

def       a__					(		UpperCAmelCase							:      int      )  ->						bool:
  UpperCAmelCase	:							int						=			(1 + 24 * n) ** 0.5
  return ((1 + root) / 6) % 1 == 0

def       a__					(		UpperCAmelCase							:      int = 5_000      )  ->						int:
  UpperCAmelCase	:							int						=			[(i * (3 * i - 1)) // 2 for i in range(1    ,			UpperCAmelCase      )]
  for i, pentagonal_i in enumerate(UpperCAmelCase      ):
    for j in range(UpperCAmelCase    ,			len(UpperCAmelCase      )      ):
      UpperCAmelCase	:							int						=			pentagonal_nums[j]
      UpperCAmelCase	:							List[Any]						=			pentagonal_i + pentagonal_j
      UpperCAmelCase	:							Optional[Any]						=			pentagonal_j - pentagonal_i
      if is_pentagonal(UpperCAmelCase      ) and is_pentagonal(UpperCAmelCase      ):
        return b

  return -1


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








import logging
import sys
from dataclasses import dataclass, field
from typing import Any, Dict, List, Optional, Union

import librosa
import torch
from datasets import DatasetDict, load_dataset
from packaging import version
from torch import nn

from transformers import (
    HfArgumentParser,
    Trainer,
    TrainingArguments,
    WavaVecaConfig,
    WavaVecaFeatureExtractor,
    WavaVecaForPreTraining,
    is_apex_available,
    trainer_utils,
)
from transformers.models.wavaveca.modeling_wavaveca import _compute_mask_indices


if is_apex_available():
     from apex import amp

if version.parse(version.parse(torch.__version__).base_version) >= version.parse("1.6"):
     _lowerCamelCase    :       List[str]        =							True
     from torch.cuda.amp import autocast


_lowerCamelCase    :       Any        =							logging.getLogger(__name__)





@dataclass
class  __UpperCAmelCase					:
   UpperCamelCase       					=					field(
       metadata={"""help""": """Path to pretrained model or model identifier from huggingface.co/models"""}						)
   UpperCamelCase       					=					field(
       default=lowerCamelCase__      ,  metadata={"""help""": """Where do you want to store the pretrained models downloaded from huggingface.co"""}      ,  )
   UpperCamelCase       					=					field(
       default=lowerCamelCase__      ,  metadata={"""help""": """Whether to freeze the feature extractor layers of the model."""}						)
   UpperCamelCase       					=					field(
       default=lowerCamelCase__      ,  metadata={"""help""": """Whether to log verbose messages or not."""}      ,  )
   UpperCamelCase       					=					field(
       default=2.0      ,  metadata={"""help""": """Maximum temperature for gumbel softmax."""}						)
   UpperCamelCase       					=					field(
       default=0.5      ,  metadata={"""help""": """Minimum temperature for gumbel softmax."""}						)
   UpperCamelCase       					=					field(
       default=0.9_9_9_9_9_5      ,  metadata={"""help""": """Decay of gumbel temperature during training."""}						)






def       a__					(		UpperCAmelCase							:      ModelArguments    ,			UpperCAmelCase							:      TrainingArguments      )  ->						Any:
  logging.basicConfig(
      format='''%(asctime)s - %(levelname)s - %(name)s - %(message)s'''    ,			datefmt='''%m/%d/%Y %H:%M:%S'''    ,			handlers=[logging.StreamHandler(sys.stdout      )]    ,			)
  UpperCAmelCase	:							Any						=			logging.WARNING
  if model_args.verbose_logging:
    UpperCAmelCase	:							Any						=			logging.DEBUG
  elif trainer_utils.is_main_process(training_args.local_rank      ):
    UpperCAmelCase	:							Any						=			logging.INFO
  logger.setLevel(UpperCAmelCase      )





@dataclass
class  __UpperCAmelCase					:
   UpperCamelCase       					=					field(
       default=lowerCamelCase__      ,  metadata={"""help""": """The name of the dataset to use (via the datasets library)."""}						)
   UpperCamelCase       					=					field(
       default=lowerCamelCase__      ,  metadata={"""help""": """The configuration name of the dataset to use (via the datasets library)."""}						)
   UpperCamelCase       					=					field(
       default="""train"""      ,  metadata={
           """help""": """The name of the training data set split to use (via the datasets library). Defaults to 'train'"""
       }      ,  )
   UpperCamelCase       					=					field(
       default="""validation"""      ,  metadata={
           """help""": (
               """The name of the validation data set split to use (via the datasets library). Defaults to 'validation'"""
           )
       }      ,  )
   UpperCamelCase       					=					field(
       default="""file"""      ,  metadata={"""help""": """Column in the dataset that contains speech file path. Defaults to 'file'"""}      ,  )
   UpperCamelCase       					=					field(
       default=lowerCamelCase__      ,  metadata={"""help""": """Overwrite the cached preprocessed datasets or not."""}						)
   UpperCamelCase       					=					field(
       default=1      ,  metadata={
           """help""": """The percentage of the train set used as validation set in case there's no validation split"""
       }      ,  )
   UpperCamelCase       					=					field(
       default=lowerCamelCase__      ,  metadata={"""help""": """The number of processes to use for the preprocessing."""}      ,  )
   UpperCamelCase       					=					field(
       default=2_0.0      ,  metadata={"""help""": """Filter audio files that are longer than `max_duration_in_seconds` seconds"""}						)






