_size=_UpperCAmelCase ,   per_device_eval_batch_size=_UpperCAmelCase ,   predict_with_generate=_UpperCAmelCase ,   evaluation_strategy="""steps""" ,   do_train=_UpperCAmelCase ,   do_eval=_UpperCAmelCase ,   warmup_steps=0 ,   eval_steps=2 ,   logging_steps=2 ,   )

							# instantiate trainer
							lowercase__	     =						SeqaSeqTrainer(
							    model=_UpperCAmelCase ,   args=_UpperCAmelCase ,   compute_metrics=_compute_metrics ,   train_dataset=_UpperCAmelCase ,   eval_dataset=_UpperCAmelCase ,   tokenizer=_UpperCAmelCase ,   )

							# start training
							trainer.train()

