


'''simple docstring'''


from math import floor, sqrt







def     snake_case_     (						SCREAMING_SNAKE_CASE__  ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE				: str  	=   0.0
				_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   1.0
				_SCREAMING_SNAKE_CASE				: Optional[int]  	=   int(sqrt(SCREAMING_SNAKE_CASE__  )  )
				_SCREAMING_SNAKE_CASE				: Optional[int]  	=   root
				_SCREAMING_SNAKE_CASE				: List[str]  	=   0
				while integer_part != 2 * root:
								_SCREAMING_SNAKE_CASE				: int  	=   denominator * integer_part - numerator
								_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   (n - numerator**2) / denominator
								_SCREAMING_SNAKE_CASE				: List[Any]  	=   int((root + numerator) / denominator  )
								period += 1
				return period







def     snake_case_     (						SCREAMING_SNAKE_CASE__ = 1_0000  ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE				: Tuple  	=   0
				for i in range(2							,   n + 1  ):
								_SCREAMING_SNAKE_CASE				: int  	=   sqrt(SCREAMING_SNAKE_CASE__  )
								if sr - floor(SCREAMING_SNAKE_CASE__  ) != 0 and continuous_fraction_period(SCREAMING_SNAKE_CASE__  ) % 2 == 1:
												count_odd_periods += 1
				return count_odd_periods


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








'''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
#
# 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)
#
# This example also demonstrates the checkpointing and sharding capabilities
#
# 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_	:     Any							     =	16
UpperCAmelCase_	:     Dict							     =	32







def     snake_case_     (						SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__  ):







				"""simple docstring"""





				if args.with_tracking:
								_SCREAMING_SNAKE_CASE				: List[str]  	=   Accelerator(
								    cpu=args.cpu							,   mixed_precision=args.mixed_precision							,   log_with="""all"""							,   project_dir=args.project_dir  )
				else:
								_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   Accelerator(cpu=args.cpu							,   mixed_precision=args.mixed_precision  )

				if hasattr(args.checkpointing_steps							,   """isdigit"""  ):
								if args.checkpointing_steps == "epoch":
												_SCREAMING_SNAKE_CASE				: str  	=   args.checkpointing_steps
								elif args.checkpointing_steps.isdigit():
												_SCREAMING_SNAKE_CASE				: Dict  	=   int(args.checkpointing_steps  )
								else:
												raise ValueError(
												    f"""Argument `checkpointing_steps` must be either a number or `epoch`. `{args.checkpointing_steps}` passed."""  )
				else:
								_SCREAMING_SNAKE_CASE				: int  	=   None
				# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
				_SCREAMING_SNAKE_CASE				: List[str]  	=   config["""lr"""]
				_SCREAMING_SNAKE_CASE				: Tuple  	=   int(config["""num_epochs"""]  )
				_SCREAMING_SNAKE_CASE				: Dict  	=   int(config["""seed"""]  )
				_SCREAMING_SNAKE_CASE				: Tuple  	=   int(config["""batch_size"""]  )

				# We need to initialize the trackers we use, and also store our configuration
				if args.with_tracking:
								_SCREAMING_SNAKE_CASE				: List[str]  	=   os.path.split(SCREAMING_SNAKE_CASE__  )[-1].split("""."""  )[0]
								accelerator.init_trackers(SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__  )

				_SCREAMING_SNAKE_CASE				: Tuple  	=   AutoTokenizer.from_pretrained("""bert-base-cased"""  )
				_SCREAMING_SNAKE_CASE				: Dict  	=   load_dataset("""glue"""							,   """mrpc"""  )
				_SCREAMING_SNAKE_CASE				: Optional[int]  	=   evaluate.load("""glue"""							,   """mrpc"""  )

