code: 
  
  
  UpperCAmelCase      :						str    =		float("inf")
  
  
  
  
  
  
  
  class 					__lowercase					:
  
  
  
  		"""simple docstring"""
  
  		def __init__(   self		,			A  )     ->   Optional[int]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase								=     [0] * n
  					lowerCamelCase								=     [0] * n
  					lowerCamelCase								=     [0] * n
  					lowerCamelCase								=     [[] for _ in range(A  )]
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A		,			A		,			A		,			A=0  )     ->   Optional[Any]:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					self.adj[a].append([b, len(self.adj[b]  ), c, 0]  )
  					self.adj[b].append([a, len(self.adj[a]  ) - 1, rcap, 0]  )
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A		,			A		,			A  )     ->   int:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					if vertex == sink or not flow:
  								return flow
  
  					for i in range(self.ptr[vertex]		,			len(self.adj[vertex]  )  ):
  								lowerCamelCase								=     self.adj[vertex][i]
  								if self.lvl[e[0]] == self.lvl[vertex] + 1:
  											lowerCamelCase								=     self.depth_first_search(e[0]		,			A		,			min(A		,			e[2] - e[3]  )  )
  											if p:
  														self.adj[vertex][i][3] += p
  														self.adj[e[0]][e[1]][3] -= p
  														return p
  								lowerCamelCase								=     self.ptr[vertex] + 1
  					return 0
  
  
  
  
  
  
  
  		def 				__A      (   self		,			A		,			A  )     ->   Tuple:
  
  
  
  
  
  
  
  					'''simple docstring'''
  
  
  
  
  
  
  
  					lowerCamelCase		,		lowerCamelCase								=     0, source
  					for l in range(31  ):  # noqa: E741  l = 30 maybe faster for random data
  								while True:
  											lowerCamelCase		,		lowerCamelCase								=     [0] * len(self.q  ), [0] * len(self.q  )
  											lowerCamelCase		,		lowerCamelCase		,		lowerCamelCase								=     0, 1, 1
  											while qi < qe and not self.lvl[sink]:
  														lowerCamelCase								=     self.q[qi]
  														qi += 1
  														for e in self.adj[v]:
  																	if not self.lvl[e[0]] and (e[2] - e[3]) >> (30 - l):
  																				lowerCamelCase								=     e[0]
  																				qe += 1
  																				lowerCamelCase								=     self.lvl[v] + 1
  
  											lowerCamelCase								=     self.depth_first_search(A		,			A		,			A  )
  											while p:
  														flow += p
  														lowerCamelCase								=     self.depth_first_search(A		,			A		,			A  )
  
  											if not self.lvl[sink]:
  														break
  
  					return flow
  UpperCAmelCase      :						Union[str, Any]    =		Dinic(10)
  UpperCAmelCase      :						Dict    =		0
  UpperCAmelCase      :						Any    =		9
  for vertex in range(1, 5):
  		graph.add_edge(source, vertex, 1)
  for vertex in range(5, 9):
  		graph.add_edge(vertex, sink, 1)
  for vertex in range(1, 5):
  		graph.add_edge(vertex, vertex + 4, 1)
  
  # Now we can know that is the maximum flow(source -> sink)
  print(graph.max_flow(source, sink))
  
  
style_context: 
  
  
  import argparse
  import os
  
  import evaluate
  import torch
  from datasets import load_dataset
  from torch.optim import AdamW
  from torch.utils.data import DataLoader
  from transformers import AutoModelForSequenceClassification, AutoTokenizer, get_linear_schedule_with_warmup, set_seed
  
  from accelerate import Accelerator, DistributedType
  
  
  ########################################################################
  # This is a fully working simple example to use Accelerate,
  # specifically showcasing the checkpointing capability,
  # and builds off the `nlp_example.py` script.
  #
  # This example trains a Bert base model on GLUE MRPC
  # in any of the following settings (with the same script):
  #   - single CPU or single GPU
  #   - multi GPUS (using PyTorch distributed mode)
  #   - (multi) TPUs
  #   - fp16 (mixed-precision) or fp32 (normal precision)
  #
  # To help focus on the differences in the code, building `DataLoaders`
  # was refactored into its own function.
  # New additions from the base script can be found quickly by
  # looking for the # New Code # tags
  #
  # To run it in each of these various modes, follow the instructions
  # in the readme for examples:
  # https://github.com/huggingface/accelerate/tree/main/examples
  #
  ########################################################################
  
  UpperCAmelCase      :						str    =		16
  UpperCAmelCase      :						Union[str, Any]    =		32
  
  
  
