"""simple docstring"""


# Copyright 2021 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.


import warnings
from typing import List
from unittest.mock import Mock

import torch
from torch.utils.data import DataLoader, IterableDataset, TensorDataset

from accelerate.accelerator import Accelerator
from accelerate.utils.dataclasses import DistributedType




class  UpperCamelCase					(				lowerCAmelCase__   ):







       def __init__( self,							lowerCAmelCase__)      ->      str:
            snake_case_					       =					data







       def __iter__( self)      ->      List[Any]:
            for element in self.data:
                 yield element







def 					UpperCAmelCase    (		UpperCAmelCase=True					)				->      int:
     snake_case_					       =					Accelerator(even_batches=UpperCAmelCase					)
     assert accelerator.num_processes == 2, "this script expects that two GPUs are available"
     return accelerator







def 					UpperCAmelCase    (		UpperCAmelCase						,					UpperCAmelCase						,					UpperCAmelCase						,					UpperCAmelCase = False					)				->      List[str]:
     if iterable:
          snake_case_					       =					DummyIterableDataset(torch.as_tensor(range(UpperCAmelCase					)					)					)
     else:
          snake_case_					       =					TensorDataset(torch.as_tensor(range(UpperCAmelCase					)					)					)

     snake_case_					       =					DataLoader(UpperCAmelCase						,					batch_size=UpperCAmelCase					)
     snake_case_					       =					accelerator.prepare(UpperCAmelCase					)

     return dl







def 					UpperCAmelCase    (		UpperCAmelCase						,					UpperCAmelCase						,					UpperCAmelCase						,					UpperCAmelCase						,					UpperCAmelCase						,					)				->      Union[str, Any]:
     snake_case_					       =					create_dataloader(accelerator=UpperCAmelCase						,					dataset_size=UpperCAmelCase						,					batch_size=UpperCAmelCase					)

     snake_case_					       =					[len(batch[0]					) for batch in dl]

     if accelerator.process_index == 0:
          assert batch_sizes == process_0_expected_batch_sizes
     elif accelerator.process_index == 1:
          assert batch_sizes == process_1_expected_batch_sizes







def 					UpperCAmelCase    (		)				->      Tuple:
     snake_case_					       =					create_accelerator()

     # without padding, we would expect a different number of batches
     verify_dataloader_batch_sizes(
         UpperCAmelCase						,					dataset_size=3						,					batch_size=1						,					process_0_expected_batch_sizes=[1, 1]						,					process_1_expected_batch_sizes=[1, 1]						,					)

     # without padding, we would expect the same number of batches, but different sizes
     verify_dataloader_batch_sizes(
         UpperCAmelCase						,					dataset_size=7						,					batch_size=2						,					process_0_expected_batch_sizes=[2, 2]						,					process_1_expected_batch_sizes=[2, 2]						,					)







def 					UpperCAmelCase    (		)				->      str:
     snake_case_					       =					create_accelerator(even_batches=UpperCAmelCase					)

     verify_dataloader_batch_sizes(
         UpperCAmelCase						,					dataset_size=3						,					batch_size=1						,					process_0_expected_batch_sizes=[1, 1]						,					process_1_expected_batch_sizes=[1]						,					)

     verify_dataloader_batch_sizes(
         UpperCAmelCase						,					dataset_size=7						,					batch_size=2						,					process_0_expected_batch_sizes=[2, 2]						,					process_1_expected_batch_sizes=[2, 1]						,					)







def 					UpperCAmelCase    (		)				->      int:
     snake_case_					       =					create_accelerator(even_batches=UpperCAmelCase					)

     snake_case_					       =					torch.nn.Linear(1						,					1					)
     snake_case_					       =					accelerator.prepare(UpperCAmelCase					)

     snake_case_					       =					create_dataloader(UpperCAmelCase						,					dataset_size=3						,					batch_size=1					)

     snake_case_					       =					[]
     with accelerator.join_uneven_inputs([ddp_model]					):
          for batch_idx, batch in enumerate(UpperCAmelCase					):
               snake_case_					       =					ddp_model(batch[0].float()					)
               snake_case_					       =					output.sum()
               loss.backward()
               batch_idxs.append(UpperCAmelCase					)

     accelerator.wait_for_everyone()

     if accelerator.process_index == 0:
          assert batch_idxs == [0, 1]
     elif accelerator.process_index == 1:
          assert batch_idxs == [0]







def 					UpperCAmelCase    (		UpperCAmelCase					)				->      Any:
     with warnings.catch_warnings(record=UpperCAmelCase					) as w:
          with accelerator.join_uneven_inputs([Mock()]					):
               pass

          assert issubclass(w[-1].category						,					UpperCAmelCase					)
          assert "only supported for multi-GPU" in str(w[-1].message					)







