code: 
  
  
  
  
  
  import argparse
  import logging
  import os
  from pathlib import Path
  from typing import Any, Dict
  
  import pytorch_lightning as pl
  from pytorch_lightning.utilities import rank_zero_info
  
  from transformers import (
      AdamW,
      AutoConfig,
      AutoModel,
      AutoModelForPreTraining,
      AutoModelForQuestionAnswering,
      AutoModelForSeqaSeqLM,
      AutoModelForSequenceClassification,
      AutoModelForTokenClassification,
      AutoModelWithLMHead,
      AutoTokenizer,
      PretrainedConfig,
      PreTrainedTokenizer,
  )
  from transformers.optimization import (
      Adafactor,
      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.utils.versions import require_version
  
  
  _lowercase		:     Union[str, Any] 					=logging.getLogger(__name__)
  
  require_version("""pytorch_lightning>=1.0.4""")
  
  _lowercase		:     int 					={
      """base""": AutoModel,
      """sequence-classification""": AutoModelForSequenceClassification,
      """question-answering""": AutoModelForQuestionAnswering,
      """pretraining""": AutoModelForPreTraining,
      """token-classification""": AutoModelForTokenClassification,
      """language-modeling""": AutoModelWithLMHead,
      """summarization""": AutoModelForSeqaSeqLM,
      """translation""": AutoModelForSeqaSeqLM,
  }
  
  
  # update this and the import above to support new schedulers from transformers.optimization
  _lowercase		:     Union[str, Any] 					={
      """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,
      # '': get_constant_schedule,             # not supported for now
      # '': get_constant_schedule_with_warmup, # not supported for now
  }
  _lowercase		:     Tuple 					=sorted(arg_to_scheduler.keys())
  _lowercase		:     Any 					="""{""" + """, """.join(arg_to_scheduler_choices) + """}"""
  
  
  
  
  
  
  class 	UpperCamelCase_     (     pl.LightningModule       ):
  
  
  
  					def __init__(		self    :    Tuple					,			lowerCamelCase    :    argparse.Namespace					,			lowerCamelCase    :    Tuple=None					,			lowerCamelCase    :    List[Any]="base"					,			lowerCamelCase    :    Tuple=None					,			lowerCamelCase    :    List[str]=None					,			lowerCamelCase    :    Dict=None					,			**lowerCamelCase    :    List[Any]					,			):
  							super().__init__()
  							# TODO: move to self.save_hyperparameters()
  							# self.save_hyperparameters()
  							# can also expand arguments into trainer signature for easier reading
  
  							self.save_hyperparameters(lowerCamelCase	)
  							lowerCamelCase_  :    Any   	=			0
  							lowerCamelCase_  :    int   	=			Path(self.hparams.output_dir	)
  							lowerCamelCase_  :    str   	=			self.hparams.cache_dir if self.hparams.cache_dir else None
  							if config is None:
  									lowerCamelCase_  :    Tuple   	=			AutoConfig.from_pretrained(
  									    self.hparams.config_name if self.hparams.config_name else self.hparams.model_name_or_path					,			**({'num_labels': num_labels} if num_labels is not None else {})					,			cache_dir=lowerCamelCase					,			**lowerCamelCase					,			)
  							else:
  									lowerCamelCase_  :    PretrainedConfig   	=			config
  
  							lowerCamelCase_  :    int   	=			('encoder_layerdrop', 'decoder_layerdrop', 'dropout', 'attention_dropout')
  							for p in extra_model_params:
  									if getattr(self.hparams					,			lowerCamelCase					,			lowerCamelCase	):
  											assert hasattr(self.config					,			lowerCamelCase	), F"model config doesn't have a `{p}` attribute"
  											setattr(self.config					,			lowerCamelCase					,			getattr(self.hparams					,			lowerCamelCase	)	)
  