  
  
  
  def   __lowerCamelCase	(       lowerCamelCase__		:	Accelerator     ,       lowerCamelCase__		:	int = 16			):
  
  
  
  
  
  			'''simple docstring'''
  
  
  
  
  			lowerCamelCase								=     AutoTokenizer.from_pretrained("""bert-base-cased"""			)
  			lowerCamelCase								=     load_dataset("""glue"""     ,       """mrpc"""			)
  
  			def tokenize_function(lowerCamelCase__		:	List[str]			):
  						# max_length=None => use the model max length (it's actually the default)
  						lowerCamelCase								=     tokenizer(examples["""sentence1"""]     ,       examples["""sentence2"""]     ,       truncation=lowerCamelCase__     ,       max_length=lowerCamelCase__			)
  						return outputs
  
  			# Apply the method we just defined to all the examples in all the splits of the dataset
  			# starting with the main process first:
  			with accelerator.main_process_first():
  						lowerCamelCase								=     datasets.map(
  						    lowerCamelCase__     ,       batched=lowerCamelCase__     ,       remove_columns=["""idx""", """sentence1""", """sentence2"""]     ,       )
  
  			# We also rename the 'label' column to 'labels' which is the expected name for labels by the models of the
  			# transformers library
  			lowerCamelCase								=     tokenized_datasets.rename_column("""label"""     ,       """labels"""			)
  
  			def collate_fn(lowerCamelCase__		:	Optional[Any]			):
  						# On TPU it's best to pad everything to the same length or training will be very slow.
  						lowerCamelCase								=     128 if accelerator.distributed_type == DistributedType.TPU else None
  						# When using mixed precision we want round multiples of 8/16
  						if accelerator.mixed_precision == "fp8":
  									lowerCamelCase								=     16
  						elif accelerator.mixed_precision != "no":
  									lowerCamelCase								=     8
  						else:
  									lowerCamelCase								=     None
  
  						return tokenizer.pad(
  						    lowerCamelCase__     ,       padding="""longest"""     ,       max_length=lowerCamelCase__     ,       pad_to_multiple_of=lowerCamelCase__     ,       return_tensors="""pt"""     ,       )
  
  			# Instantiate dataloaders.
  			lowerCamelCase								=     DataLoader(
  			    tokenized_datasets["""train"""]     ,       shuffle=lowerCamelCase__     ,       collate_fn=lowerCamelCase__     ,       batch_size=lowerCamelCase__			)
  			lowerCamelCase								=     DataLoader(
  			    tokenized_datasets["""validation"""]     ,       shuffle=lowerCamelCase__     ,       collate_fn=lowerCamelCase__     ,       batch_size=lowerCamelCase__			)
  
  			return train_dataloader, eval_dataloader
  
  
  # For testing only
  if os.environ.get("TESTING_MOCKED_DATALOADERS", None) == "1":
  		from accelerate.test_utils.training import mocked_dataloaders
  
  		UpperCAmelCase      :						Tuple    =		mocked_dataloaders  # noqa: F811
  
  
  
  
  
  
  def   __lowerCamelCase	(       lowerCamelCase__		:	List[str]     ,       lowerCamelCase__		:	Optional[int]			):
  
  
  
  
  
  			'''simple docstring'''
  
  
  
  
  			if os.environ.get("""TESTING_MOCKED_DATALOADERS"""     ,       lowerCamelCase__			) == "1":
  						lowerCamelCase								=     2
  			# Initialize accelerator
  			lowerCamelCase								=     Accelerator(cpu=args.cpu     ,       mixed_precision=args.mixed_precision			)
  			# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
  			lowerCamelCase								=     config["""lr"""]
  			lowerCamelCase								=     int(config["""num_epochs"""]			)
  			lowerCamelCase								=     int(config["""seed"""]			)
  			lowerCamelCase								=     int(config["""batch_size"""]			)
  
  			# New Code #
  			# Parse out whether we are saving every epoch or after a certain number of batches
  			if hasattr(args.checkpointing_steps     ,       """isdigit"""			):
  						if args.checkpointing_steps == "epoch":
  									lowerCamelCase								=     args.checkpointing_steps
  						elif args.checkpointing_steps.isdigit():
  									lowerCamelCase								=     int(args.checkpointing_steps			)
  						else:
  									raise ValueError(
  									    f'Argument `checkpointing_steps` must be either a number or `epoch`. `{args.checkpointing_steps}` passed.'			)
  			else:
  						lowerCamelCase								=     None
  
  			set_seed(lowerCamelCase__			)
  
  			lowerCamelCase		,		lowerCamelCase								=     get_dataloaders(lowerCamelCase__     ,       lowerCamelCase__			)
  			lowerCamelCase								=     evaluate.load("""glue"""     ,       """mrpc"""			)
  
