"""simple docstring"""







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 how to properly calculate the metrics on the
# validation dataset when in a distributed system, 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
#
########################################################################


_a					:					Any=			16
_a					:					Dict=			32
def   __UpperCAmelCase    (   UpperCAmelCase_   :    Accelerator      ,							UpperCAmelCase_   :    int = 16  )							->      Union[str, Any]:

	'''simple docstring'''





	__snake_case      :							Union[str, Any]						=			AutoTokenizer.from_pretrained('bert-base-cased'  )
	__snake_case      :							Optional[Any]						=			load_dataset('glue'      ,							'mrpc'  )

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

	def collate_fn(UpperCAmelCase_   :    Optional[Any]  ):
		# On TPU it's best to pad everything to the same length or training will be very slow.
		__snake_case      :							Dict						=			1_28 if accelerator.distributed_type == DistributedType.TPU else None
		# When using mixed precision we want round multiples of 8/16
		if accelerator.mixed_precision == "fp8":
			__snake_case      :							Optional[Any]						=			16
		elif accelerator.mixed_precision != "no":
			__snake_case      :							Optional[int]						=			8
		else:
			__snake_case      :							List[Any]						=			None

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

	# Instantiate dataloaders.
	__snake_case      :							List[Any]						=			DataLoader(
	    tokenized_datasets['train']      ,							shuffle=UpperCAmelCase_      ,							collate_fn=UpperCAmelCase_      ,							batch_size=UpperCAmelCase_  )
	__snake_case      :							Union[str, Any]						=			DataLoader(
	    tokenized_datasets['validation']      ,							shuffle=UpperCAmelCase_      ,							collate_fn=UpperCAmelCase_      ,							batch_size=UpperCAmelCase_  )

	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

	_a					:					Optional[Any]=			mocked_dataloaders  # noqa: F811
def   __UpperCAmelCase    (   UpperCAmelCase_   :    int      ,							UpperCAmelCase_   :    List[Any]  )							->      List[str]:

	'''simple docstring'''





	if os.environ.get('TESTING_MOCKED_DATALOADERS'      ,							UpperCAmelCase_  ) == "1":
		__snake_case      :							str						=			2
	# Initialize accelerator
	__snake_case      :							Any						=			Accelerator(cpu=args.cpu      ,							mixed_precision=args.mixed_precision  )
	# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
	__snake_case      :							str						=			config['lr']
	__snake_case      :							Tuple						=			int(config['num_epochs']  )
	__snake_case      :							Any						=			int(config['seed']  )
	__snake_case      :							Union[str, Any]						=			int(config['batch_size']  )

	__snake_case      :							int						=			evaluate.load('glue'      ,							'mrpc'  )

	# If the batch size is too big we use gradient accumulation
	__snake_case      :							Optional[int]						=			1
	if batch_size > MAX_GPU_BATCH_SIZE and accelerator.distributed_type != DistributedType.TPU:
		__snake_case      :							Any						=			batch_size // MAX_GPU_BATCH_SIZE
		__snake_case      :							Dict						=			MAX_GPU_BATCH_SIZE

	set_seed(UpperCAmelCase_  )
	__snake_case		,    __snake_case      :							List[Any]						=			get_dataloaders(UpperCAmelCase_      ,							UpperCAmelCase_  )
	# Instantiate the model (we build the model here so that the seed also control new weights initialization)
	__snake_case      :							List[Any]						=			AutoModelForSequenceClassification.from_pretrained('bert-base-cased'      ,							return_dict=UpperCAmelCase_  )

	# 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).
	__snake_case      :							str						=			model.to(accelerator.device  )

	# Instantiate optimizer
	__snake_case      :							Optional[int]						=			AdamW(params=model.parameters()      ,							lr=UpperCAmelCase_  )

	# Instantiate scheduler
	__snake_case      :							str						=			get_linear_schedule_with_warmup(
	    optimizer=UpperCAmelCase_      ,							num_warmup_steps=1_00      ,							num_training_steps=(len(UpperCAmelCase_  ) * 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.
	__snake_case		,    __snake_case		,    __snake_case		,    __snake_case		,    __snake_case      :							str						=			accelerator.prepare(
	    UpperCAmelCase_      ,							UpperCAmelCase_      ,							UpperCAmelCase_      ,							UpperCAmelCase_      ,							UpperCAmelCase_  )

