






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__   :      Dict				=		logging.get_logger(__name__)

SCREAMING_SNAKE_CASE__   :      List[str]				=		{
    """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_					(   lowerCamelCase			):







				def __init__(    self							,       __lowerCAmelCase=None							,       __lowerCAmelCase=None							,       *__lowerCAmelCase							,       **__lowerCAmelCase  ):
								"""simple docstring"""
								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__}'''
												)
												__magic_name__		:Dict   =   self.model.config
								else:
												__magic_name__		:List[Any]   =   config

								__magic_name__		:Tuple   =   data_args
								__magic_name__		:Any   =   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:
												__magic_name__		:List[Any]   =   torch.nn.CrossEntropyLoss(ignore_index=self.config.pad_token_id  )
								else:
												# dynamically import label_smoothed_nll_loss
												from utils import label_smoothed_nll_loss

												__magic_name__		:str   =   label_smoothed_nll_loss







				def       A						(    self							,       __lowerCAmelCase  ):
								"""simple docstring"""
								if self.optimizer is None:
												__magic_name__		:int   =   ['''bias''', '''LayerNorm.weight''']
												__magic_name__		:Union[str, Any]   =   [
												    {
												        '''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,
												    },
												]
												__magic_name__		:Tuple   =   Adafactor if self.args.adafactor else AdamW
												if self.args.adafactor:
																__magic_name__		:List[Any]   =   Adafactor
																__magic_name__		:Union[str, Any]   =   {'''scale_parameter''': False, '''relative_step''': False}
												else:
																__magic_name__		:Union[str, Any]   =   AdamW
																__magic_name__		:int   =   {
																    '''betas''': (self.args.adam_betaa, self.args.adam_betaa),
																    '''eps''': self.args.adam_epsilon,
																}
												__magic_name__		:List[str]   =   self.args.learning_rate
												if self.sharded_ddp:
																__magic_name__		:List[str]   =   OSS(
																    params=__lowerCAmelCase							,       optim=__lowerCAmelCase							,       **__lowerCAmelCase							,       )
												else:
																__magic_name__		:List[str]   =   optimizer_cls(__lowerCAmelCase							,       **__lowerCAmelCase  )

								if self.lr_scheduler is None:
												__magic_name__		:Union[str, Any]   =   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  ):
								"""simple docstring"""
								__magic_name__		:Optional[int]   =   arg_to_scheduler[self.args.lr_scheduler]
								if self.args.lr_scheduler == "constant":
												__magic_name__		:int   =   schedule_func(self.optimizer  )
								elif self.args.lr_scheduler == "constant_w_warmup":
												__magic_name__		:List[str]   =   schedule_func(self.optimizer							,       num_warmup_steps=self.args.warmup_steps  )
								else:
												__magic_name__		:str   =   schedule_func(
												    self.optimizer							,       num_warmup_steps=self.args.warmup_steps							,       num_training_steps=__lowerCAmelCase  )
								return scheduler







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







				def       A						(    self							,       __lowerCAmelCase							,       __lowerCAmelCase  ):
								"""simple docstring"""
								__magic_name__		:str   =   inputs.pop('''labels'''  )
								__magic_name__  ,					__magic_name__		:Optional[Any]   =   self._compute_loss(__lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase  )
								return loss







				def       A						(    self							,       __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase = None							,       ):
								"""simple docstring"""
								__magic_name__		:Optional[int]   =   self._prepare_inputs(__lowerCAmelCase  )

								__magic_name__		:Optional[int]   =   {
								    '''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:
												__magic_name__		:Optional[Any]   =   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"]:
																__magic_name__		:Optional[Any]   =   self._pad_tensors_to_max_len(__lowerCAmelCase							,       gen_kwargs['''max_length''']  )

								__magic_name__		:int   =   inputs.pop('''labels'''  )
								with torch.no_grad():
												# compute loss on predict data
												__magic_name__  ,					__magic_name__		:Optional[int]   =   self._compute_loss(__lowerCAmelCase							,       __lowerCAmelCase							,       __lowerCAmelCase  )

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

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

								if labels.shape[-1] < gen_kwargs["max_length"]:
												__magic_name__		:Any   =   self._pad_tensors_to_max_len(__lowerCAmelCase							,       gen_kwargs['''max_length''']  )

								return (loss, logits, labels)







				def       A						(    self							,       __lowerCAmelCase							,       __lowerCAmelCase  ):
								"""simple docstring"""
								# If PAD token is not defined at least EOS token has to be defined
								__magic_name__		:Optional[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}'''  )

								__magic_name__		:str   =   pad_token_id * torch.ones(
								    (tensor.shape[0], max_length)							,       dtype=tensor.dtype							,       device=tensor.device  )
								__magic_name__		:Optional[Any]   =   tensor
								return padded_tensor














import sys

SCREAMING_SNAKE_CASE__   :      Optional[Any]				=		(
    """73167176531330624919225119674426574742355349194934"""
    """96983520312774506326239578318016984801869478851843"""
    """85861560789112949495459501737958331952853208805511"""
    """12540698747158523863050715693290963295227443043557"""
    """66896648950445244523161731856403098711121722383113"""
    """62229893423380308135336276614282806444486645238749"""
    """30358907296290491560440772390713810515859307960866"""
    """70172427121883998797908792274921901699720888093776"""
    """65727333001053367881220235421809751254540594752243"""
    """52584907711670556013604839586446706324415722155397"""
    """53697817977846174064955149290862569321978468622482"""
    """83972241375657056057490261407972968652414535100474"""
    """82166370484403199890008895243450658541227588666881"""
    """16427171479924442928230863465674813919123162824586"""
    """17866458359124566529476545682848912883142607690042"""
    """24219022671055626321111109370544217506941658960408"""
    """07198403850962455444362981230987879927244284909188"""
    """84580156166097919133875499200524063689912560717606"""
    """05886116467109405077541002256983155200055935729725"""
    """71636269561882670428252483600823257530420752963450"""
)

def   __lowercase       (			snake_case = N			):







				"""simple docstring"""






				__magic_name__		:Optional[int]   =   -sys.maxsize - 1
				for i in range(len(snake_case			) - 1_2			):
								__magic_name__		:List[Any]   =   1
								for j in range(1_3			):
												product *= int(n[i + j]			)
								if product > largest_product:
												__magic_name__		:str   =   product
				return largest_product


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






