




import math
import time
from typing import Dict, List, Optional

from torch.utils.data import Dataset

from transformers import SeqaSeqTrainer, is_torch_tpu_available
from transformers.trainer_utils import PredictionOutput, speed_metrics


if is_torch_tpu_available(check_device=False):
       import torch_xla.core.xla_model as xm
       import torch_xla.debug.metrics as met





class     lowerCamelCase__(					__lowerCamelCase):
      def __init__(				self: Dict    ,       *UpperCamelCase_: Any    ,       UpperCamelCase_: int=None    ,       UpperCamelCase_: List[str]=None    ,       **UpperCamelCase_: str   ):
             super().__init__(*UpperCamelCase_    ,       **UpperCamelCase_   )
             __lowerCamelCase   =						eval_examples
             __lowerCamelCase   =						post_process_function
      def 			lowerCAmelCase__						(				self: Any    ,       UpperCamelCase_: Optional[Dataset] = None    ,       UpperCamelCase_: List[str]=None    ,       UpperCamelCase_: Optional[List[str]] = None    ,       UpperCamelCase_: str = "eval"    ,       **UpperCamelCase_: int    ,       ):
             __lowerCamelCase   =						gen_kwargs.copy()
             __lowerCamelCase   =						(
                 gen_kwargs["""max_length"""] if gen_kwargs.get("""max_length"""   ) is not None else self.args.generation_max_length
             )
             __lowerCamelCase   =						(
                 gen_kwargs["""num_beams"""] if gen_kwargs.get("""num_beams"""   ) is not None else self.args.generation_num_beams
             )
             __lowerCamelCase   =						gen_kwargs

             __lowerCamelCase   =						self.eval_dataset if eval_dataset is None else eval_dataset
             __lowerCamelCase   =						self.get_eval_dataloader(UpperCamelCase_   )
             __lowerCamelCase   =						self.eval_examples if eval_examples is None else eval_examples

             # Temporarily disable metric computation, we will do it in the loop here.
             __lowerCamelCase   =						self.compute_metrics
             __lowerCamelCase   =						None
             __lowerCamelCase   =						time.time()
             __lowerCamelCase   =						self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
             try:
                    __lowerCamelCase   =						eval_loop(
                        UpperCamelCase_    ,       description="""Evaluation"""    ,       prediction_loss_only=True if compute_metrics is None else None    ,       ignore_keys=UpperCamelCase_    ,       metric_key_prefix=UpperCamelCase_    ,       )
             finally:
                    __lowerCamelCase   =						compute_metrics
             __lowerCamelCase   =						self.args.eval_batch_size * self.args.world_size
             if F'{metric_key_prefix}_jit_compilation_time' in output.metrics:
                    start_time += output.metrics[F'{metric_key_prefix}_jit_compilation_time']
             output.metrics.update(
                 speed_metrics(
                     UpperCamelCase_    ,       UpperCamelCase_    ,       num_samples=output.num_samples    ,       num_steps=math.ceil(output.num_samples / total_batch_size   )    ,       )   )

             if self.post_process_function is not None and self.compute_metrics is not None and self.args.should_save:
                    # Only the main node write the results by default
                    __lowerCamelCase   =						self.post_process_function(UpperCamelCase_    ,       UpperCamelCase_    ,       UpperCamelCase_   )
                    __lowerCamelCase   =						self.compute_metrics(UpperCamelCase_   )

                    # Prefix all keys with metric_key_prefix + '_'
                    for key in list(metrics.keys()   ):
                           if not key.startswith(F'{metric_key_prefix}_'   ):
                                  __lowerCamelCase   =						metrics.pop(UpperCamelCase_   )

                    metrics.update(output.metrics   )
             else:
                    __lowerCamelCase   =						output.metrics

             if self.args.should_log:
                    # Only the main node log the results by default
                    self.log(UpperCamelCase_   )

             if self.args.tpu_metrics_debug or self.args.debug:
                    # tpu-comment: Logging debug metrics for PyTorch/XLA (compile, execute times, ops, etc.)
                    xm.master_print(met.metrics_report()   )

             __lowerCamelCase   =						self.callback_handler.on_evaluate(self.args    ,       self.state    ,       self.control    ,       UpperCamelCase_   )
             return metrics




      def 			lowerCAmelCase__						(				self: List[str]    ,       UpperCamelCase_: Dict    ,       UpperCamelCase_: Optional[Any]    ,       UpperCamelCase_: List[Any]=None    ,       UpperCamelCase_: str = "test"    ,       **UpperCamelCase_: Dict   ):
             __lowerCamelCase   =						gen_kwargs.copy()

             __lowerCamelCase   =						self.get_test_dataloader(UpperCamelCase_   )

             # Temporarily disable metric computation, we will do it in the loop here.
             __lowerCamelCase   =						self.compute_metrics
             __lowerCamelCase   =						None
             __lowerCamelCase   =						time.time()
             __lowerCamelCase   =						self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
             try:
                    __lowerCamelCase   =						eval_loop(
                        UpperCamelCase_    ,       description="""Prediction"""    ,       prediction_loss_only=True if compute_metrics is None else None    ,       ignore_keys=UpperCamelCase_    ,       metric_key_prefix=UpperCamelCase_    ,       )
             finally:
                    __lowerCamelCase   =						compute_metrics

             __lowerCamelCase   =						self.args.eval_batch_size * self.args.world_size
             if F'{metric_key_prefix}_jit_compilation_time' in output.metrics:
                    start_time += output.metrics[F'{metric_key_prefix}_jit_compilation_time']
             output.metrics.update(
                 speed_metrics(
                     UpperCamelCase_    ,       UpperCamelCase_    ,       num_samples=output.num_samples    ,       num_steps=math.ceil(output.num_samples / total_batch_size   )    ,       )   )
             if self.post_process_function is None or self.compute_metrics is None:
                    return output

             __lowerCamelCase   =						self.post_process_function(UpperCamelCase_    ,       UpperCamelCase_    ,       UpperCamelCase_    ,       """predict"""   )
             __lowerCamelCase   =						self.compute_metrics(UpperCamelCase_   )

             # Prefix all keys with metric_key_prefix + '_'
             for key in list(metrics.keys()   ):
                    if not key.startswith(F'{metric_key_prefix}_'   ):
                           __lowerCamelCase   =						metrics.pop(UpperCamelCase_   )
             metrics.update(output.metrics   )
             return PredictionOutput(predictions=predictions.predictions    ,       label_ids=predictions.label_ids    ,       metrics=UpperCamelCase_   )







from __future__ import annotations




def 					lowerCamelCase__       (						A__       :					list[int]  ,			A__       :					list[int]  ,			A__       :					list[int]  ,			A__       :					list[list[str]]  ,			A__       :					int  ,			):





       '''simple docstring'''



       __lowerCamelCase   =						len(A__	)

       # 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(A__	):
              # 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]  ,			A__  ,			A__  ,			)




def 					lowerCamelCase__       (						A__       :					int	):





       '''simple docstring'''



       __lowerCamelCase   =						[]
       depth_first_search([]  ,			[]  ,			[]  ,			A__  ,			A__	)

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

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


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       n_queens_solution(4)

