

import argparse
import os

# New Code #
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
from accelerate.utils import find_executable_batch_size


########################################################################
# This is a fully working simple example to use Accelerate,
# specifically showcasing how to combine both the gradient accumulation
# and automatic batch size finder utilities of Accelerate to perfrom
# automatic 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)
#
# 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    	=			32


def 			__UpperCamelCase    (lowerCAmelCase					:  Optional[Any],    lowerCAmelCase					:  Tuple = 16     )     ->  Optional[int]:
      A    =				AutoTokenizer.from_pretrained('bert-base-cased'     )
      A    =				load_dataset('glue',    'mrpc'     )

      def tokenize_function(lowerCAmelCase					:  str     ):
            # max_length=None => use the model max length (it's actually the default)
            A    =				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():
            A    =				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
      A    =				tokenized_datasets.rename_column('label',    'labels'     )

      def collate_fn(lowerCAmelCase					:  Optional[int]     ):
            # 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(
                lowerCAmelCase,    padding='longest',    pad_to_multiple_of=lowerCAmelCase,    return_tensors='pt',    )

      # Instantiate dataloaders.
      A    =				DataLoader(
          tokenized_datasets['train'],    shuffle=lowerCAmelCase,    collate_fn=lowerCAmelCase,    batch_size=lowerCAmelCase     )
      A    =				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    	=			mocked_dataloaders  # noqa: F811


def 			__UpperCamelCase    (lowerCAmelCase					:  List[Any],    lowerCAmelCase					:  int     )     ->  Dict:
      # For testing only
      if os.environ.get('TESTING_MOCKED_DATALOADERS',    lowerCAmelCase     ) == "1":
            A    =				2
      # Initialize accelerator
      A    =				Accelerator(cpu=args.cpu,    mixed_precision=args.mixed_precision     )
      # 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'     )

      # New Code #
      # We use the `find_executable_batch_size` decorator, passing in the desired observed batch size
      # to train on. If a CUDA OOM error occurs, it will retry this loop cutting the batch size in
      # half each time. From this, we can calculate the number of gradient accumulation steps needed
      # and modify the Accelerator object as a result
      @find_executable_batch_size(starting_batch_size=int(lowerCAmelCase     )     )
      def inner_training_loop(lowerCAmelCase					:  Union[str, Any]     ):
            # Since we need to modify the outside accelerator object, we need to bring it
            # to the local scope
            nonlocal accelerator

            # We can calculate the number of gradient accumulation steps based on the current
            # batch size vs the starting batch size
            A    =				observed_batch_size // batch_size

            # And then set it in the Accelerator directly:
            A    =				num_gradient_accumulation_steps

            # Next we need to free all of the stored model references in the Accelerator each time
            accelerator.free_memory()

            # And set the seed so our results are reproducable each reset
            set_seed(lowerCAmelCase     )

            # 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=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).
            A    =				model.to(accelerator.device     )

            # Instantiate optimizer
            A    =				AdamW(params=model.parameters(),    lr=lowerCAmelCase     )
            A    =				get_dataloaders(lowerCAmelCase,    lowerCAmelCase     )

            # Instantiate scheduler
            A    =				get_linear_schedule_with_warmup(
                optimizer=lowerCAmelCase,    num_warmup_steps=100,    num_training_steps=(len(lowerCAmelCase     ) * 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    =				accelerator.prepare(
                lowerCAmelCase,    lowerCAmelCase,    lowerCAmelCase,    lowerCAmelCase,    lowerCAmelCase     )

            # Now we train the model
            for epoch in range(lowerCAmelCase     ):
                  model.train()
                  for step, batch in enumerate(lowerCAmelCase     ):
                        # And perform gradient accumulation
                        with accelerator.accumulate(lowerCAmelCase     ):
                              # We could avoid this line since we set the accelerator with `device_placement=True`.
                              batch.to(accelerator.device     )
                              A    =				model(**lowerCAmelCase     )
                              A    =				outputs.loss
                              accelerator.backward(lowerCAmelCase     )
                              optimizer.step()
                              lr_scheduler.step()
                              optimizer.zero_grad()

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

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

    # New Code #
    # And call it at the end with no arguments
    # Note: You could also refactor this outside of your training loop function
      inner_training_loop()


def 			__UpperCamelCase    ()     ->  Optional[int]:
      A    =				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.'     )
      A    =				parser.parse_args()
      # New Code #
      # We modify the starting batch size to be an observed batch size of 256, to guarentee an initial CUDA OOM
      A    =				{"lr": 2E-5, "num_epochs": 3, "seed": 42, "batch_size": 256}
      training_function(lowerCAmelCase,    lowerCAmelCase     )


if __name__ == "__main__":
   main()






from math import floor, sqrt


def 			__UpperCamelCase    (lowerCAmelCase					:  int     )     ->  int:
      A    =				0.0
      A    =				1.0
      A    =				int(sqrt(lowerCAmelCase     )     )
      A    =				root
      A    =				0
      while integer_part != 2 * root:
            A    =				denominator * integer_part - numerator
            A    =				(n - numerator**2) / denominator
            A    =				int((root + numerator) / denominator     )
            period += 1
      return period


def 			__UpperCamelCase    (lowerCAmelCase					:  int = 10_000     )     ->  int:
      A    =				0
      for i in range(2,    n + 1     ):
            A    =				sqrt(lowerCAmelCase     )
            if sr - floor(lowerCAmelCase     ) != 0 and continuous_fraction_period(lowerCAmelCase     ) % 2 == 1:
                  count_odd_periods += 1
      return count_odd_periods


if __name__ == "__main__":
  print(F'''{solution(int(input().strip()))}''')



