

"""simple docstring"""

import math
from itertools import permutations





def 					__UpperCamelCase (     a__:			int      )					->      bool:




					"""simple docstring"""



					if 1 < number < 4:
										# 2 and 3 are primes
										return True
					elif number < 2 or number % 2 == 0 or number % 3 == 0:
										# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
										return False

					# All primes number are in format of 6k +/- 1
					for i in range(5			,						int(math.sqrt(a__      ) + 1      )			,						6      ):
										if number % i == 0 or number % (i + 2) == 0:
															return False
					return True





def 					__UpperCamelCase (     a__:			Union[str, Any]			,						a__:			str      )					->      bool:




					"""simple docstring"""



					__lowercase        =      0, len(a__      ) - 1
					while left <= right:
										__lowercase        =      (left + right) // 2
										if prime_list[middle] == target:
															return True
										elif prime_list[middle] < target:
															__lowercase        =      middle + 1
										else:
															__lowercase        =      middle - 1

					return False





def 					__UpperCamelCase (     )					->      Optional[int]:




					"""simple docstring"""



					__lowercase        =      [n for n in range(10_01			,						1_00_00			,						2      ) if is_prime(a__      )]
					__lowercase        =      []

					for number in prime_list:
										__lowercase        =      []

										for prime_member in permutations(list(str(a__      )      )      ):
															__lowercase        =      int(''''''.join(a__      )      )

															if prime % 2 == 0:
																				continue

															if search(a__			,						a__      ):
																				tmp_numbers.append(a__      )

										tmp_numbers.sort()
										if len(a__      ) >= 3:
															candidates.append(a__      )

					__lowercase        =      []
					for candidate in candidates:
										__lowercase        =      len(a__      )
										__lowercase        =      False

										for i in range(a__      ):
															for j in range(i + 1			,						a__      ):
																				for k in range(j + 1			,						a__      ):
																									if (
																									    abs(candidate[i] - candidate[j]      )
																									    == abs(candidate[j] - candidate[k]      )
																									    and len({candidate[i], candidate[j], candidate[k]}      ) == 3
																									):
																														passed.append(
																														    sorted([candidate[i], candidate[j], candidate[k]]      )      )
																														__lowercase        =      True

																									if found:
																														break
																				if found:
																									break
															if found:
																				break

					__lowercase        =      set()
					for seq in passed:
										answer.add(''''''.join([str(a__      ) for i in seq]      )      )

					return max(int(a__      ) for x in answer      )


if __name__ == "__main__":
							print(solution())








'''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,
# specifically showcasing the checkpointing capability,
# 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
#
########################################################################

lowercase						:   Optional[int]      						=							16
lowercase						:   str      						=							32




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






       '''simple docstring'''




       lowercase	:		List[Any]    =   AutoTokenizer.from_pretrained('''bert-base-cased'''   )
       lowercase	:		List[Any]    =   load_dataset('''glue''' ,					'''mrpc'''   )

       def tokenize_function(lowerCamelCase   ):
              # max_length=None => use the model max length (it's actually the default)
              lowercase	:		Any    =   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():
              lowercase	:		Any    =   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
       lowercase	:		List[str]    =   tokenized_datasets.rename_column('''label''' ,					'''labels'''   )

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

              return tokenizer.pad(
                  lowerCamelCase ,					padding='''longest''' ,					max_length=lowerCamelCase ,					pad_to_multiple_of=lowerCamelCase ,					return_tensors='''pt''' ,					)

       # Instantiate dataloaders.
       lowercase	:		Optional[Any]    =   DataLoader(
           tokenized_datasets['''train'''] ,					shuffle=lowerCamelCase ,					collate_fn=lowerCamelCase ,					batch_size=lowerCamelCase   )
       lowercase	:		Optional[Any]    =   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

      lowercase						:   str      						=							mocked_dataloaders  # noqa: F811




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






       '''simple docstring'''




       if os.environ.get('''TESTING_MOCKED_DATALOADERS''' ,					lowerCamelCase   ) == "1":
              lowercase	:		Optional[int]    =   2
       # Initialize accelerator
       lowercase	:		Optional[Any]    =   Accelerator(cpu=args.cpu ,					mixed_precision=args.mixed_precision   )
       # Sample hyper-parameters for learning rate, batch size, seed and a few other HPs
       lowercase	:		int    =   config['''lr''']
       lowercase	:		int    =   int(config['''num_epochs''']   )
       lowercase	:		Tuple    =   int(config['''seed''']   )
       lowercase	:		Union[str, Any]    =   int(config['''batch_size''']   )

       # New Code #
       # Parse out whether we are saving every epoch or after a certain number of batches
       if hasattr(args.checkpointing_steps ,					'''isdigit'''   ):
              if args.checkpointing_steps == "epoch":
                     lowercase	:		Any    =   args.checkpointing_steps
              elif args.checkpointing_steps.isdigit():
                     lowercase	:		List[Any]    =   int(args.checkpointing_steps   )
              else:
                     raise ValueError(
                         f"""Argument `checkpointing_steps` must be either a number or `epoch`. `{args.checkpointing_steps}` passed."""   )
       else:
              lowercase	:		Any    =   None

       set_seed(lowerCamelCase   )

       lowercase,  lowercase	:		List[str]    =   get_dataloaders(lowerCamelCase ,					lowerCamelCase   )
       lowercase	:		List[Any]    =   evaluate.load('''glue''' ,					'''mrpc'''   )