@dataclass
class  __UpperCAmelCase					:
   UpperCamelCase       					=					42
   UpperCamelCase       					=					42
   UpperCamelCase       					=					"longest"
   UpperCamelCase       					=					None
   UpperCamelCase       					=					None



   def __call__(							self							:					int,		__A							:					List[Dict[str, Union[List[int], torch.Tensor]]]						):
     # reformat list to dict and set to pytorch format
     UpperCAmelCase	:							List[Any]						=			self.feature_extractor.pad(
         __A,		max_length=self.max_length,		padding=self.padding,		pad_to_multiple_of=self.pad_to_multiple_of,		return_tensors='''pt''',		)
     UpperCAmelCase	:							int						=			self.model._get_feat_extract_output_lengths(batch['''input_values'''].shape[-1]						)

     UpperCAmelCase	:							Tuple						=			batch['''input_values'''].shape[0]

     # make sure that no loss is computed on padded inputs
     if batch["attention_mask"] is not None:
       # compute real output lengths according to convolution formula
       UpperCAmelCase	:							Tuple						=			self.model._get_feat_extract_output_lengths(batch['''attention_mask'''].sum(-1						)						).to(
           torch.long						)

       UpperCAmelCase	:							Dict						=			torch.zeros(
           (batch_size, mask_indices_seq_length),		dtype=torch.long,		device=batch['''input_values'''].device						)

       # these two operations makes sure that all values
       # before the output lengths indices are attended to
       UpperCAmelCase	:							Tuple						=			1
       UpperCAmelCase	:							int						=			attention_mask.flip([-1]						).cumsum(-1						).flip([-1]						).bool()

     # sample randomly masked indices
     UpperCAmelCase	:							Dict						=			_compute_mask_indices(
         (batch_size, mask_indices_seq_length),		self.model.config.mask_time_prob,		self.model.config.mask_time_length,		attention_mask=__A,		min_masks=2,		)

     return batch






class  __UpperCAmelCase					(	lowerCamelCase__						):



   def __init__(							self							:					Union[str, Any],		*__A							:					int,		__A							:					Dict=1,		__A							:					Any=0,		__A							:					Optional[Any]=1.0,		**__A							:					Any						):
     super().__init__(*__A,		**__A						)
     UpperCAmelCase	:							Any						=			0
     UpperCAmelCase	:							Any						=			max_gumbel_temp
     UpperCAmelCase	:							Optional[Any]						=			min_gumbel_temp
     UpperCAmelCase	:							str						=			gumbel_temp_decay





   def 	__magic_name__   (							self							:					Dict,		__A							:					nn.Module,		__A							:					Dict[str, Union[torch.Tensor, Any]]						):
     model.train()
     UpperCAmelCase	:							List[Any]						=			self._prepare_inputs(__A						)

     if self.use_amp:
       with autocast():
         UpperCAmelCase	:							Optional[Any]						=			self.compute_loss(__A,		__A						)
     else:
       UpperCAmelCase	:							Optional[int]						=			self.compute_loss(__A,		__A						)

     if self.args.n_gpu > 1 or self.deepspeed:
       if model.module.config.ctc_loss_reduction == "mean":
         UpperCAmelCase	:							Optional[Any]						=			loss.mean()
       elif model.module.config.ctc_loss_reduction == "sum":
         UpperCAmelCase	:							str						=			loss.sum() / (inputs['''mask_time_indices''']).sum()
       else:
         raise ValueError(F'''{model.config.ctc_loss_reduction} is not valid. Choose one of [\'mean\', \'sum\']'''						)

     if self.args.gradient_accumulation_steps > 1:
       UpperCAmelCase	:							Any						=			loss / self.args.gradient_accumulation_steps

     if self.use_amp:
       self.scaler.scale(__A						).backward()
     elif self.use_apex:
       with amp.scale_loss(__A,		self.optimizer						) as scaled_loss:
         scaled_loss.backward()
     elif self.deepspeed:
       self.deepspeed.backward(__A						)
     else:
       loss.backward()

     self.num_update_step += 1
     # make sure gumbel softmax temperature is decayed
     if self.args.n_gpu > 1 or self.deepspeed:
       model.module.set_gumbel_temperature(
           max(self.max_gumbel_temp * self.gumbel_temp_decay**self.num_update_step,		self.min_gumbel_temp						)						)
     else:
       model.set_gumbel_temperature(
           max(self.max_gumbel_temp * self.gumbel_temp_decay**self.num_update_step,		self.min_gumbel_temp						)						)

     return loss.detach()






def       a__					(		)  ->						Union[str, Any]:
  # See all possible arguments in src/transformers/training_args.py
  # or by passing the --help flag to this script.
  # We now keep distinct sets of args, for a cleaner separation of concerns.

