"""simple docstring"""



from typing import Any, Dict, List, Optional, Tuple, Union

import torch
from torch import nn
from torch.utils.data import DistributedSampler, RandomSampler

from transformers import PreTrainedModel, Trainer, logging
from transformers.integrations import is_fairscale_available
from transformers.models.fsmt.configuration_fsmt import FSMTConfig
from transformers.optimization import (
    Adafactor,
    AdamW,
    get_constant_schedule,
    get_constant_schedule_with_warmup,
    get_cosine_schedule_with_warmup,
    get_cosine_with_hard_restarts_schedule_with_warmup,
    get_linear_schedule_with_warmup,
    get_polynomial_decay_schedule_with_warmup,
)
from transformers.trainer_pt_utils import get_tpu_sampler
from transformers.training_args import ParallelMode
from transformers.utils import is_torch_tpu_available


if is_fairscale_available():
   from fairscale.optim import OSS


SCREAMING_SNAKE_CASE__:Union[str, Any]			=	logging.get_logger(__name__)

SCREAMING_SNAKE_CASE__:Union[str, Any]			=	{
    """linear""": get_linear_schedule_with_warmup,
    """cosine""": get_cosine_schedule_with_warmup,
    """cosine_w_restarts""": get_cosine_with_hard_restarts_schedule_with_warmup,
    """polynomial""": get_polynomial_decay_schedule_with_warmup,
    """constant""": get_constant_schedule,
    """constant_w_warmup""": get_constant_schedule_with_warmup,
}






class 				snake_case__     (   snake_case_   ):


 def __init__(				self  ,						lowerCamelCase=None  ,						lowerCamelCase=None  ,						*lowerCamelCase  ,						**lowerCamelCase		):
        super().__init__(*lowerCamelCase  ,						**lowerCamelCase		)

        if config is None:
               assert isinstance(self.model  ,						lowerCamelCase		), (
                   "If no `config` is passed the model to be trained has to be of type `PreTrainedModel`, but is"
                   F" {self.model.__class__}"
               )
               __a     				=  self.model.config
        else:
               __a     				=  config

        __a     				=  data_args
        __a     				=  self.config.tgt_vocab_size if isinstance(self.config  ,						lowerCamelCase		) else self.config.vocab_size

        if self.args.label_smoothing != 0 or (self.data_args is not None and self.data_args.ignore_pad_token_for_loss):
               assert self.config.pad_token_id is not None, (
                   "Make sure that `config.pad_token_id` is correcly defined when ignoring `pad_token` for loss"
                   " calculation or doing label smoothing."
               )

        if self.config.pad_token_id is None and self.config.eos_token_id is not None:
               logger.warning(
                   F"The `config.pad_token_id` is `None`. Using `config.eos_token_id` = {self.config.eos_token_id} for"
                   " padding.."		)

        if self.args.label_smoothing == 0:
               __a     				=  torch.nn.CrossEntropyLoss(ignore_index=self.config.pad_token_id		)
        else:
               # dynamically import label_smoothed_nll_loss
               from utils import label_smoothed_nll_loss

               __a     				=  label_smoothed_nll_loss


 def 		a__ (				self  ,						lowerCamelCase		):
        if self.optimizer is None:
               __a     				=  ["bias", "LayerNorm.weight"]
               __a     				=  [
                   {
                       "params": [p for n, p in self.model.named_parameters() if not any(nd in n for nd in no_decay		)],
                       "weight_decay": self.args.weight_decay,
                   },
                   {
                       "params": [p for n, p in self.model.named_parameters() if any(nd in n for nd in no_decay		)],
                       "weight_decay": 0.0,
                   },
               ]
               __a     				=  Adafactor if self.args.adafactor else AdamW
               if self.args.adafactor:
                      __a     				=  Adafactor
                      __a     				=  {"scale_parameter": False, "relative_step": False}
               else:
                      __a     				=  AdamW
                      __a     				=  {
                          "betas": (self.args.adam_betaa, self.args.adam_betaa),
                          "eps": self.args.adam_epsilon,
                      }
               __a     				=  self.args.learning_rate
               if self.sharded_ddp:
                      __a     				=  OSS(
                          params=lowerCamelCase  ,						optim=lowerCamelCase  ,						**lowerCamelCase  ,						)
               else:
                      __a     				=  optimizer_cls(lowerCamelCase  ,						**lowerCamelCase		)

        if self.lr_scheduler is None:
               __a     				=  self._get_lr_scheduler(lowerCamelCase		)
        else:  # ignoring --lr_scheduler
               logger.warning("scheduler is passed to `Seq2SeqTrainer`, `--lr_scheduler` arg is ignored."		)