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

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

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

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

				# Instantiate dataloaders.
				_SCREAMING_SNAKE_CASE				: Dict  	=   DataLoader(
				    tokenized_datasets["""train"""]							,   shuffle=SCREAMING_SNAKE_CASE__							,   collate_fn=SCREAMING_SNAKE_CASE__							,   batch_size=SCREAMING_SNAKE_CASE__  )
				_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   DataLoader(
				    tokenized_datasets["""validation"""]							,   shuffle=SCREAMING_SNAKE_CASE__							,   collate_fn=SCREAMING_SNAKE_CASE__							,   batch_size=SCREAMING_SNAKE_CASE__  )

				set_seed(SCREAMING_SNAKE_CASE__  )

				# Instantiate the model (we build the model here so that the seed also control new weights initialization)
				_SCREAMING_SNAKE_CASE				: List[str]  	=   AutoModelForSequenceClassification.from_pretrained("""bert-base-cased"""							,   return_dict=SCREAMING_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).
				_SCREAMING_SNAKE_CASE				: Any  	=   model.to(accelerator.device  )

				# Instantiate optimizer
				_SCREAMING_SNAKE_CASE				: List[str]  	=   AdamW(params=model.parameters()							,   lr=SCREAMING_SNAKE_CASE__  )

				# Instantiate scheduler
				_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   get_linear_schedule_with_warmup(
				    optimizer=SCREAMING_SNAKE_CASE__							,   num_warmup_steps=100							,   num_training_steps=(len(SCREAMING_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.
				_SCREAMING_SNAKE_CASE	, _SCREAMING_SNAKE_CASE	, _SCREAMING_SNAKE_CASE	, _SCREAMING_SNAKE_CASE	, _SCREAMING_SNAKE_CASE				: Optional[Any]  	=   accelerator.prepare(
				    SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__  )

				# We need to keep track of how many total steps we have iterated over
				_SCREAMING_SNAKE_CASE				: Optional[int]  	=   0
				# We also need to keep track of the stating epoch so files are named properly
				_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   0

				# Potentially load in the weights and states from a previous save
				if args.resume_from_checkpoint:
								if args.resume_from_checkpoint is not None or args.resume_from_checkpoint != "":
												accelerator.print(f"""Resumed from checkpoint: {args.resume_from_checkpoint}"""  )
												accelerator.load_state(args.resume_from_checkpoint  )
												_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   os.path.basename(args.resume_from_checkpoint  )
								else:
												# Get the most recent checkpoint
												_SCREAMING_SNAKE_CASE				: int  	=   [f.name for f in os.scandir(os.getcwd()  ) if f.is_dir()]
												dirs.sort(key=os.path.getctime  )
												_SCREAMING_SNAKE_CASE				: Dict  	=   dirs[-1]  # Sorts folders by date modified, most recent checkpoint is the last
								# Extract `epoch_{i}` or `step_{i}`
								_SCREAMING_SNAKE_CASE				: str  	=   os.path.splitext(SCREAMING_SNAKE_CASE__  )[0]

								if "epoch" in training_difference:
												_SCREAMING_SNAKE_CASE				: List[Any]  	=   int(training_difference.replace("""epoch_"""							,   """"""  )  ) + 1
												_SCREAMING_SNAKE_CASE				: List[str]  	=   None
								else:
												_SCREAMING_SNAKE_CASE				: List[str]  	=   int(training_difference.replace("""step_"""							,   """"""  )  )
												_SCREAMING_SNAKE_CASE				: Any  	=   resume_step // len(SCREAMING_SNAKE_CASE__  )
												resume_step -= starting_epoch * len(SCREAMING_SNAKE_CASE__  )