  UpperCAmelCase	:							Optional[Any]						=			HfArgumentParser((ModelArguments, DataTrainingArguments, TrainingArguments)      )

  UpperCAmelCase			,						UpperCAmelCase			,						UpperCAmelCase	:							List[Any]						=			parser.parse_args_into_dataclasses()
  configure_logger(UpperCAmelCase    ,			UpperCAmelCase      )

  # Downloading and loading a dataset from the hub.
  UpperCAmelCase	:							int						=			load_dataset(data_args.dataset_name    ,			data_args.dataset_config_name    ,			cache_dir=model_args.cache_dir      )

  if "validation" not in datasets.keys():
    # make sure only "validation" and "train" keys remain"
    UpperCAmelCase	:							Union[str, Any]						=			DatasetDict()
    UpperCAmelCase	:							Any						=			load_dataset(
        data_args.dataset_name    ,			data_args.dataset_config_name    ,			split=f'''{data_args.train_split_name}[:{data_args.validation_split_percentage}%]'''    ,			cache_dir=model_args.cache_dir    ,			)
    UpperCAmelCase	:							Tuple						=			load_dataset(
        data_args.dataset_name    ,			data_args.dataset_config_name    ,			split=f'''{data_args.train_split_name}[{data_args.validation_split_percentage}%:]'''    ,			cache_dir=model_args.cache_dir    ,			)
  else:
    # make sure only "validation" and "train" keys remain"
    UpperCAmelCase	:							Optional[Any]						=			DatasetDict()
    UpperCAmelCase	:							List[Any]						=			load_dataset(
        data_args.dataset_name    ,			data_args.dataset_config_name    ,			split='''validation'''    ,			cache_dir=model_args.cache_dir    ,			)
    UpperCAmelCase	:							int						=			load_dataset(
        data_args.dataset_name    ,			data_args.dataset_config_name    ,			split=f'''{data_args.train_split_name}'''    ,			cache_dir=model_args.cache_dir    ,			)

  # only normalized-inputs-training is supported
  UpperCAmelCase	:							Optional[Any]						=			WavaVecaFeatureExtractor.from_pretrained(
      model_args.model_name_or_path    ,			cache_dir=model_args.cache_dir    ,			do_normalize=UpperCAmelCase      )

  def prepare_dataset(UpperCAmelCase							:      Dict      ):
    # check that all files have the correct sampling rate
    UpperCAmelCase			,						UpperCAmelCase	:							Optional[Any]						=			librosa.load(batch[data_args.speech_file_column]    ,			sr=feature_extractor.sampling_rate      )
    return batch

  # load audio files into numpy arrays
  UpperCAmelCase	:							str						=			datasets.map(
      UpperCAmelCase    ,			num_proc=data_args.preprocessing_num_workers    ,			remove_columns=datasets['''train'''].column_names      )

  # filter audio files that are too long
  UpperCAmelCase	:							int						=			vectorized_datasets.filter(
      lambda UpperCAmelCase      : len(data['''speech''']      ) < int(data_args.max_duration_in_seconds * feature_extractor.sampling_rate      )      )

  def normalize(UpperCAmelCase							:      Dict      ):
    return feature_extractor(batch['''speech''']    ,			sampling_rate=feature_extractor.sampling_rate      )

  # normalize and transform to `BatchFeatures`
  UpperCAmelCase	:							Any						=			vectorized_datasets.map(
      UpperCAmelCase    ,			batched=UpperCAmelCase    ,			num_proc=data_args.preprocessing_num_workers    ,			load_from_cache_file=not data_args.overwrite_cache    ,			remove_columns=vectorized_datasets['''train'''].column_names    ,			)

  # pretraining is only supported for "newer" stable layer norm architecture
  # apply_spec_augment has to be True, mask_feature_prob has to be 0.0
  UpperCAmelCase	:							Optional[int]						=			WavaVecaConfig.from_pretrained(
      model_args.model_name_or_path    ,			cache_dir=model_args.cache_dir    ,			gradient_checkpointing=training_args.gradient_checkpointing    ,			)

  if not config.do_stable_layer_norm or config.feat_extract_norm != "layer":
    raise ValueError(
        '''PreTraining is only supported for ``config.do_stable_layer_norm=True`` and'''
        ''' ``config.feat_extract_norm=\'layer\''''      )

  UpperCAmelCase	:							Any						=			WavaVecaForPreTraining(UpperCAmelCase      )

  UpperCAmelCase	:							int						=			DataCollatorForWavaVecaPretraining(model=UpperCAmelCase    ,			feature_extractor=UpperCAmelCase      )

  UpperCAmelCase	:							Any						=			WavaVecaPreTrainer(
      model=UpperCAmelCase    ,			data_collator=UpperCAmelCase    ,			args=UpperCAmelCase    ,			train_dataset=vectorized_datasets['''train''']    ,			eval_dataset=vectorized_datasets['''validation''']    ,			tokenizer=UpperCAmelCase    ,			max_gumbel_temp=model_args.max_gumbel_temperature    ,			min_gumbel_temp=model_args.min_gumbel_temperature    ,			gumbel_temp_decay=model_args.gumbel_temperature_decay    ,			)
  trainer.train()


if __name__ == "__main__":
     main()





