



def    UpperCamelCase		(  _A					: int = 600851475143							)->  Tuple:





						"""simple docstring"""





						try:
												A__					=  int(_A							)
						except (TypeError, ValueError):
												raise TypeError("Parameter n must be int or castable to int."							)
						if n <= 0:
												raise ValueError("Parameter n must be greater than or equal to one."							)
						A__					=  2
						A__					=  0
						if n == 2:
												return 2
						while n > 2:
												while n % i != 0:
																		i += 1
												A__					=  i
												while n % i == 0:
																		A__					=  n // i
												i += 1
						return int(_A							)


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












"""simple docstring"""





import argparse
from typing import List

import evaluate
import numpy as np
import torch
from datasets import DatasetDict, load_dataset

# New Code #
# We'll be using StratifiedKFold for this example
from sklearn.model_selection import StratifiedKFold
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,
# specifically showcasing how to perform Cross Validation,
# and builds off the `nlp_example.py` script.
#
# 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 help focus on the differences in the code, building `DataLoaders`
# was refactored into its own function.
# 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					      =   16
_UpperCamelCase					      =   32



def 					lowerCAmelCase_      (   SCREAMING_SNAKE_CASE							:				Accelerator     ,    SCREAMING_SNAKE_CASE							:				DatasetDict     ,    SCREAMING_SNAKE_CASE							:				List[int]     ,    SCREAMING_SNAKE_CASE							:				List[int]     ,    SCREAMING_SNAKE_CASE							:				int = 16 ):


							'''simple docstring'''







							__lowerCamelCase   :   Union[str, Any]       =AutoTokenizer.from_pretrained('''bert-base-cased''' )
							__lowerCamelCase   :   List[str]       =DatasetDict(
							    {
							        '''train''': dataset['''train'''].select(SCREAMING_SNAKE_CASE ),
							        '''validation''': dataset['''train'''].select(SCREAMING_SNAKE_CASE ),
							        '''test''': dataset['''validation'''],
							    } )

							def tokenize_function(SCREAMING_SNAKE_CASE							:				Optional[Any] ):
														# max_length=None => use the model max length (it's actually the default)
														__lowerCamelCase   :   Optional[int]       =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():
														__lowerCamelCase   :   Optional[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
							__lowerCamelCase   :   Dict       =tokenized_datasets.rename_column('''label'''     ,    '''labels''' )

							def collate_fn(SCREAMING_SNAKE_CASE							:				List[str] ):
														# On TPU it's best to pad everything to the same length or training will be very slow.
														__lowerCamelCase   :   Tuple       =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":
																					__lowerCamelCase   :   List[str]       =16
														elif accelerator.mixed_precision != "no":
																					__lowerCamelCase   :   Tuple       =8
														else:
																					__lowerCamelCase   :   Optional[int]       =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.
							__lowerCamelCase   :   int       =DataLoader(
							    tokenized_datasets['''train''']     ,    shuffle=SCREAMING_SNAKE_CASE     ,    collate_fn=SCREAMING_SNAKE_CASE     ,    batch_size=SCREAMING_SNAKE_CASE )
							__lowerCamelCase   :   Optional[Any]       =DataLoader(
							    tokenized_datasets['''validation''']     ,    shuffle=SCREAMING_SNAKE_CASE     ,    collate_fn=SCREAMING_SNAKE_CASE     ,    batch_size=SCREAMING_SNAKE_CASE )

							__lowerCamelCase   :   Tuple       =DataLoader(
							    tokenized_datasets['''test''']     ,    shuffle=SCREAMING_SNAKE_CASE     ,    collate_fn=SCREAMING_SNAKE_CASE     ,    batch_size=SCREAMING_SNAKE_CASE )

							return train_dataloader, eval_dataloader, test_dataloader



def 					lowerCAmelCase_      (   SCREAMING_SNAKE_CASE							:				Any     ,    SCREAMING_SNAKE_CASE							:				List[Any] ):


							'''simple docstring'''







							__lowerCamelCase   :   Optional[Any]       =[]
							# Download the dataset
							__lowerCamelCase   :   Any       =load_dataset('''glue'''     ,    '''mrpc''' )
							# Create our splits
							__lowerCamelCase   :   Optional[Any]       =StratifiedKFold(n_splits=int(args.num_folds ) )
							# Initialize accelerator
							__lowerCamelCase   :   str       =Accelerator(cpu=args.cpu     ,    mixed_precision=args.mixed_precision )
							# Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
							__lowerCamelCase   :   Any       =config['''lr''']
							__lowerCamelCase   :   int       =int(config['''num_epochs'''] )
							__lowerCamelCase   :   Optional[int]       =int(config['''seed'''] )
							__lowerCamelCase   :   Any       =int(config['''batch_size'''] )

							__lowerCamelCase   :   List[str]       =evaluate.load('''glue'''     ,    '''mrpc''' )

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

							set_seed(SCREAMING_SNAKE_CASE )