    # Now we train the model
				for epoch in range(SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__  ):
								model.train()
								if args.with_tracking:
												_SCREAMING_SNAKE_CASE				: str  	=   0
								if args.resume_from_checkpoint and epoch == starting_epoch and resume_step is not None:
												# We need to skip steps until we reach the resumed step
												_SCREAMING_SNAKE_CASE				: List[str]  	=   accelerator.skip_first_batches(SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__  )
												overall_step += resume_step
								else:
												# After the first iteration though, we need to go back to the original dataloader
												_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   train_dataloader
								for step, batch in enumerate(SCREAMING_SNAKE_CASE__  ):
												# We could avoid this line since we set the accelerator with `device_placement=True`.
												batch.to(accelerator.device  )
												_SCREAMING_SNAKE_CASE				: Tuple  	=   model(**SCREAMING_SNAKE_CASE__  )
												_SCREAMING_SNAKE_CASE				: Optional[int]  	=   outputs.loss
												_SCREAMING_SNAKE_CASE				: List[Any]  	=   loss / gradient_accumulation_steps
												# We keep track of the loss at each epoch
												if args.with_tracking:
																total_loss += loss.detach().float()
												accelerator.backward(SCREAMING_SNAKE_CASE__  )
												if step % gradient_accumulation_steps == 0:
																optimizer.step()
																lr_scheduler.step()
																optimizer.zero_grad()

												overall_step += 1

												if isinstance(SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__  ):
																_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   f"""step_{overall_step}"""
																if overall_step % checkpointing_steps == 0:
																				if args.output_dir is not None:
																								_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   os.path.join(args.output_dir							,   SCREAMING_SNAKE_CASE__  )
																				accelerator.save_state(SCREAMING_SNAKE_CASE__  )

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

								_SCREAMING_SNAKE_CASE				: List[str]  	=   metric.compute()
								# Use accelerator.print to print only on the main process.
								accelerator.print(f"""epoch {epoch}:"""							,   SCREAMING_SNAKE_CASE__  )
								if args.with_tracking:
												accelerator.log(
												    {
												        """accuracy""": eval_metric["""accuracy"""],
												        """f1""": eval_metric["""f1"""],
												        """train_loss""": total_loss.item() / len(SCREAMING_SNAKE_CASE__  ),
												        """epoch""": epoch,
												    }							,   step=SCREAMING_SNAKE_CASE__							,   )

								if checkpointing_steps == "epoch":
												_SCREAMING_SNAKE_CASE				: Optional[int]  	=   f"""epoch_{epoch}"""
												if args.output_dir is not None:
																_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   os.path.join(args.output_dir							,   SCREAMING_SNAKE_CASE__  )
												accelerator.save_state(SCREAMING_SNAKE_CASE__  )

				if args.with_tracking:
								accelerator.end_training()







def     snake_case_     (						):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   argparse.ArgumentParser(description="""Simple example of training script."""  )
				parser.add_argument(
				    """--mixed_precision"""							,   type=SCREAMING_SNAKE_CASE__							,   default=SCREAMING_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."""  )
				parser.add_argument(
				    """--checkpointing_steps"""							,   type=SCREAMING_SNAKE_CASE__							,   default=SCREAMING_SNAKE_CASE__							,   help="""Whether the various states should be saved at the end of every n steps, or 'epoch' for each epoch."""							,   )
				parser.add_argument(
				    """--resume_from_checkpoint"""							,   type=SCREAMING_SNAKE_CASE__							,   default=SCREAMING_SNAKE_CASE__							,   help="""If the training should continue from a checkpoint folder."""							,   )
				parser.add_argument(
				    """--with_tracking"""							,   action="""store_true"""							,   help="""Whether to load in all available experiment trackers from the environment and use them for logging."""							,   )
				parser.add_argument(
				    """--output_dir"""							,   type=SCREAMING_SNAKE_CASE__							,   default="""."""							,   help="""Optional save directory where all checkpoint folders will be stored. Default is the current working directory."""							,   )
				parser.add_argument(
				    """--project_dir"""							,   type=SCREAMING_SNAKE_CASE__							,   default="""logs"""							,   help="""Location on where to store experiment tracking logs` and relevent project information"""							,   )
				_SCREAMING_SNAKE_CASE				: List[str]  	=   parser.parse_args()
				_SCREAMING_SNAKE_CASE				: str  	=   {"""lr""": 2E-5, """num_epochs""": 3, """seed""": 42, """batch_size""": 16}
				training_function(SCREAMING_SNAKE_CASE__							,   SCREAMING_SNAKE_CASE__  )


if __name__ == "__main__":
				main()