  			# If the batch size is too big we use gradient accumulation
  			lowerCamelCase								=     1
  			if batch_size > MAX_GPU_BATCH_SIZE and accelerator.distributed_type != DistributedType.TPU:
  						lowerCamelCase								=     batch_size // MAX_GPU_BATCH_SIZE
  						lowerCamelCase								=     MAX_GPU_BATCH_SIZE
  
  			# Instantiate the model (we build the model here so that the seed also control new weights initialization)
  			lowerCamelCase								=     AutoModelForSequenceClassification.from_pretrained("""bert-base-cased"""     ,       return_dict=lowerCamelCase__			)
  
  			# We could avoid this line since the accelerator is set with `device_placement=True` (default value).
  			# Note that if you are placing tensors on devices manually, this line absolutely needs to be before the optimizer
  			# creation otherwise training will not work on TPU (`accelerate` will kindly throw an error to make us aware of that).
  			lowerCamelCase								=     model.to(accelerator.device			)
  
  			# Instantiate optimizer
  			lowerCamelCase								=     AdamW(params=model.parameters()     ,       lr=lowerCamelCase__			)
  
  			# Instantiate scheduler
  			lowerCamelCase								=     get_linear_schedule_with_warmup(
  			    optimizer=lowerCamelCase__     ,       num_warmup_steps=100     ,       num_training_steps=(len(lowerCamelCase__			) * num_epochs) // gradient_accumulation_steps     ,       )
  
  			# Prepare everything
  			# There is no specific order to remember, we just need to unpack the objects in the same order we gave them to the
  			# prepare method.
  			lowerCamelCase		,		lowerCamelCase		,		lowerCamelCase		,		lowerCamelCase		,		lowerCamelCase								=     accelerator.prepare(
  			    lowerCamelCase__     ,       lowerCamelCase__     ,       lowerCamelCase__     ,       lowerCamelCase__     ,       lowerCamelCase__			)
  
  			# New Code #
  			# We need to keep track of how many total steps we have iterated over
  			lowerCamelCase								=     0
  			# We also need to keep track of the stating epoch so files are named properly
  			lowerCamelCase								=     0
  
  			# We need to load the checkpoint back in before training here with `load_state`
  			# The total number of epochs is adjusted based on where the state is being loaded from,
  			# as we assume continuation of the same training script
  			if args.resume_from_checkpoint:
  						if args.resume_from_checkpoint is not None or args.resume_from_checkpoint != "":
  									accelerator.print(f'Resumed from checkpoint: {args.resume_from_checkpoint}'			)
  									accelerator.load_state(args.resume_from_checkpoint			)
  									lowerCamelCase								=     os.path.basename(args.resume_from_checkpoint			)
  						else:
  									# Get the most recent checkpoint
  									lowerCamelCase								=     [f.name for f in os.scandir(os.getcwd()			) if f.is_dir()]
  									dirs.sort(key=os.path.getctime			)
  									lowerCamelCase								=     dirs[-1]  # Sorts folders by date modified, most recent checkpoint is the last
  						# Extract `epoch_{i}` or `step_{i}`
  						lowerCamelCase								=     os.path.splitext(lowerCamelCase__			)[0]
  
  						if "epoch" in training_difference:
  									lowerCamelCase								=     int(training_difference.replace("""epoch_"""     ,       """"""			)			) + 1
  									lowerCamelCase								=     None
  						else:
  									lowerCamelCase								=     int(training_difference.replace("""step_"""     ,       """"""			)			)
  									lowerCamelCase								=     resume_step // len(lowerCamelCase__			)
  									resume_step -= starting_epoch * len(lowerCamelCase__			)
  
      # Now we train the model
  			for epoch in range(lowerCamelCase__     ,       lowerCamelCase__			):
  						model.train()
  						# New Code #
  						if args.resume_from_checkpoint and epoch == starting_epoch and resume_step is not None:
  									# We need to skip steps until we reach the resumed step
  									lowerCamelCase								=     accelerator.skip_first_batches(lowerCamelCase__     ,       lowerCamelCase__			)
  									overall_step += resume_step
  						else:
  									# After the first iteration though, we need to go back to the original dataloader
  									lowerCamelCase								=     train_dataloader
  						for step, batch in enumerate(lowerCamelCase__			):
  									# We could avoid this line since we set the accelerator with `device_placement=True`.
  									batch.to(accelerator.device			)
  									lowerCamelCase								=     model(**lowerCamelCase__			)
  									lowerCamelCase								=     outputs.loss
  									lowerCamelCase								=     loss / gradient_accumulation_steps
  									accelerator.backward(lowerCamelCase__			)
  									if step % gradient_accumulation_steps == 0:
  												optimizer.step()
  												lr_scheduler.step()
  												optimizer.zero_grad()
  									# New Code #
  									overall_step += 1
  
