




from collections import defaultdict


def 				A	( lowercase			)       ->  int:
		'''simple docstring'''

		UpperCamelCase          =					1
		UpperCamelCase          =					True
		for v in tree[start]:
				if v not in visited:
						ret += dfs(_UpperCamelCase			)
		if ret % 2 == 0:
				cuts.append(_UpperCamelCase			)
		return ret


def 				A	( )       ->  List[Any]:
		'''simple docstring'''

		dfs(1			)


if __name__ == "__main__":
					_UpperCAmelCase :			List[str]              =	10, 9
					_UpperCAmelCase :			Optional[Any]              =	defaultdict(list)
					_UpperCAmelCase :			dict[int, bool]              =	{}
					_UpperCAmelCase :			list[int]              =	[]
					_UpperCAmelCase :			Dict              =	0
					_UpperCAmelCase :			Tuple              =	[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
					for u, v in edges:
										tree[u].append(v)
										tree[v].append(u)
					even_tree()
					print(len(cuts) - 1)


import argparse

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
#
# 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 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 :			Union[str, Any]              =	16
_UpperCAmelCase :			Dict              =	32


def 				A	( lowercase   ,	lowercase = 16			)       ->  str:
		'''simple docstring'''

		UpperCamelCase          =					AutoTokenizer.from_pretrained('bert-base-cased'			)
		UpperCamelCase          =					load_dataset('glue'   ,	'mrpc'			)

		def tokenize_function(lowercase			):
				# max_length=None => use the model max length (it's actually the default)
				UpperCamelCase          =					tokenizer(examples['sentence1']   ,	examples['sentence2']   ,	truncation=lowercase   ,	max_length=lowercase			)
				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():
				UpperCamelCase          =					datasets.map(
				    lowercase   ,	batched=lowercase   ,	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
		UpperCamelCase          =					tokenized_datasets.rename_column('label'   ,	'labels'			)

		def collate_fn(lowercase			):
				# On TPU it's best to pad everything to the same length or training will be very slow.
				UpperCamelCase          =					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":
						UpperCamelCase          =					16
				elif accelerator.mixed_precision != "no":
						UpperCamelCase          =					8
				else:
						UpperCamelCase          =					None

				return tokenizer.pad(
				    lowercase   ,	padding='longest'   ,	max_length=lowercase   ,	pad_to_multiple_of=lowercase   ,	return_tensors='pt'   ,	)

		# Instantiate dataloaders.
		UpperCamelCase          =					DataLoader(
		    tokenized_datasets['train']   ,	shuffle=lowercase   ,	collate_fn=lowercase   ,	batch_size=lowercase   ,	drop_last=lowercase			)
		UpperCamelCase          =					DataLoader(
		    tokenized_datasets['validation']   ,	shuffle=lowercase   ,	collate_fn=lowercase   ,	batch_size=lowercase   ,	drop_last=(accelerator.mixed_precision == 'fp8')   ,	)

		return train_dataloader, eval_dataloader


def 				A	( lowercase   ,	lowercase			)       ->  Optional[Any]:
		'''simple docstring'''

		UpperCamelCase          =					Accelerator(cpu=args.cpu   ,	mixed_precision=args.mixed_precision			)
		# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
		UpperCamelCase          =					config['lr']
		UpperCamelCase          =					int(config['num_epochs']			)
		UpperCamelCase          =					int(config['seed']			)
		UpperCamelCase          =					int(config['batch_size']			)

		UpperCamelCase          =					evaluate.load('glue'   ,	'mrpc'			)

		# If the batch size is too big we use gradient accumulation
		UpperCamelCase          =					1
		if batch_size > MAX_GPU_BATCH_SIZE and accelerator.distributed_type != DistributedType.TPU:
				UpperCamelCase          =					batch_size // MAX_GPU_BATCH_SIZE
				UpperCamelCase          =					MAX_GPU_BATCH_SIZE

		set_seed(lowercase			)
		UpperCamelCase     ,  UpperCamelCase          =					get_dataloaders(lowercase   ,	lowercase			)
		# Instantiate the model (we build the model here so that the seed also control new weights initialization)
		UpperCamelCase          =					AutoModelForSequenceClassification.from_pretrained('bert-base-cased'   ,	return_dict=lowercase			)

		# 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).
		UpperCamelCase          =					model.to(accelerator.device			)
		# Instantiate optimizer
		UpperCamelCase          =					AdamW(params=model.parameters()   ,	lr=lowercase			)

		# Instantiate scheduler
		UpperCamelCase          =					get_linear_schedule_with_warmup(
		    optimizer=lowercase   ,	num_warmup_steps=100   ,	num_training_steps=(len(lowercase			) * 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.

		UpperCamelCase     ,  UpperCamelCase     ,  UpperCamelCase     ,  UpperCamelCase     ,  UpperCamelCase          =					accelerator.prepare(
		    lowercase   ,	lowercase   ,	lowercase   ,	lowercase   ,	lowercase			)

		# Now we train the model
		for epoch in range(lowercase			):
				model.train()
				for step, batch in enumerate(lowercase			):
						# We could avoid this line since we set the accelerator with `device_placement=True`.
						batch.to(accelerator.device			)
						UpperCamelCase          =					model(**lowercase			)
						UpperCamelCase          =					outputs.loss
						UpperCamelCase          =					loss / gradient_accumulation_steps
						accelerator.backward(lowercase			)
						if step % gradient_accumulation_steps == 0:
								optimizer.step()
								lr_scheduler.step()
								optimizer.zero_grad()

				model.eval()
				for step, batch in enumerate(lowercase			):
						# We could avoid this line since we set the accelerator with `device_placement=True`.
						batch.to(accelerator.device			)
						with torch.no_grad():
								UpperCamelCase          =					model(**lowercase			)
						UpperCamelCase          =					outputs.logits.argmax(dim=-1			)
						UpperCamelCase     ,  UpperCamelCase          =					accelerator.gather_for_metrics((predictions, batch['labels'])			)
						metric.add_batch(
						    predictions=lowercase   ,	references=lowercase   ,	)

				UpperCamelCase          =					metric.compute()
				# Use accelerator.print to print only on the main process.
				accelerator.print(f'''epoch {epoch}:'''   ,	lowercase			)


def 				A	( )       ->  Union[str, Any]:
		'''simple docstring'''

		UpperCamelCase          =					argparse.ArgumentParser(description='Simple example of training script.'			)
		parser.add_argument(
		    '--mixed_precision'   ,	type=lowercase   ,	default=lowercase   ,	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.'			)
		UpperCamelCase          =					parser.parse_args()
		UpperCamelCase          =					{'lr': 2e-5, 'num_epochs': 3, 'seed': 42, 'batch_size': 16}
		training_function(lowercase   ,	lowercase			)


if __name__ == "__main__":
					main()
