
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


lowerCamelCase__	=							logging.get_logger(__name__)

lowerCamelCase__	=							{
    "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        lowerCAmelCase__      (   __lowercase	):

						def __init__(			self       ,							a=None       ,							a=None       ,							*a       ,							**a				)					->      int:


								'''simple docstring'''

								super().__init__(*a       ,							**a				)

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

								_UpperCamelCase						    =	data_args
								_UpperCamelCase						    =	self.config.tgt_vocab_size if isinstance(self.config       ,							a				) 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:
										_UpperCamelCase						    =	torch.nn.CrossEntropyLoss(ignore_index=self.config.pad_token_id				)
								else:
										# dynamically import label_smoothed_nll_loss
										from utils import label_smoothed_nll_loss

										_UpperCamelCase						    =	label_smoothed_nll_loss

						def  A_				(			self       ,							a				)					->      Union[str, Any]:


								'''simple docstring'''

								if self.optimizer is None:
										_UpperCamelCase						    =	["""bias""", """LayerNorm.weight"""]
										_UpperCamelCase						    =	[
										    {
										        """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,
										    },
										]
										_UpperCamelCase						    =	Adafactor if self.args.adafactor else AdamW
										if self.args.adafactor:
												_UpperCamelCase						    =	Adafactor
												_UpperCamelCase						    =	{"""scale_parameter""": False, """relative_step""": False}
										else:
												_UpperCamelCase						    =	AdamW
												_UpperCamelCase						    =	{
												    """betas""": (self.args.adam_betaa, self.args.adam_betaa),
												    """eps""": self.args.adam_epsilon,
												}
										_UpperCamelCase						    =	self.args.learning_rate
										if self.sharded_ddp:
												_UpperCamelCase						    =	OSS(
												    params=a       ,							optim=a       ,							**a       ,							)
										else:
												_UpperCamelCase						    =	optimizer_cls(a       ,							**a				)

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

						def  A_				(			self       ,							a				)					->      Optional[Any]:


								'''simple docstring'''

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

						def  A_				(			self				)					->      Optional[torch.utils.data.Sampler]:


								'''simple docstring'''

								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       ,							a       ,							a       ,							a				)					->      Tuple:


								'''simple docstring'''

								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
												_UpperCamelCase						    =	model(**a       ,							use_cache=a				)[0]
												_UpperCamelCase						    =	self.loss_fn(logits.view(-1       ,							logits.shape[-1]				)       ,							labels.view(-1				)				)
										else:
												# compute usual loss via models
												_UpperCamelCase    ,	_UpperCamelCase						    =	model(**a       ,							labels=a       ,							use_cache=a				)[:2]
								else:
										# compute label smoothed loss
										_UpperCamelCase						    =	model(**a       ,							use_cache=a				)[0]
										_UpperCamelCase						    =	torch.nn.functional.log_softmax(a       ,							dim=-1				)
										_UpperCamelCase    ,	_UpperCamelCase						    =	self.loss_fn(a       ,							a       ,							self.args.label_smoothing       ,							ignore_index=self.config.pad_token_id				)
								return loss, logits

						def  A_				(			self       ,							a       ,							a				)					->      str:


								'''simple docstring'''

								_UpperCamelCase						    =	inputs.pop("""labels"""				)
								_UpperCamelCase    ,	_UpperCamelCase						    =	self._compute_loss(a       ,							a       ,							a				)
								return loss

						def  A_				(			self       ,							a       ,							a       ,							a       ,							a = None       ,							)					->      Tuple[Optional[float], Optional[torch.Tensor], Optional[torch.Tensor]]:


								'''simple docstring'''

								_UpperCamelCase						    =	self._prepare_inputs(a				)

								_UpperCamelCase						    =	{
								    """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:
										_UpperCamelCase						    =	self.model.generate(
										    inputs["""input_ids"""]       ,							attention_mask=inputs["""attention_mask"""]       ,							**a       ,							)
										# in case the batch is shorter than max length, the output should be padded
										if generated_tokens.shape[-1] < gen_kwargs["max_length"]:
												_UpperCamelCase						    =	self._pad_tensors_to_max_len(a       ,							gen_kwargs["""max_length"""]				)

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

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

								_UpperCamelCase						    =	generated_tokens if self.args.predict_with_generate else logits

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

								return (loss, logits, labels)







						def  A_				(			self       ,							a       ,							a				)					->      Any:


								'''simple docstring'''

								_UpperCamelCase						    =	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}'				)

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





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)