  							if tokenizer is None:
  									lowerCamelCase_  :    Any   	=			AutoTokenizer.from_pretrained(
  									    self.hparams.tokenizer_name if self.hparams.tokenizer_name else self.hparams.model_name_or_path					,			cache_dir=lowerCamelCase					,			)
  							else:
  									lowerCamelCase_  :    PreTrainedTokenizer   	=			tokenizer
  							lowerCamelCase_  :    Dict   	=			MODEL_MODES[mode]
  							if model is None:
  									lowerCamelCase_  :    int   	=			self.model_type.from_pretrained(
  									    self.hparams.model_name_or_path					,			from_tf=bool('.ckpt' in self.hparams.model_name_or_path	)					,			config=self.config					,			cache_dir=lowerCamelCase					,			)
  							else:
  									lowerCamelCase_  :    Optional[int]   	=			model
  
  
  
  					def      __a    (		self    :    Tuple					,			*lowerCamelCase    :    Optional[int]					,			**lowerCamelCase    :    Dict	):
  							lowerCamelCase_  :    List[Any]   	=			self.model_type.from_pretrained(*lowerCamelCase					,			**lowerCamelCase	)
  
  
  
  					def      __a    (		self    :    str	):
  							lowerCamelCase_  :    Any   	=			arg_to_scheduler[self.hparams.lr_scheduler]
  							lowerCamelCase_  :    int   	=			get_schedule_func(
  							    self.opt					,			num_warmup_steps=self.hparams.warmup_steps					,			num_training_steps=self.total_steps()	)
  							lowerCamelCase_  :    Union[str, Any]   	=			{'scheduler': scheduler, 'interval': 'step', 'frequency': 1}
  							return scheduler
  
  
  
  					def      __a    (		self    :    Optional[Any]	):
  							lowerCamelCase_  :    Any   	=			self.model
  							lowerCamelCase_  :    str   	=			['bias', 'LayerNorm.weight']
  							lowerCamelCase_  :    Tuple   	=			[
  							    {
  							        'params': [p for n, p in model.named_parameters() if not any(nd in n for nd in no_decay	)],
  							        'weight_decay': self.hparams.weight_decay,
  							    },
  							    {
  							        'params': [p for n, p in model.named_parameters() if any(nd in n for nd in no_decay	)],
  							        'weight_decay': 0.0,
  							    },
  							]
  							if self.hparams.adafactor:
  									lowerCamelCase_  :    int   	=			Adafactor(
  									    lowerCamelCase					,			lr=self.hparams.learning_rate					,			scale_parameter=lowerCamelCase					,			relative_step=lowerCamelCase	)
  
  							else:
  									lowerCamelCase_  :    int   	=			AdamW(
  									    lowerCamelCase					,			lr=self.hparams.learning_rate					,			eps=self.hparams.adam_epsilon	)
  							lowerCamelCase_  :    Any   	=			optimizer
  
  							lowerCamelCase_  :    List[str]   	=			self.get_lr_scheduler()
  
  							return [optimizer], [scheduler]
  
  
  
  					def      __a    (		self    :    List[Any]					,			lowerCamelCase    :    Optional[int]					,			lowerCamelCase    :    Dict	):
  							return self.validation_step(lowerCamelCase					,			lowerCamelCase	)
  
  
  
  					def      __a    (		self    :    List[str]					,			lowerCamelCase    :    int	):
  							return self.validation_end(lowerCamelCase	)
  
  
  
  					def      __a    (		self    :    Tuple	):
  							lowerCamelCase_  :    Union[str, Any]   	=			max(1					,			self.hparams.gpus	)  # TODO: consider num_tpu_cores
  							lowerCamelCase_  :    Any   	=			self.hparams.train_batch_size * self.hparams.accumulate_grad_batches * num_devices
  							return (self.dataset_size / effective_batch_size) * self.hparams.max_epochs
  
  
  
  					def      __a    (		self    :    Dict					,			lowerCamelCase    :    int	):
  							if stage == "test":
  									lowerCamelCase_  :    str   	=			len(self.test_dataloader().dataset	)
  							else:
  									lowerCamelCase_  :    Optional[int]   	=			self.get_dataloader('train'					,			self.hparams.train_batch_size					,			shuffle=lowerCamelCase	)
  									lowerCamelCase_  :    Any   	=			len(self.train_dataloader().dataset	)
  
