





"""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


__UpperCAmelCase						=			logging.get_logger(__name__)

__UpperCAmelCase						=			{
    '''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 					__UpperCAmelCase							(						_UpperCamelCase  ):
				def __init__(		self    :			List[Any]	, a_    :			List[str]=None	, a_    :			Union[str, Any]=None	, *a_    :			Dict	, **a_    :			Optional[int]    )	->	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__}"
										)
										a__  :	Union[str, Any]		 =			self.model.config
							else:
										a__  :	str		 =			config

							a__  :	Optional[Any]		 =			data_args
							a__  :	str		 =			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:
										a__  :	Dict		 =			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__  :	Tuple		 =			label_smoothed_nll_loss
				def       UpperCAmelCase      (		self    :			int	, a_    :			int    )	->	Union[str, Any]:



							'''simple docstring'''



							if self.optimizer is None:
										a__  :	Dict		 =			["bias", "LayerNorm.weight"]
										a__  :	Tuple		 =			[
										    {
										        "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__  :	Optional[int]		 =			Adafactor if self.args.adafactor else AdamW
										if self.args.adafactor:
													a__  :	Any		 =			Adafactor
													a__  :	List[Any]		 =			{"scale_parameter": False, "relative_step": False}
										else:
													a__  :	Any		 =			AdamW
													a__  :	Dict		 =			{
													    "betas": (self.args.adam_betaa, self.args.adam_betaa),
													    "eps": self.args.adam_epsilon,
													}
										a__  :	List[str]		 =			self.args.learning_rate
										if self.sharded_ddp:
													a__  :	Optional[Any]		 =			OSS(
													    params=a_	, optim=a_	, **a_	, )
										else:
													a__  :	Any		 =			optimizer_cls(a_	, **a_    )

							if self.lr_scheduler is None:
										a__  :	str		 =			self._get_lr_scheduler(a_    )
							else:  # ignoring --lr_scheduler
										logger.warning("scheduler is passed to `Seq2SeqTrainer`, `--lr_scheduler` arg is ignored."    )
				def       UpperCAmelCase      (		self    :			List[str]	, a_    :			str    )	->	List[str]:



							'''simple docstring'''



							a__  :	Optional[int]		 =			arg_to_scheduler[self.args.lr_scheduler]
							if self.args.lr_scheduler == "constant":
										a__  :	Dict		 =			schedule_func(self.optimizer    )
							elif self.args.lr_scheduler == "constant_w_warmup":
										a__  :	Union[str, Any]		 =			schedule_func(self.optimizer	, num_warmup_steps=self.args.warmup_steps    )
							else:
										a__  :	List[Any]		 =			schedule_func(
										    self.optimizer	, num_warmup_steps=self.args.warmup_steps	, num_training_steps=a_    )
							return scheduler
				def       UpperCAmelCase      (		self    :			Any    )	->	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       UpperCAmelCase      (		self    :			str	, a_    :			Tuple	, a_    :			Optional[int]	, a_    :			Optional[Any]    )	->	int:



							'''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
													a__  :	Optional[int]		 =			model(**a_	, use_cache=a_    )[0]
													a__  :	List[str]		 =			self.loss_fn(logits.view(-1	, logits.shape[-1]    )	, labels.view(-1    )    )
										else:
													# compute usual loss via models
													a__ ,	a__  :	Tuple		 =			model(**a_	, labels=a_	, use_cache=a_    )[:2]
							else:
										# compute label smoothed loss
										a__  :	Dict		 =			model(**a_	, use_cache=a_    )[0]
										a__  :	int		 =			torch.nn.functional.log_softmax(a_	, dim=-1    )
										a__ ,	a__  :	Optional[Any]		 =			self.loss_fn(a_	, a_	, self.args.label_smoothing	, ignore_index=self.config.pad_token_id    )
							return loss, logits
				def       UpperCAmelCase      (		self    :			str	, a_    :			Dict	, a_    :			str    )	->	Optional[Any]:



							'''simple docstring'''



							a__  :	List[str]		 =			inputs.pop("labels"    )
							a__ ,	a__  :	Tuple		 =			self._compute_loss(a_	, a_	, a_    )
							return loss
				def       UpperCAmelCase      (		self    :			Optional[int]	, a_    :			nn.Module	, a_    :			Dict[str, Union[torch.Tensor, Any]]	, a_    :			bool	, a_    :			Optional[List[str]] = None	, )	->	Tuple[Optional[float], Optional[torch.Tensor], Optional[torch.Tensor]]:



							'''simple docstring'''



							a__  :	str		 =			self._prepare_inputs(a_    )

							a__  :	List[str]		 =			{
							    "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__  :	Optional[int]		 =			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"]:
													a__  :	str		 =			self._pad_tensors_to_max_len(a_	, gen_kwargs["max_length"]    )

							a__  :	Optional[Any]		 =			inputs.pop("labels"    )
							with torch.no_grad():
										# compute loss on predict data
										a__ ,	a__  :	Optional[Any]		 =			self._compute_loss(a_	, a_	, a_    )

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

							a__  :	Any		 =			generated_tokens if self.args.predict_with_generate else logits

							if labels.shape[-1] < gen_kwargs["max_length"]:
										a__  :	Tuple		 =			self._pad_tensors_to_max_len(a_	, gen_kwargs["max_length"]    )

							return (loss, logits, labels)






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



							'''simple docstring'''



							a__  :	Dict		 =			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__  :	Union[str, Any]		 =			pad_token_id * torch.ones(
							    (tensor.shape[0], max_length)	, dtype=tensor.dtype	, device=tensor.device    )
							a__  :	Optional[int]		 =			tensor
							return padded_tensor






"""simple docstring"""






from __future__ import annotations






def      lowercase__ (					lowerCAmelCase__   :			int			)    ->			list[int]:



			'''simple docstring'''
			a__  :	Tuple		 =			[True] * limit
			a__  :	Tuple		 =			False
			a__  :	int		 =			False
			a__  :	Tuple		 =			True

			for i in range(3							,			int(limit**0.5 + 1			)							,			2			):
						a__  :	int		 =			i * 2
						while index < limit:
									a__  :	Union[str, Any]		 =			False
									a__  :	int		 =			index + i

			a__  :	str		 =			[2]

			for i in range(3							,			lowerCAmelCase__							,			2			):
						if is_prime[i]:
									primes.append(lowerCAmelCase__			)

			return primes






def      lowercase__ (					lowerCAmelCase__   :			int = 1_0_0_0_0_0_0			)    ->			int:



			'''simple docstring'''
			a__  :	List[Any]		 =			prime_sieve(lowerCAmelCase__			)
			a__  :	int		 =			0
			a__  :	str		 =			0

			for i in range(len(lowerCAmelCase__			)			):
						for j in range(i + length							,			len(lowerCAmelCase__			)			):
									a__  :	List[str]		 =			sum(primes[i:j]			)
									if sol >= ceiling:
												break

									if sol in primes:
												a__  :	Tuple		 =			j - i
												a__  :	Union[str, Any]		 =			sol

			return largest


if __name__ == "__main__":
		print(f"{solution() = }")