  									# New Code #
  									# We save the model, optimizer, lr_scheduler, and seed states by calling `save_state`
  									# These are saved to folders named `step_{overall_step}`
  									# Will contain files: "pytorch_model.bin", "optimizer.bin", "scheduler.bin", and "random_states.pkl"
  									# If mixed precision was used, will also save a "scalar.bin" file
  									if isinstance(lowerCamelCase__     ,       lowerCamelCase__			):
  												lowerCamelCase								=     f'step_{overall_step}'
  												if overall_step % checkpointing_steps == 0:
  															if args.output_dir is not None:
  																		lowerCamelCase								=     os.path.join(args.output_dir     ,       lowerCamelCase__			)
  															accelerator.save_state(lowerCamelCase__			)
  
  						model.eval()
  						for step, batch in enumerate(lowerCamelCase__			):
  									# We could avoid this line since we set the accelerator with `device_placement=True` (the default).
  									batch.to(accelerator.device			)
  									with torch.no_grad():
  												lowerCamelCase								=     model(**lowerCamelCase__			)
  									lowerCamelCase								=     outputs.logits.argmax(dim=-1			)
  									lowerCamelCase		,		lowerCamelCase								=     accelerator.gather_for_metrics((predictions, batch["""labels"""])			)
  									metric.add_batch(
  									    predictions=lowerCamelCase__     ,       references=lowerCamelCase__     ,       )
  
  						lowerCamelCase								=     metric.compute()
  						# Use accelerator.print to print only on the main process.
  						accelerator.print(f'epoch {epoch}:'     ,       lowerCamelCase__			)
  
  						# New Code #
  						# We save the model, optimizer, lr_scheduler, and seed states by calling `save_state`
  						# These are saved to folders named `epoch_{epoch}`
  						# Will contain files: "pytorch_model.bin", "optimizer.bin", "scheduler.bin", and "random_states.pkl"
  						# If mixed precision was used, will also save a "scalar.bin" file
  						if checkpointing_steps == "epoch":
  									lowerCamelCase								=     f'epoch_{epoch}'
  									if args.output_dir is not None:
  												lowerCamelCase								=     os.path.join(args.output_dir     ,       lowerCamelCase__			)
  									accelerator.save_state(lowerCamelCase__			)
  
  
  
  
  
  
  def   __lowerCamelCase	(       ):
  
  
  
  
  
  			'''simple docstring'''
  
  
  
  
  			lowerCamelCase								=     argparse.ArgumentParser(description="""Simple example of training script."""			)
  			parser.add_argument(
  			    """--mixed_precision"""     ,       type=lowerCamelCase__     ,       default=lowerCamelCase__     ,       choices=["""no""", """fp16""", """bf16""", """fp8"""]     ,       help="""Whether to use mixed precision. Choose"""
  			    """between fp16 and bf16 (bfloat16). Bf16 requires PyTorch >= 1.10."""
  			    """and an Nvidia Ampere GPU."""     ,       )
  			parser.add_argument("""--cpu"""     ,       action="""store_true"""     ,       help="""If passed, will train on the CPU."""			)
  			parser.add_argument(
  			    """--checkpointing_steps"""     ,       type=lowerCamelCase__     ,       default=lowerCamelCase__     ,       help="""Whether the various states should be saved at the end of every n steps, or 'epoch' for each epoch."""     ,       )
  			parser.add_argument(
  			    """--output_dir"""     ,       type=lowerCamelCase__     ,       default="""."""     ,       help="""Optional save directory where all checkpoint folders will be stored. Default is the current working directory."""     ,       )
  			parser.add_argument(
  			    """--resume_from_checkpoint"""     ,       type=lowerCamelCase__     ,       default=lowerCamelCase__     ,       help="""If the training should continue from a checkpoint folder."""     ,       )
  			lowerCamelCase								=     parser.parse_args()
  			lowerCamelCase								=     {"""lr""": 2E-5, """num_epochs""": 3, """seed""": 42, """batch_size""": 16}
  			training_function(lowerCamelCase__     ,       lowerCamelCase__			)
  
  
  if __name__ == "__main__":
  		main()
  
  