  
  
  					def      __a    (		self    :    Optional[int]					,			lowerCamelCase    :    str					,			lowerCamelCase    :    int					,			lowerCamelCase    :    bool = False	):
  							raise NotImplementedError('You must implement this for your task'	)
  
  
  
  					def      __a    (		self    :    Any	):
  							return self.train_loader
  
  
  
  					def      __a    (		self    :    Dict	):
  							return self.get_dataloader('dev'					,			self.hparams.eval_batch_size					,			shuffle=lowerCamelCase	)
  
  
  
  					def      __a    (		self    :    int	):
  							return self.get_dataloader('test'					,			self.hparams.eval_batch_size					,			shuffle=lowerCamelCase	)
  
  
  
  					def      __a    (		self    :    Dict					,			lowerCamelCase    :    List[str]	):
  							return os.path.join(
  							    self.hparams.data_dir					,			'cached_{}_{}_{}'.format(
  							        lowerCamelCase					,			list(filter(lowerCamelCase					,			self.hparams.model_name_or_path.split('/'	)	)	).pop()					,			str(self.hparams.max_seq_length	)					,			)					,			)
  
  
  
  					@pl.utilities.rank_zero_only
  					def      __a    (		self    :    str					,			lowerCamelCase    :    Dict[str, Any]	):
  							lowerCamelCase_  :    List[Any]   	=			self.output_dir.joinpath('best_tfmr'	)
  							lowerCamelCase_  :    List[Any]   	=			self.step_count
  							self.model.save_pretrained(lowerCamelCase	)
  							self.tokenizer.save_pretrained(lowerCamelCase	)
  
  
  
  
  
  					@staticmethod
  					def      __a    (		lowerCamelCase    :    Tuple					,			lowerCamelCase    :    int	):
  							parser.add_argument(
  							    '--model_name_or_path'					,			default=lowerCamelCase					,			type=lowerCamelCase					,			required=lowerCamelCase					,			help='Path to pretrained model or model identifier from huggingface.co/models'					,			)
  							parser.add_argument(
  							    '--config_name'					,			default=''					,			type=lowerCamelCase					,			help='Pretrained config name or path if not the same as model_name'	)
  							parser.add_argument(
  							    '--tokenizer_name'					,			default=lowerCamelCase					,			type=lowerCamelCase					,			help='Pretrained tokenizer name or path if not the same as model_name'					,			)
  							parser.add_argument(
  							    '--cache_dir'					,			default=''					,			type=lowerCamelCase					,			help='Where do you want to store the pre-trained models downloaded from huggingface.co'					,			)
  							parser.add_argument(
  							    '--encoder_layerdrop'					,			type=lowerCamelCase					,			help='Encoder layer dropout probability (Optional). Goes into model.config'					,			)
  							parser.add_argument(
  							    '--decoder_layerdrop'					,			type=lowerCamelCase					,			help='Decoder layer dropout probability (Optional). Goes into model.config'					,			)
  							parser.add_argument(
  							    '--dropout'					,			type=lowerCamelCase					,			help='Dropout probability (Optional). Goes into model.config'					,			)
  							parser.add_argument(
  							    '--attention_dropout'					,			type=lowerCamelCase					,			help='Attention dropout probability (Optional). Goes into model.config'					,			)
  							parser.add_argument('--learning_rate'					,			default=5E-5					,			type=lowerCamelCase					,			help='The initial learning rate for Adam.'	)
  							parser.add_argument(
  							    '--lr_scheduler'					,			default='linear'					,			choices=lowerCamelCase					,			metavar=lowerCamelCase					,			type=lowerCamelCase					,			help='Learning rate scheduler'					,			)
  							parser.add_argument('--weight_decay'					,			default=0.0					,			type=lowerCamelCase					,			help='Weight decay if we apply some.'	)
  							parser.add_argument('--adam_epsilon'					,			default=1E-8					,			type=lowerCamelCase					,			help='Epsilon for Adam optimizer.'	)
  							parser.add_argument('--warmup_steps'					,			default=0					,			type=lowerCamelCase					,			help='Linear warmup over warmup_steps.'	)
  							parser.add_argument('--num_workers'					,			default=4					,			type=lowerCamelCase					,			help='kwarg passed to DataLoader'	)
  							parser.add_argument('--num_train_epochs'					,			dest='max_epochs'					,			default=3					,			type=lowerCamelCase	)
  							parser.add_argument('--train_batch_size'					,			default=32					,			type=lowerCamelCase	)
  							parser.add_argument('--eval_batch_size'					,			default=32					,			type=lowerCamelCase	)
  							parser.add_argument('--adafactor'					,			action='store_true'	)
  