							# New Code #
							# Create our folds:
							__lowerCamelCase   :   str       =kfold.split(np.zeros(datasets['''train'''].num_rows )     ,    datasets['''train''']['''label'''] )
							__lowerCamelCase   :   Tuple       =[]
							# Iterate over them
							for i, (train_idxs, valid_idxs) in enumerate(SCREAMING_SNAKE_CASE ):
														__lowerCamelCase     ,    __lowerCamelCase     ,    __lowerCamelCase   :   Any       =get_fold_dataloaders(
														    SCREAMING_SNAKE_CASE     ,    SCREAMING_SNAKE_CASE     ,    SCREAMING_SNAKE_CASE     ,    SCREAMING_SNAKE_CASE     ,    )
														# Instantiate the model (we build the model here so that the seed also control new weights initialization)
														__lowerCamelCase   :   Optional[int]       =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).
														__lowerCamelCase   :   Optional[Any]       =model.to(accelerator.device )

														# Instantiate optimizer
														__lowerCamelCase   :   Any       =AdamW(params=model.parameters()     ,    lr=SCREAMING_SNAKE_CASE )

														# Instantiate scheduler
														__lowerCamelCase   :   Dict       =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.
														__lowerCamelCase     ,    __lowerCamelCase     ,    __lowerCamelCase     ,    __lowerCamelCase     ,    __lowerCamelCase   :   Any       =accelerator.prepare(
														    SCREAMING_SNAKE_CASE     ,    SCREAMING_SNAKE_CASE     ,    SCREAMING_SNAKE_CASE     ,    SCREAMING_SNAKE_CASE     ,    SCREAMING_SNAKE_CASE )

														# Now we train the model
														for epoch in range(SCREAMING_SNAKE_CASE ):
																					model.train()
																					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 )
																												__lowerCamelCase   :   Dict       =model(**SCREAMING_SNAKE_CASE )
																												__lowerCamelCase   :   Optional[Any]       =outputs.loss
																												__lowerCamelCase   :   int       =loss / gradient_accumulation_steps
																												accelerator.backward(SCREAMING_SNAKE_CASE )
																												if step % gradient_accumulation_steps == 0:
																																			optimizer.step()
																																			lr_scheduler.step()
																																			optimizer.zero_grad()

																					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():
																																			__lowerCamelCase   :   Optional[int]       =model(**SCREAMING_SNAKE_CASE )
																												__lowerCamelCase   :   int       =outputs.logits.argmax(dim=-1 )
																												__lowerCamelCase     ,    __lowerCamelCase   :   Union[str, Any]       =accelerator.gather_for_metrics((predictions, batch['''labels''']) )
																												metric.add_batch(
																												    predictions=SCREAMING_SNAKE_CASE     ,    references=SCREAMING_SNAKE_CASE     ,    )

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

														# New Code #
														# We also run predictions on the test set at the very end
														__lowerCamelCase   :   Tuple       =[]
														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():
																												__lowerCamelCase   :   List[Any]       =model(**SCREAMING_SNAKE_CASE )
																					__lowerCamelCase   :   int       =outputs.logits
																					__lowerCamelCase     ,    __lowerCamelCase   :   Union[str, Any]       =accelerator.gather_for_metrics((predictions, batch['''labels''']) )
																					fold_predictions.append(predictions.cpu() )
																					if i == 0:
																												# We need all of the test predictions
																												test_references.append(references.cpu() )
        # Use accelerator.print to print only on the main process.
														test_predictions.append(torch.cat(SCREAMING_SNAKE_CASE     ,    dim=0 ) )
														# We now need to release all our memory and get rid of the current model, optimizer, etc
														accelerator.free_memory()
							# New Code #
							# Finally we check the accuracy of our folded results:
							__lowerCamelCase   :   Optional[Any]       =torch.cat(SCREAMING_SNAKE_CASE     ,    dim=0 )
							__lowerCamelCase   :   int       =torch.stack(SCREAMING_SNAKE_CASE     ,    dim=0 ).sum(dim=0 ).div(int(args.num_folds ) ).argmax(dim=-1 )
							__lowerCamelCase   :   Tuple       =metric.compute(predictions=SCREAMING_SNAKE_CASE     ,    references=SCREAMING_SNAKE_CASE )
							accelerator.print('''Average test metrics from all folds:'''     ,    SCREAMING_SNAKE_CASE )



def 					lowerCAmelCase_      (   ):


							'''simple docstring'''







							__lowerCamelCase   :   int       =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.''' )
							# New Code #
							parser.add_argument('''--num_folds'''     ,    type=SCREAMING_SNAKE_CASE     ,    default=3     ,    help='''The number of splits to perform across the dataset''' )
							__lowerCamelCase   :   Any       =parser.parse_args()
							__lowerCamelCase   :   Optional[int]       ={'''lr''': 2E-5, '''num_epochs''': 3, '''seed''': 42, '''batch_size''': 16}
							training_function(SCREAMING_SNAKE_CASE     ,    SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
							main()




