





def    A_(			A				,      A   ):
	UpperCAmelCase_								=     [1]
	for i in range(2				,      A   ):
		factorials.append(factorials[-1] * i   )
	assert 0 <= k < factorials[-1] * n, "k out of bounds"

	UpperCAmelCase_								=     []
	UpperCAmelCase_								=     list(range(A   )   )

	# Find permutation
	while factorials:
		UpperCAmelCase_								=     factorials.pop()
		UpperCAmelCase_						,	UpperCAmelCase_								=     divmod(A				,      A   )
		permutation.append(elements[number]   )
		elements.remove(elements[number]   )
	permutation.append(elements[0]   )

	return permutation


if __name__ == "__main__":
				import doctest

				doctest.testmod()









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
# and perform gradient accumulation
#
# 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__   : Tuple					  = 32




def    A_(			A				,      A = 16   ):
	UpperCAmelCase_								=     AutoTokenizer.from_pretrained("""bert-base-cased"""   )
	UpperCAmelCase_								=     load_dataset("""glue"""				,      """mrpc"""   )

	def tokenize_function(A   ):
		# max_length=None => use the model max length (it's actually the default)
		UpperCAmelCase_								=     tokenizer(examples["""sentence1"""]				,      examples["""sentence2"""]				,      truncation=A				,      max_length=A   )
		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(
		    A				,      batched=A				,      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(A   ):
		# 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(
		    A				,      padding="""longest"""				,      max_length=A				,      pad_to_multiple_of=A				,      return_tensors="""pt"""				,      )

	# Instantiate dataloaders.
	UpperCAmelCase_								=     DataLoader(
	    tokenized_datasets["""train"""]				,      shuffle=A				,      collate_fn=A				,      batch_size=A   )
	UpperCAmelCase_								=     DataLoader(
	    tokenized_datasets["""validation"""]				,      shuffle=A				,      collate_fn=A				,      batch_size=A   )

	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__   : str					  = mocked_dataloaders  # noqa: F811




def    A_(			A				,      A   ):
	# For testing only
	if os.environ.get("""TESTING_MOCKED_DATALOADERS"""				,      A   ) == "1":
		UpperCAmelCase_								=     2
	# New Code #
	UpperCAmelCase_								=     int(args.gradient_accumulation_steps   )
	# Initialize accelerator
	UpperCAmelCase_								=     Accelerator(
	    cpu=args.cpu				,      mixed_precision=args.mixed_precision				,      gradient_accumulation_steps=A   )
	if accelerator.distributed_type == DistributedType.TPU and gradient_accumulation_steps > 1:
		raise NotImplementedError(
		    """Gradient accumulation on TPUs is currently not supported. Pass `gradient_accumulation_steps=1`"""   )
	# 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"""   )

	set_seed(A   )
	UpperCAmelCase_						,	UpperCAmelCase_								=     get_dataloaders(A				,      A   )
	# 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=A   )

	# 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=A   )

	# Instantiate scheduler
	UpperCAmelCase_								=     get_linear_schedule_with_warmup(
	    optimizer=A				,      num_warmup_steps=100				,      num_training_steps=(len(A   ) * num_epochs)				,      )

	# 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(
	    A				,      A				,      A				,      A				,      A   )

	# Now we train the model
	for epoch in range(A   ):
		model.train()
		for step, batch in enumerate(A   ):
			# We could avoid this line since we set the accelerator with `device_placement=True`.
			batch.to(accelerator.device   )
			# New code #
			# We use the new `accumulate` context manager to perform gradient accumulation
			# We also currently do not support TPUs nor advise it as bugs were found on the XLA side when running our tests.
			with accelerator.accumulate(A   ):
				UpperCAmelCase_								=     model(**A   )
				UpperCAmelCase_								=     output.loss
				accelerator.backward(A   )
				optimizer.step()
				lr_scheduler.step()
				optimizer.zero_grad()

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

		UpperCAmelCase_								=     metric.compute()
		# Use accelerator.print to print only on the main process.
		accelerator.print(f"""epoch {epoch}:"""				,      A   )




def    A_(			):
	UpperCAmelCase_								=     argparse.ArgumentParser(description="""Simple example of training script."""   )
	parser.add_argument(
	    """--mixed_precision"""				,      type=A				,      default=A				,      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."""				,      )
	# New Code #
	parser.add_argument(
	    """--gradient_accumulation_steps"""				,      type=A				,      default=1				,      help="""The number of minibatches to be ran before gradients are accumulated."""				,      )
	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(A				,      A   )


if __name__ == "__main__":
				main()