  
  
  
  
  
  class 	UpperCamelCase_     (     pl.Callback       ):
  
  
  
  					def      __a    (		self    :    List[Any]					,			lowerCamelCase    :    int					,			lowerCamelCase    :    int	):
  							if (
  							    trainer.is_global_zero and trainer.global_rank == 0
  							):  # we initialize the retriever only on master worker with RAY. In new pytorch-lightning accelorators are removed.
  									pl_module.model.rag.retriever.init_retrieval()  # better to use hook functions.
  
  
  
  
  
  
  class 	UpperCamelCase_     (     pl.Callback       ):
  
  
  
  					def      __a    (		self    :    Union[str, Any]					,			lowerCamelCase    :    Dict					,			lowerCamelCase    :    List[str]	):
  							lowerCamelCase_  :    Any   	=			trainer.lr_schedulers[0]['scheduler']
  							lowerCamelCase_  :    List[str]   	=			{F"lr_group_{i}": lr for i, lr in enumerate(lr_scheduler.get_lr()	)}
  							pl_module.logger.log_metrics(lowerCamelCase	)
  
  
  
  					def      __a    (		self    :    List[str]					,			lowerCamelCase    :    pl.Trainer					,			lowerCamelCase    :    pl.LightningModule	):
  							rank_zero_info('***** Validation results *****'	)
  							lowerCamelCase_  :    List[str]   	=			trainer.callback_metrics
  							# Log results
  							for key in sorted(lowerCamelCase	):
  									if key not in ["log", "progress_bar"]:
  											rank_zero_info('{} = {}\n'.format(lowerCamelCase					,			str(metrics[key]	)	)	)
  
  
  
  
  
  					def      __a    (		self    :    Dict					,			lowerCamelCase    :    pl.Trainer					,			lowerCamelCase    :    pl.LightningModule	):
  							rank_zero_info('***** Test results *****'	)
  							lowerCamelCase_  :    Any   	=			trainer.callback_metrics
  							# Log and save results to file
  							lowerCamelCase_  :    str   	=			os.path.join(pl_module.hparams.output_dir					,			'test_results.txt'	)
  							with open(lowerCamelCase					,			'w'	) as writer:
  									for key in sorted(lowerCamelCase	):
  											if key not in ["log", "progress_bar"]:
  													rank_zero_info('{} = {}\n'.format(lowerCamelCase					,			str(metrics[key]	)	)	)
  													writer.write('{} = {}\n'.format(lowerCamelCase					,			str(metrics[key]	)	)	)
  
  
  def 		_SCREAMING_SNAKE_CASE    (   lowerCAmelCase__       ,lowerCAmelCase__	):
  		#  To allow all pl args uncomment the following line
  		#  parser = pl.Trainer.add_argparse_args(parser)
  		parser.add_argument(
  		    '--output_dir'       ,default=lowerCAmelCase__       ,type=lowerCAmelCase__       ,required=lowerCAmelCase__       ,help='The output directory where the model predictions and checkpoints will be written.'       ,)
  		parser.add_argument(
  		    '--fp16'       ,action='store_true'       ,help='Whether to use 16-bit (mixed) precision (through NVIDIA apex) instead of 32-bit'       ,)
  