 def 		a__ (				self  ,						lowerCamelCase		):
        __a     				=  arg_to_scheduler[self.args.lr_scheduler]
        if self.args.lr_scheduler == "constant":
               __a     				=  schedule_func(self.optimizer		)
        elif self.args.lr_scheduler == "constant_w_warmup":
               __a     				=  schedule_func(self.optimizer  ,						num_warmup_steps=self.args.warmup_steps		)
        else:
               __a     				=  schedule_func(
                   self.optimizer  ,						num_warmup_steps=self.args.warmup_steps  ,						num_training_steps=lowerCamelCase		)
        return scheduler


 def 		a__ (				self		):
        if isinstance(self.train_dataset  ,						torch.utils.data.IterableDataset		):
               return None
        elif is_torch_tpu_available():
               return get_tpu_sampler(self.train_dataset		)
        else:
               if self.args.sortish_sampler:
                      self.train_dataset.make_sortish_sampler(
                          self.args.per_device_train_batch_size  ,						distributed=(self.args.parallel_mode == ParallelMode.DISTRIBUTED)  ,						)

               return (
                   RandomSampler(self.train_dataset		)
                   if self.args.local_rank == -1
                   else DistributedSampler(self.train_dataset		)
               )


 def 		a__ (				self  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase		):
        if self.args.label_smoothing == 0:
               if self.data_args is not None and self.data_args.ignore_pad_token_for_loss:
                      # force training to ignore pad token
                      __a     				=  model(**lowerCamelCase  ,						use_cache=lowerCamelCase		)[0]
                      __a     				=  self.loss_fn(logits.view(-1  ,						logits.shape[-1]		)  ,						labels.view(-1		)		)
               else:
                      # compute usual loss via models
                      __a				, __a     				=  model(**lowerCamelCase  ,						labels=lowerCamelCase  ,						use_cache=lowerCamelCase		)[:2]
        else:
               # compute label smoothed loss
               __a     				=  model(**lowerCamelCase  ,						use_cache=lowerCamelCase		)[0]
               __a     				=  torch.nn.functional.log_softmax(lowerCamelCase  ,						dim=-1		)
               __a				, __a     				=  self.loss_fn(lowerCamelCase  ,						lowerCamelCase  ,						self.args.label_smoothing  ,						ignore_index=self.config.pad_token_id		)
        return loss, logits


 def 		a__ (				self  ,						lowerCamelCase  ,						lowerCamelCase		):
        __a     				=  inputs.pop("labels"		)
        __a				, __a     				=  self._compute_loss(lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase		)
        return loss


 def 		a__ (				self  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase = None  ,						):
        __a     				=  self._prepare_inputs(lowerCamelCase		)

        __a     				=  {
            "max_length": self.data_args.val_max_target_length
            if self.data_args is not None
            else self.config.max_length,
            "num_beams": self.data_args.eval_beams if self.data_args is not None else self.config.num_beams,
        }

        if self.args.predict_with_generate and not self.args.prediction_loss_only:
               __a     				=  self.model.generate(
                   inputs["input_ids"]  ,						attention_mask=inputs["attention_mask"]  ,						**lowerCamelCase  ,						)
               # in case the batch is shorter than max length, the output should be padded
               if generated_tokens.shape[-1] < gen_kwargs["max_length"]:
                      __a     				=  self._pad_tensors_to_max_len(lowerCamelCase  ,						gen_kwargs["max_length"]		)

        __a     				=  inputs.pop("labels"		)
        with torch.no_grad():
               # compute loss on predict data
               __a				, __a     				=  self._compute_loss(lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase		)

        __a     				=  loss.mean().detach()
        if self.args.prediction_loss_only:
               return (loss, None, None)

        __a     				=  generated_tokens if self.args.predict_with_generate else logits

        if labels.shape[-1] < gen_kwargs["max_length"]:
               __a     				=  self._pad_tensors_to_max_len(lowerCamelCase  ,						gen_kwargs["max_length"]		)

        return (loss, logits, labels)






 def 		a__ (				self  ,						lowerCamelCase  ,						lowerCamelCase		):
        # If PAD token is not defined at least EOS token has to be defined
        __a     				=  self.config.pad_token_id if self.config.pad_token_id is not None else self.config.eos_token_id

        if pad_token_id is None:
               raise ValueError(
                   "Make sure that either `config.pad_token_id` or `config.eos_token_id` is defined if tensor has to be"
                   F" padded to `max_length`={max_length}"		)

        __a     				=  pad_token_id * torch.ones(
            (tensor.shape[0], max_length)  ,						dtype=tensor.dtype  ,						device=tensor.device		)
        __a     				=  tensor
        return padded_tensor

"""simple docstring"""



from __future__ import annotations



def 					_lowerCamelCase(					a ,  a ,  a ,  a ,  a ,  ):
       __a     				=  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							):
       __a     				=  []
       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)
