

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


snake_case_							=			logging.get_logger(__name__)

snake_case_							=			{
    '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_		(			UpperCamelCase_):







		def __init__(		self			,     __lowercase=None			,     __lowercase=None			,     *__lowercase			,     **__lowercase   )				->   List[Any]:
				super().__init__(*UpperCamelCase__			,     **UpperCamelCase__   )

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

				lowerCamelCase   : List[Any]								=data_args
				lowerCamelCase   : str								=self.config.tgt_vocab_size if isinstance(self.config			,     UpperCamelCase__   ) 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:
						lowerCamelCase   : int								=torch.nn.CrossEntropyLoss(ignore_index=self.config.pad_token_id   )
				else:
						# dynamically import label_smoothed_nll_loss
						from utils import label_smoothed_nll_loss

						lowerCamelCase   : List[str]								=label_smoothed_nll_loss







		def 			__lowercase   (		self			,     __lowercase   )				->   Tuple:





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

				if self.lr_scheduler is None:
						lowerCamelCase   : List[Any]								=self._get_lr_scheduler(UpperCamelCase__   )
				else:  # ignoring --lr_scheduler
						logger.warning('''scheduler is passed to `Seq2SeqTrainer`, `--lr_scheduler` arg is ignored.'''   )







		def 			__lowercase   (		self			,     __lowercase   )				->   List[str]:
				lowerCamelCase   : Union[str, Any]								=arg_to_scheduler[self.args.lr_scheduler]
				if self.args.lr_scheduler == "constant":
						lowerCamelCase   : List[str]								=schedule_func(self.optimizer   )
				elif self.args.lr_scheduler == "constant_w_warmup":
						lowerCamelCase   : Optional[Any]								=schedule_func(self.optimizer			,     num_warmup_steps=self.args.warmup_steps   )
				else:
						lowerCamelCase   : str								=schedule_func(
						    self.optimizer			,     num_warmup_steps=self.args.warmup_steps			,     num_training_steps=UpperCamelCase__   )
				return scheduler







		def 			__lowercase   (		self   )				->   Any:





				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 			__lowercase   (		self			,     __lowercase			,     __lowercase			,     __lowercase   )				->   Optional[Any]:





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







		def 			__lowercase   (		self			,     __lowercase			,     __lowercase   )				->   Optional[int]:
				lowerCamelCase   : List[str]								=inputs.pop('''labels'''   )
				lowerCamelCase   : List[Any]								=self._compute_loss(UpperCamelCase__			,     UpperCamelCase__			,     UpperCamelCase__   )
				return loss







		def 			__lowercase   (		self			,     __lowercase			,     __lowercase			,     __lowercase			,     __lowercase = None			,     )				->   Union[str, Any]:
				lowerCamelCase   : Union[str, Any]								=self._prepare_inputs(UpperCamelCase__   )

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

				lowerCamelCase   : Tuple								=inputs.pop('''labels'''   )
				with torch.no_grad():
						# compute loss on predict data
						lowerCamelCase   : int								=self._compute_loss(UpperCamelCase__			,     UpperCamelCase__			,     UpperCamelCase__   )

				lowerCamelCase   : Optional[Any]								=loss.mean().detach()
				if self.args.prediction_loss_only:
						return (loss, None, None)

				lowerCamelCase   : int								=generated_tokens if self.args.predict_with_generate else logits

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

				return (loss, logits, labels)







		def 			__lowercase   (		self			,     __lowercase			,     __lowercase   )				->   str:
				lowerCamelCase   : Union[str, Any]								=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}"   )

				lowerCamelCase   : List[Any]								=pad_token_id * torch.ones(
				    (tensor.shape[0], max_length)			,     dtype=tensor.dtype			,     device=tensor.device   )
				lowerCamelCase   : Tuple								=tensor
				return padded_tensor








from collections import defaultdict
from math import ceil, sqrt


def 					A__	(       SCREAMING_SNAKE_CASE_ = 1_0_0_0_0_0_0							,       SCREAMING_SNAKE_CASE_ = 1_0		)   ->     int:
		lowerCamelCase   : defaultdict								=defaultdict(SCREAMING_SNAKE_CASE_		)

		for outer_width in range(3							,       (t_limit // 4) + 2		):
				if outer_width * outer_width > t_limit:
						lowerCamelCase   : Any								=max(
						    ceil(sqrt(outer_width * outer_width - t_limit		)		)							,       1		)
				else:
						lowerCamelCase   : str								=1

				hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

				for hole_width in range(SCREAMING_SNAKE_CASE_							,       outer_width - 1							,       2		):
						count[outer_width * outer_width - hole_width * hole_width] += 1

		return sum(1 for n in count.values() if 1 <= n <= 1_0		)


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