  		parser.add_argument(
  		    '--fp16_opt_level'       ,type=lowerCAmelCase__       ,default='O2'       ,help=(
  		        'For fp16: Apex AMP optimization level selected in [\'O0\', \'O1\', \'O2\', and \'O3\'].'
  		        'See details at https://nvidia.github.io/apex/amp.html'
  		    )       ,)
  		parser.add_argument('--n_tpu_cores'       ,dest='tpu_cores'       ,type=lowerCAmelCase__	)
  		parser.add_argument('--max_grad_norm'       ,dest='gradient_clip_val'       ,default=1.0       ,type=lowerCAmelCase__       ,help='Max gradient norm'	)
  		parser.add_argument('--do_train'       ,action='store_true'       ,help='Whether to run training.'	)
  		parser.add_argument('--do_predict'       ,action='store_true'       ,help='Whether to run predictions on the test set.'	)
  		parser.add_argument(
  		    '--gradient_accumulation_steps'       ,dest='accumulate_grad_batches'       ,type=lowerCAmelCase__       ,default=1       ,help='Number of updates steps to accumulate before performing a backward/update pass.'       ,)
  		parser.add_argument('--seed'       ,type=lowerCAmelCase__       ,default=42       ,help='random seed for initialization'	)
  		parser.add_argument(
  		    '--data_dir'       ,default=lowerCAmelCase__       ,type=lowerCAmelCase__       ,required=lowerCAmelCase__       ,help='The input data dir. Should contain the training files for the CoNLL-2003 NER task.'       ,)
  
  
  
  
  
  def 		_SCREAMING_SNAKE_CASE    (   lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__=None       ,lowerCAmelCase__=True       ,lowerCAmelCase__=None       ,lowerCAmelCase__=[]       ,lowerCAmelCase__=None       ,lowerCAmelCase__=None       ,**lowerCAmelCase__       ,):
  		pl.seed_everything(args.seed	)
  
  		# init model
  		lowerCamelCase_  :    List[str]   	=			Path(model.hparams.output_dir	)
  		odir.mkdir(exist_ok=lowerCAmelCase__	)
  
  		# add custom checkpoints
  		if checkpoint_callback is None:
  				lowerCamelCase_  :    Optional[int]   	=			pl.callbacks.ModelCheckpoint(
  				    filepath=args.output_dir       ,prefix='checkpoint'       ,monitor='val_loss'       ,mode='min'       ,save_top_k=1	)
  		if early_stopping_callback:
  				extra_callbacks.append(lowerCAmelCase__	)
  		if logging_callback is None:
  				lowerCamelCase_  :    Tuple   	=			LoggingCallback()
  
  		lowerCamelCase_  :    List[str]   	=			{}
  
  		# TODO: remove with PyTorch 1.6 since pl uses native amp
  		if args.fpaa:
  				lowerCamelCase_  :    int   	=			16
  				# train_params["amp_level"] = args.fp16_opt_level
  
  		if args.gpus > 1:
  				lowerCamelCase_  :    Optional[Any]   	=			'auto'  # "ddp"
  				lowerCamelCase_  :    int   	=			'ddp'
  
  		lowerCamelCase_  :    Dict   	=			args.accumulate_grad_batches
  		lowerCamelCase_  :    List[str]   	=			None  # extra_train_kwargs.get("profiler", None) #get unwanted logs
  		lowerCamelCase_  :    int   	=			'auto'
  
  		lowerCamelCase_  :    int   	=			pl.Trainer.from_argparse_args(
  		    lowerCAmelCase__       ,weights_summary=lowerCAmelCase__       ,callbacks=[logging_callback] + extra_callbacks + [checkpoint_callback] + [InitCallback()]       ,logger=lowerCAmelCase__       ,**lowerCAmelCase__       ,)
  
  		if args.do_train:
  				trainer.fit(lowerCAmelCase__	)
  
  		return trainer
  
style_context: 
  
  
  
  
  
  class 	UpperCamelCase_     :
  
  
  
  					def __init__(		self    :    List[Any]					,			lowerCamelCase    :    int	):
  							lowerCamelCase_  :    Union[str, Any]   	=			val
  							# Number of nodes in left subtree
  							lowerCamelCase_  :    Dict   	=			0
  							lowerCamelCase_  :    str   	=			None
  							lowerCamelCase_  :    int   	=			None
  							lowerCamelCase_  :    Dict   	=			None
  