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

		model.eval()
		__snake_case      :							Optional[Any]						=			0
		for step, batch in enumerate(UpperCAmelCase_  ):
			# We could avoid this line since we set the accelerator with `device_placement=True`.
			batch.to(accelerator.device  )
			with torch.no_grad():
				__snake_case      :							Union[str, Any]						=			model(**UpperCAmelCase_  )
			__snake_case      :							List[Any]						=			outputs.logits.argmax(dim=-1  )
			__snake_case		,    __snake_case      :							int						=			accelerator.gather((predictions, batch['labels'])  )
			# New Code #
			# First we check if it's a distributed system
			if accelerator.use_distributed:
				# Then see if we're on the last batch of our eval dataloader
				if step == len(UpperCAmelCase_  ) - 1:
					# Last batch needs to be truncated on distributed systems as it contains additional samples
					__snake_case      :							Tuple						=			predictions[: len(eval_dataloader.dataset  ) - samples_seen]
					__snake_case      :							Optional[Any]						=			references[: len(eval_dataloader.dataset  ) - samples_seen]
				else:
					# Otherwise we add the number of samples seen
					samples_seen += references.shape[0]
            # All of this can be avoided if you use `Accelerator.gather_for_metrics` instead of `Accelerator.gather`:
            # accelerator.gather_for_metrics((predictions, batch["labels"]))
			metric.add_batch(
			    predictions=UpperCAmelCase_      ,							references=UpperCAmelCase_      ,							)

		__snake_case      :							Any						=			metric.compute()
		# Use accelerator.print to print only on the main process.
		accelerator.print(F"epoch {epoch}:"      ,							UpperCAmelCase_  )
def   __UpperCAmelCase    (   )							->      Tuple:

	'''simple docstring'''





	__snake_case      :							Union[str, Any]						=			argparse.ArgumentParser(description='Simple example of training script.'  )
	parser.add_argument(
	    '--mixed_precision'      ,							type=UpperCAmelCase_      ,							default=UpperCAmelCase_      ,							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.'  )
	__snake_case      :							Dict						=			parser.parse_args()
	__snake_case      :							Optional[Any]						=			{'lr': 2E-5, 'num_epochs': 3, 'seed': 42, 'batch_size': 16}
	training_function(UpperCAmelCase_      ,							UpperCAmelCase_  )


if __name__ == "__main__":
	main()






"""simple docstring"""







from __future__ import annotations

import math
def   __UpperCAmelCase    (   UpperCAmelCase_   :    int  )							->      bool:

	'''simple docstring'''





	if 1 < number < 4:
		# 2 and 3 are primes
		return True
	elif number < 2 or number % 2 == 0 or number % 3 == 0:
		# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
		return False

	# All primes number are in format of 6k +/- 1
	for i in range(5      ,							int(math.sqrt(UpperCAmelCase_  ) + 1  )      ,							6  ):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True


_a					:					Any=			[num for num in range(3, 100_001, 2) if not is_prime(num)]
def   __UpperCAmelCase    (   UpperCAmelCase_   :    int  )							->      list[int]:

	'''simple docstring'''





	if not isinstance(UpperCAmelCase_      ,							UpperCAmelCase_  ):
		raise ValueError('n must be an integer'  )
	if n <= 0:
		raise ValueError('n must be >= 0'  )

	__snake_case      :							int						=			[]
	for num in range(len(UpperCAmelCase_  )  ):
		__snake_case      :							List[str]						=			0
		while 2 * i * i <= odd_composites[num]:
			__snake_case      :							List[Any]						=			odd_composites[num] - 2 * i * i
			if is_prime(UpperCAmelCase_  ):
				break
			i += 1
		else:
			list_nums.append(odd_composites[num]  )
			if len(UpperCAmelCase_  ) == n:
				return list_nums

	return []
def   __UpperCAmelCase    (   )							->      int:

	'''simple docstring'''





	return compute_nums(1  )[0]


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





