






'''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
# 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
#
########################################################################


lowerCamelCase_				   =   16
lowerCamelCase_				   =   32

def    __lowercase		(     __lowercase  ,    __lowercase = 16			)			->		Union[str, Any]:

      '''simple docstring'''


      _A     	=      AutoTokenizer.from_pretrained("bert-base-cased"			)
      _A     	=      load_dataset("glue"  ,    "mrpc"			)

      def tokenize_function(__lowercase			):
            # max_length=None => use the model max length (it's actually the default)
            _A     	=      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():
            _A     	=      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
      _A     	=      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.
            _A     	=      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":
                  _A     	=      16
            elif accelerator.mixed_precision != "no":
                  _A     	=      8
            else:
                  _A     	=      None

            return tokenizer.pad(
                __A  ,    padding="longest"  ,    max_length=__A  ,    pad_to_multiple_of=__A  ,    return_tensors="pt"  ,    )

      # Instantiate dataloaders.
      _A     	=      DataLoader(
          tokenized_datasets["train"]  ,    shuffle=__A  ,    collate_fn=__A  ,    batch_size=__A			)
      _A     	=      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

    lowerCamelCase_				   =   mocked_dataloaders  # noqa: F811

def    __lowercase		(     __lowercase  ,    __lowercase			)			->		Union[str, Any]:

      '''simple docstring'''


      if os.environ.get("TESTING_MOCKED_DATALOADERS"  ,    __A			) == "1":
            _A     	=      2
      # New Code #
      _A     	=      int(args.gradient_accumulation_steps			)
      # Initialize accelerator
      _A     	=      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
      _A     	=      config["lr"]
      _A     	=      int(config["num_epochs"]			)
      _A     	=      int(config["seed"]			)
      _A     	=      int(config["batch_size"]			)

      _A     	=      evaluate.load("glue"  ,    "mrpc"			)

      set_seed(__A			)
      _A	,      _A     	=      get_dataloaders(__A  ,    __A			)
      # Instantiate the model (we build the model here so that the seed also control new weights initialization)
      _A     	=      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).
      _A     	=      model.to(accelerator.device			)

      # Instantiate optimizer
      _A     	=      AdamW(params=model.parameters()  ,    lr=__A			)

      # Instantiate scheduler
      _A     	=      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.
      _A	,      _A	,      _A	,      _A	,      _A     	=      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			):
                        _A     	=      model(**__A			)
                        _A     	=      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():
                        _A     	=      model(**__A			)
                  _A     	=      outputs.logits.argmax(dim=-1			)
                  _A	,      _A     	=      accelerator.gather_for_metrics((predictions, batch["labels"])			)
                  metric.add_batch(
                      predictions=__A  ,    references=__A  ,    )

            _A     	=      metric.compute()
            # Use accelerator.print to print only on the main process.
            accelerator.print(F'''epoch {epoch}:'''  ,    __A			)

def    __lowercase		(     )			->		Optional[int]:

      '''simple docstring'''


      _A     	=      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."			)
      _A     	=      parser.parse_args()
      _A     	=      {"lr": 2e-5, "num_epochs": 3, "seed": 42, "batch_size": 16}
      training_function(__A  ,    __A			)


if __name__ == "__main__":
    main()








from math import isqrt, loga







def 						lowerCamelCase__      ( __A    :int		):


       """simple docstring"""




       __snake_case       	=							[True] * max_number
       for i in range(2	,isqrt(max_number - 1		) + 1		):
              if is_prime[i]:
                     for j in range(i**2	,__A	,__A		):
                            __snake_case       	=							False

       return [i for i in range(2	,__A		) if is_prime[i]]







def 						lowerCamelCase__      ( __A    :int = 8_0_0_8_0_0	,__A    :int = 8_0_0_8_0_0		):


       """simple docstring"""




       __snake_case       	=							degree * loga(__A		)
       __snake_case       	=							int(__A		)
       __snake_case       	=							calculate_prime_numbers(__A		)

       __snake_case       	=							0
       __snake_case       	=							0
       __snake_case       	=							len(__A		) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left]		)
                  + prime_numbers[left] * loga(prime_numbers[right]		)
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


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