  
  
  
  
  					def      __a    (		self    :    Optional[int]					,			lowerCamelCase    :    List[Any]	):
  							assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"
  
  							if self.val < other.val:
  									lowerCamelCase_  :    int   	=			self.right
  									lowerCamelCase_  :    Any   	=			None
  									if self.right:
  											lowerCamelCase_  :    Optional[Any]   	=			other
  									lowerCamelCase_  :    Union[str, Any]   	=			other
  									lowerCamelCase_  :    List[Any]   	=			self.left_tree_size * 2 + 1
  									return self
  							else:
  									lowerCamelCase_  :    str   	=			other.right
  									lowerCamelCase_  :    List[Any]   	=			None
  									if other.right:
  											lowerCamelCase_  :    Union[str, Any]   	=			self
  									lowerCamelCase_  :    Optional[int]   	=			self
  									lowerCamelCase_  :    Optional[int]   	=			other.left_tree_size * 2 + 1
  									return other
  
  
  
  
  
  
  class 	UpperCamelCase_     :
  
  
  
  					def __init__(		self    :    List[str]					,			lowerCamelCase    :    Optional[int]=None					,			lowerCamelCase    :    str=None					,			lowerCamelCase    :    List[Any]=0	):
  							lowerCamelCase_  :    Any   	=			heap_size
  							lowerCamelCase_  :    int   	=			bottom_root
  							lowerCamelCase_  :    Any   	=			min_node
  
  
  
  					def      __a    (		self    :    int					,			lowerCamelCase    :    int	):
  
  							# Empty heaps corner cases
  							if other.size == 0:
  									return None
  							if self.size == 0:
  									lowerCamelCase_  :    List[str]   	=			other.size
  									lowerCamelCase_  :    Tuple   	=			other.bottom_root
  									lowerCamelCase_  :    Tuple   	=			other.min_node
  									return None
  							# Update size
  							lowerCamelCase_  :    Optional[Any]   	=			self.size + other.size
  
  							# Update min.node
  							if self.min_node.val > other.min_node.val:
  									lowerCamelCase_  :    Optional[Any]   	=			other.min_node
  							# Merge
  
  							# Order roots by left_subtree_size
  							lowerCamelCase_  :    Dict   	=			[]
  							lowerCamelCase_	,			lowerCamelCase_  :    Optional[Any]   	=			self.bottom_root, other.bottom_root
  							while i or j:
  									if i and ((not j) or i.left_tree_size < j.left_tree_size):
  											combined_roots_list.append((i, True)	)
  											lowerCamelCase_  :    Tuple   	=			i.parent
  									else:
  											combined_roots_list.append((j, False)	)
  											lowerCamelCase_  :    Optional[Any]   	=			j.parent
          # Insert links between them
  							for i in range(len(lowerCamelCase	) - 1	):
  									if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
  											lowerCamelCase_  :    Dict   	=			combined_roots_list[i + 1][0]
  											lowerCamelCase_  :    Optional[int]   	=			combined_roots_list[i][0]
          # Consecutively merge roots with same left_tree_size
  							lowerCamelCase_  :    Any   	=			combined_roots_list[0][0]
  							while i.parent:
  									if (
  									    (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
  									) or (
  									    i.left_tree_size == i.parent.left_tree_size
  									    and i.left_tree_size != i.parent.parent.left_tree_size
  									):
  											# Neighbouring Nodes
  											lowerCamelCase_  :    Dict   	=			i.left
  											lowerCamelCase_  :    int   	=			i.parent.parent
  
