

'''simple docstring'''
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
#
########################################################################


_snake_case         =  16
_snake_case         =  32







def  _A		(     snake_case		,							snake_case = 16					)      ->     int:
   _lowercase      :				Tuple      					=       AutoTokenizer.from_pretrained("bert-base-cased"					)
   _lowercase      :				List[str]      					=       load_dataset("glue"		,							"mrpc"					)

   def tokenize_function(snake_case					):
      # max_length=None => use the model max length (it's actually the default)
      _lowercase      :				Tuple      					=       tokenizer(examples["sentence1"]		,							examples["sentence2"]		,							truncation=snake_case		,							max_length=snake_case					)
      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():
      _lowercase      :				List[Any]      					=       datasets.map(
          snake_case		,							batched=snake_case		,							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
   _lowercase      :				Union[str, Any]      					=       tokenized_datasets.rename_column("label"		,							"labels"					)

   def collate_fn(snake_case					):
      # On TPU it's best to pad everything to the same length or training will be very slow.
      _lowercase      :				Union[str, Any]      					=       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":
         _lowercase      :				Union[str, Any]      					=       16
      elif accelerator.mixed_precision != "no":
         _lowercase      :				str      					=       8
      else:
         _lowercase      :				Optional[int]      					=       None

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

   # Instantiate dataloaders.
   _lowercase      :				Union[str, Any]      					=       DataLoader(
       tokenized_datasets["train"]		,							shuffle=snake_case		,							collate_fn=snake_case		,							batch_size=snake_case		,							drop_last=snake_case					)
   _lowercase      :				Tuple      					=       DataLoader(
       tokenized_datasets["validation"]		,							shuffle=snake_case		,							collate_fn=snake_case		,							batch_size=snake_case		,							drop_last=(accelerator.mixed_precision == "fp8")		,							)

   return train_dataloader, eval_dataloader







def  _A		(     snake_case		,							snake_case					)      ->     int:
   # Initialize accelerator
   _lowercase      :				Tuple      					=       Accelerator(cpu=args.cpu		,							mixed_precision=args.mixed_precision					)
   # Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
   _lowercase      :				Dict      					=       config["lr"]
   _lowercase      :				int      					=       int(config["num_epochs"]					)
   _lowercase      :				Union[str, Any]      					=       int(config["seed"]					)
   _lowercase      :				Union[str, Any]      					=       int(config["batch_size"]					)

   _lowercase      :				Optional[int]      					=       evaluate.load("glue"		,							"mrpc"					)

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

   set_seed(snake_case					)
   _lowercase					,				_lowercase      :				List[str]      					=       get_dataloaders(snake_case		,							snake_case					)
   # Instantiate the model (we build the model here so that the seed also control new weights initialization)
   _lowercase      :				Tuple      					=       AutoModelForSequenceClassification.from_pretrained("bert-base-cased"		,							return_dict=snake_case					)

   # 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).
   _lowercase      :				List[Any]      					=       model.to(accelerator.device					)
   # Instantiate optimizer
   _lowercase      :				Optional[int]      					=       AdamW(params=model.parameters()		,							lr=snake_case					)

   # Instantiate scheduler
   _lowercase      :				Tuple      					=       get_linear_schedule_with_warmup(
       optimizer=snake_case		,							num_warmup_steps=1_00		,							num_training_steps=(len(snake_case					) * 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.

   _lowercase					,				_lowercase					,				_lowercase					,				_lowercase					,				_lowercase      :				Optional[int]      					=       accelerator.prepare(
       snake_case		,							snake_case		,							snake_case		,							snake_case		,							snake_case					)

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

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

      _lowercase      :				Union[str, Any]      					=       metric.compute()
      # Use accelerator.print to print only on the main process.
      accelerator.print(F'''epoch {epoch}:'''		,							snake_case					)







def  _A		(     )      ->     Optional[int]:
   _lowercase      :				str      					=       argparse.ArgumentParser(description="Simple example of training script."					)
   parser.add_argument(
       "--mixed_precision"		,							type=snake_case		,							default=snake_case		,							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."					)
   _lowercase      :				Tuple      					=       parser.parse_args()
   _lowercase      :				Optional[int]      					=       {"lr": 2E-5, "num_epochs": 3, "seed": 42, "batch_size": 16}
   training_function(snake_case		,							snake_case					)


if __name__ == "__main__":
    main()









'''simple docstring'''
from math import sqrt







def  _A		(     snake_case					)      ->     int:
   _lowercase      :				str      					=       0
   for i in range(1		,							int(sqrt(snake_case					) + 1					)					):
      if n % i == 0 and i != sqrt(snake_case					):
         total += i + n // i
      elif i == sqrt(snake_case					):
         total += i
   return total - n







def  _A		(     snake_case = 1_00_00					)      ->     int:
   _lowercase      :				List[Any]      					=       sum(
       i
       for i in range(1		,							snake_case					)
       if sum_of_divisors(sum_of_divisors(snake_case					)					) == i and sum_of_divisors(snake_case					) != i					)
   return total


if __name__ == "__main__":
    print(solution(int(str(input()).strip())))