       # If the batch size is too big we use gradient accumulation
       lowercase	:		int    =   1
       if batch_size > MAX_GPU_BATCH_SIZE and accelerator.distributed_type != DistributedType.TPU:
              lowercase	:		Dict    =   batch_size // MAX_GPU_BATCH_SIZE
              lowercase	:		Tuple    =   MAX_GPU_BATCH_SIZE

       # Instantiate the model (we build the model here so that the seed also control new weights initialization)
       lowercase	:		Dict    =   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).
       lowercase	:		List[Any]    =   model.to(accelerator.device   )

       # Instantiate optimizer
       lowercase	:		List[Any]    =   AdamW(params=model.parameters() ,					lr=lowerCamelCase   )

       # Instantiate scheduler
       lowercase	:		Tuple    =   get_linear_schedule_with_warmup(
           optimizer=lowerCamelCase ,					num_warmup_steps=100 ,					num_training_steps=(len(lowerCamelCase   ) * 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	:		Union[str, Any]    =   accelerator.prepare(
           lowerCamelCase ,					lowerCamelCase ,					lowerCamelCase ,					lowerCamelCase ,					lowerCamelCase   )

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

       # We need to load the checkpoint back in before training here with `load_state`
       # The total number of epochs is adjusted based on where the state is being loaded from,
       # as we assume continuation of the same training script
       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   )
                     lowercase	:		Optional[Any]    =   os.path.basename(args.resume_from_checkpoint   )
              else:
                     # Get the most recent checkpoint
                     lowercase	:		Optional[Any]    =   [f.name for f in os.scandir(os.getcwd()   ) if f.is_dir()]
                     dirs.sort(key=os.path.getctime   )
                     lowercase	:		Any    =   dirs[-1]  # Sorts folders by date modified, most recent checkpoint is the last
              # Extract `epoch_{i}` or `step_{i}`
              lowercase	:		Any    =   os.path.splitext(lowerCamelCase   )[0]

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

    # Now we train the model
       for epoch in range(lowerCamelCase ,					lowerCamelCase   ):
              model.train()
              # New Code #
              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
                     lowercase	:		Dict    =   accelerator.skip_first_batches(lowerCamelCase ,					lowerCamelCase   )
                     overall_step += resume_step
              else:
                     # After the first iteration though, we need to go back to the original dataloader
                     lowercase	:		Tuple    =   train_dataloader
              for step, batch in enumerate(lowerCamelCase   ):
                     # We could avoid this line since we set the accelerator with `device_placement=True`.
                     batch.to(accelerator.device   )
                     lowercase	:		Dict    =   model(**lowerCamelCase   )
                     lowercase	:		Any    =   outputs.loss
                     lowercase	:		Dict    =   loss / gradient_accumulation_steps
                     accelerator.backward(lowerCamelCase   )
                     if step % gradient_accumulation_steps == 0:
                            optimizer.step()
                            lr_scheduler.step()
                            optimizer.zero_grad()
                     # New Code #
                     overall_step += 1

                     # New Code #
                     # We save the model, optimizer, lr_scheduler, and seed states by calling `save_state`
                     # These are saved to folders named `step_{overall_step}`
                     # Will contain files: "pytorch_model.bin", "optimizer.bin", "scheduler.bin", and "random_states.pkl"
                     # If mixed precision was used, will also save a "scalar.bin" file
                     if isinstance(lowerCamelCase ,					lowerCamelCase   ):
                            lowercase	:		str    =   f"""step_{overall_step}"""
                            if overall_step % checkpointing_steps == 0:
                                   if args.output_dir is not None:
                                          lowercase	:		List[str]    =   os.path.join(args.output_dir ,					lowerCamelCase   )
                                   accelerator.save_state(lowerCamelCase   )

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

              lowercase	:		List[Any]    =   metric.compute()
              # Use accelerator.print to print only on the main process.
              accelerator.print(f"""epoch {epoch}:""" ,					lowerCamelCase   )

              # New Code #
              # We save the model, optimizer, lr_scheduler, and seed states by calling `save_state`
              # These are saved to folders named `epoch_{epoch}`
              # Will contain files: "pytorch_model.bin", "optimizer.bin", "scheduler.bin", and "random_states.pkl"
              # If mixed precision was used, will also save a "scalar.bin" file
              if checkpointing_steps == "epoch":
                     lowercase	:		List[str]    =   f"""epoch_{epoch}"""
                     if args.output_dir is not None:
                            lowercase	:		Any    =   os.path.join(args.output_dir ,					lowerCamelCase   )
                     accelerator.save_state(lowerCamelCase   )




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






       '''simple docstring'''




       lowercase	:		Union[str, Any]    =   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.'''   )
       parser.add_argument(
           '''--checkpointing_steps''' ,					type=lowerCamelCase ,					default=lowerCamelCase ,					help='''Whether the various states should be saved at the end of every n steps, or \'epoch\' for each epoch.''' ,					)
       parser.add_argument(
           '''--output_dir''' ,					type=lowerCamelCase ,					default='''.''' ,					help='''Optional save directory where all checkpoint folders will be stored. Default is the current working directory.''' ,					)
       parser.add_argument(
           '''--resume_from_checkpoint''' ,					type=lowerCamelCase ,					default=lowerCamelCase ,					help='''If the training should continue from a checkpoint folder.''' ,					)
       lowercase	:		List[Any]    =   parser.parse_args()
       lowercase	:		Optional[Any]    =   {'''lr''': 2E-5, '''num_epochs''': 3, '''seed''': 42, '''batch_size''': 16}
       training_function(lowerCamelCase ,					lowerCamelCase   )


if __name__ == "__main__":
      main()