  											# Merging trees
  											lowerCamelCase_  :    str   	=			i.merge_trees(i.parent	)
  
  											# Updating links
  											lowerCamelCase_  :    Union[str, Any]   	=			previous_node
  											lowerCamelCase_  :    List[Any]   	=			next_node
  											if previous_node:
  													lowerCamelCase_  :    List[str]   	=			i
  											if next_node:
  													lowerCamelCase_  :    Dict   	=			i
  									else:
  											lowerCamelCase_  :    List[str]   	=			i.parent
          # Updating self.bottom_root
  							while i.left:
  									lowerCamelCase_  :    Union[str, Any]   	=			i.left
  							lowerCamelCase_  :    Any   	=			i
  
  							# Update other
  							lowerCamelCase_  :    Optional[int]   	=			self.size
  							lowerCamelCase_  :    Optional[Any]   	=			self.bottom_root
  							lowerCamelCase_  :    str   	=			self.min_node
  
  							# Return the merged heap
  							return self
  
  
  
  					def      __a    (		self    :    Any					,			lowerCamelCase    :    Dict	):
  							if self.size == 0:
  									lowerCamelCase_  :    Tuple   	=			Node(lowerCamelCase	)
  									lowerCamelCase_  :    Optional[int]   	=			1
  									lowerCamelCase_  :    Optional[int]   	=			self.bottom_root
  							else:
  									# Create new node
  									lowerCamelCase_  :    List[Any]   	=			Node(lowerCamelCase	)
  
  									# Update size
  									self.size += 1
  
  									# update min_node
  									if val < self.min_node.val:
  											lowerCamelCase_  :    List[str]   	=			new_node
  									# Put new_node as a bottom_root in heap
  									lowerCamelCase_  :    int   	=			new_node
  									lowerCamelCase_  :    Tuple   	=			self.bottom_root
  									lowerCamelCase_  :    Any   	=			new_node
  
  									# Consecutively merge roots with same left_tree_size
  									while (
  									    self.bottom_root.parent
  									    and self.bottom_root.left_tree_size
  									    == self.bottom_root.parent.left_tree_size
  									):
  											# Next node
  											lowerCamelCase_  :    Any   	=			self.bottom_root.parent.parent
  
  											# Merge
  											lowerCamelCase_  :    int   	=			self.bottom_root.merge_trees(self.bottom_root.parent	)
  
  											# Update Links
  											lowerCamelCase_  :    Dict   	=			next_node
  											lowerCamelCase_  :    Optional[Any]   	=			None
  											if next_node:
  													lowerCamelCase_  :    Union[str, Any]   	=			self.bottom_root
  
  
  
  					def      __a    (		self    :    Dict	):
  							return self.min_node.val
  
  
  
  					def      __a    (		self    :    int	):
  							return self.size == 0
  
  
  
  					def      __a    (		self    :    List[Any]	):
  							lowerCamelCase_  :    Tuple   	=			self.min_node.val
  
  							# Last element in heap corner case
  							if self.size == 1:
  									# Update size
  									lowerCamelCase_  :    Optional[Any]   	=			0
  
  									# Update bottom root
  									lowerCamelCase_  :    Any   	=			None
  
  									# Update min_node
  									lowerCamelCase_  :    List[str]   	=			None
  
  									return min_value
  							# No right subtree corner case
  							# The structure of the tree implies that this should be the bottom root
  							# and there is at least one other root
  							if self.min_node.right is None:
  									# Update size
  									self.size -= 1
  
  									# Update bottom root
  									lowerCamelCase_  :    Union[str, Any]   	=			self.bottom_root.parent
  									lowerCamelCase_  :    Union[str, Any]   	=			None
  
  									# Update min_node
  									lowerCamelCase_  :    Union[str, Any]   	=			self.bottom_root
  									lowerCamelCase_  :    Union[str, Any]   	=			self.bottom_root.parent
  									while i:
  											if i.val < self.min_node.val:
  													lowerCamelCase_  :    Union[str, Any]   	=			i
  											lowerCamelCase_  :    Optional[int]   	=			i.parent
  									return min_value
  							# General case
  							# Find the BinomialHeap of the right subtree of min_node
  							lowerCamelCase_  :    Dict   	=			self.min_node.right
  							lowerCamelCase_  :    Dict   	=			None
  							lowerCamelCase_  :    Tuple   	=			bottom_of_new
  							lowerCamelCase_  :    Dict   	=			1
  
  							# Size, min_node and bottom_root
  							while bottom_of_new.left:
  									lowerCamelCase_  :    Any   	=			size_of_new * 2 + 1
  									lowerCamelCase_  :    Tuple   	=			bottom_of_new.left
  									if bottom_of_new.val < min_of_new.val:
  											lowerCamelCase_  :    int   	=			bottom_of_new
          # Corner case of single root on top left path
  							if (not self.min_node.left) and (not self.min_node.parent):
  									lowerCamelCase_  :    Union[str, Any]   	=			size_of_new
  									lowerCamelCase_  :    Union[str, Any]   	=			bottom_of_new
  									lowerCamelCase_  :    Tuple   	=			min_of_new
  									# print("Single root, multiple nodes case")
  									return min_value
  							# Remaining cases
  							# Construct heap of right subtree
  							lowerCamelCase_  :    Optional[Any]   	=			BinomialHeap(
  							    bottom_root=lowerCamelCase					,			min_node=lowerCamelCase					,			heap_size=lowerCamelCase	)
  
  							# Update size
  							lowerCamelCase_  :    Union[str, Any]   	=			self.size - 1 - size_of_new
  
  							# Neighbour nodes
  							lowerCamelCase_  :    Union[str, Any]   	=			self.min_node.left
  							lowerCamelCase_  :    Optional[Any]   	=			self.min_node.parent
  
  							# Initialize new bottom_root and min_node
  							lowerCamelCase_  :    Optional[int]   	=			previous_node or next_node
  							lowerCamelCase_  :    Tuple   	=			next_node
  
  							# Update links of previous_node and search below for new min_node and
  							# bottom_root
  							if previous_node:
  									lowerCamelCase_  :    Dict   	=			next_node
  
  									# Update bottom_root and search for min_node below
  									lowerCamelCase_  :    int   	=			previous_node
  									lowerCamelCase_  :    Tuple   	=			previous_node
  									while self.bottom_root.left:
  											lowerCamelCase_  :    Union[str, Any]   	=			self.bottom_root.left
  											if self.bottom_root.val < self.min_node.val:
  													lowerCamelCase_  :    Any   	=			self.bottom_root
  							if next_node:
  									lowerCamelCase_  :    Any   	=			previous_node
  
  									# Search for new min_node above min_node
  									lowerCamelCase_  :    List[str]   	=			next_node
  									while i:
  											if i.val < self.min_node.val:
  													lowerCamelCase_  :    List[Any]   	=			i
  											lowerCamelCase_  :    Dict   	=			i.parent
          # Merge heaps
  							self.merge_heaps(lowerCamelCase	)
  
  							return min_value
  
  
  
  					def      __a    (		self    :    Optional[int]	):
  							lowerCamelCase_  :    List[Any]   	=			self.bottom_root
  							while top_root.parent:
  									lowerCamelCase_  :    Tuple   	=			top_root.parent
  							# preorder
  							lowerCamelCase_  :    str   	=			[]
  							self.__traversal(lowerCamelCase					,			lowerCamelCase	)
  							return heap_pre_order
  
  
  
  					def      __a    (		self    :    Dict					,			lowerCamelCase    :    Tuple					,			lowerCamelCase    :    Dict					,			lowerCamelCase    :    List[str]=0	):
  							if curr_node:
  									preorder.append((curr_node.val, level)	)
  									self.__traversal(curr_node.left					,			lowerCamelCase					,			level + 1	)
  									self.__traversal(curr_node.right					,			lowerCamelCase					,			level + 1	)
  							else:
  									preorder.append(('#', level)	)
  
  
  
  
  
  					def __str__(		self    :    List[Any]	):
  							if self.is_empty():
  									return ""
  							lowerCamelCase_  :    str   	=			self.pre_order()
  
  							return "\n".join(('-' * level + str(lowerCamelCase	)) for value, level in preorder_heap	)
  
  
  # Unit Tests
  if __name__ == "__main__":
  		import doctest
  
  		doctest.testmod()
  