def 					UpperCAmelCase    (		)				->      Optional[int]:
     snake_case_					       =					True
     snake_case_					       =					False
     snake_case_					       =					create_accelerator(even_batches=UpperCAmelCase					)
     snake_case_					       =					torch.nn.Linear(1						,					1					)
     snake_case_					       =					accelerator.prepare(UpperCAmelCase					)
     snake_case_					       =					create_dataloader(UpperCAmelCase						,					dataset_size=3						,					batch_size=1					)
     snake_case_					       =					create_dataloader(UpperCAmelCase						,					dataset_size=3						,					batch_size=1					)

     with accelerator.join_uneven_inputs([ddp_model]						,					even_batches=UpperCAmelCase					):
          snake_case_					       =					train_dl.batch_sampler.even_batches
          snake_case_					       =					valid_dl.batch_sampler.even_batches

     assert train_dl_overridden_value == overridden_even_batches
     assert valid_dl_overridden_value == overridden_even_batches
     assert train_dl.batch_sampler.even_batches == default_even_batches
     assert valid_dl.batch_sampler.even_batches == default_even_batches







def 					UpperCAmelCase    (		)				->      int:
     snake_case_					       =					True
     snake_case_					       =					False
     snake_case_					       =					create_accelerator(even_batches=UpperCAmelCase					)
     snake_case_					       =					torch.nn.Linear(1						,					1					)
     snake_case_					       =					accelerator.prepare(UpperCAmelCase					)
     create_dataloader(UpperCAmelCase						,					dataset_size=3						,					batch_size=1						,					iterable=UpperCAmelCase					)
     snake_case_					       =					create_dataloader(UpperCAmelCase						,					dataset_size=3						,					batch_size=1					)

     with warnings.catch_warnings():
          warnings.filterwarnings('ignore'					)
          try:
               with accelerator.join_uneven_inputs([ddp_model]						,					even_batches=UpperCAmelCase					):
                    snake_case_					       =					batch_dl.batch_sampler.even_batches
          except AttributeError:
               # ensure attribute error is not raised when processing iterable dl
               raise AssertionError

     assert batch_dl_overridden_value == overridden_even_batches
     assert batch_dl.batch_sampler.even_batches == default_even_batches







def 					UpperCAmelCase    (		)				->      Any:
     snake_case_					       =					create_accelerator()
     snake_case_					       =					torch.nn.Linear(1						,					1					)
     snake_case_					       =					accelerator.prepare(UpperCAmelCase					)
     create_dataloader(UpperCAmelCase						,					dataset_size=3						,					batch_size=1						,					iterable=UpperCAmelCase					)

     with warnings.catch_warnings(record=UpperCAmelCase					) as w:
          with accelerator.join_uneven_inputs([ddp_model]						,					even_batches=UpperCAmelCase					):
               pass

          assert issubclass(w[-1].category						,					UpperCAmelCase					)
          assert "only supported for map-style datasets" in str(w[-1].message					)







def 					UpperCAmelCase    (		)				->      Optional[int]:
     snake_case_					       =					create_accelerator()

     accelerator.print('Test that even_batches variable ensures uniform batches across processes'					)
     test_default_ensures_even_batch_sizes()

     accelerator.print('Run tests with even_batches disabled'					)
     test_can_disable_even_batches()

     accelerator.print('Test joining uneven inputs'					)
     test_can_join_uneven_inputs()

     accelerator.print('Test overriding even_batches when joining uneven inputs'					)
     test_join_can_override_even_batches()

     accelerator.print('Test overriding even_batches for mixed dataloader types'					)
     test_join_can_override_for_mixed_type_dataloaders()

     accelerator.print('Test overriding even_batches raises a warning for iterable dataloaders'					)
     test_join_raises_warning_for_iterable_when_overriding_even_batches()

     accelerator.print('Test join with non DDP distributed raises warning'					)
     snake_case_					       =					accelerator.state.distributed_type
     snake_case_					       =					DistributedType.FSDP
     test_join_raises_warning_for_non_ddp_distributed(UpperCAmelCase					)
     snake_case_					       =					original_state


if __name__ == "__main__":
    main()









import math
def 						_a    (      a :int )							->			list:
 a		  =      [True] * n
 a		  =      False
 a		  =      False
 a		  =      True

 for i in range(3	,							int(n**0.5 + 1 )	,							2 ):
  a		  =      i * 2
  while index < n:
   a		  =      False
   a		  =      index + i

 a		  =      [2]

 for i in range(3	,							a	,							2 ):
  if is_prime[i]:
   primes.append(a )

 return primes
def 						_a    (      a :int = 999_966_663_333 )							->			int:
 a		  =      math.floor(math.sqrt(a ) ) + 100
 a		  =      prime_sieve(a )

 a		  =      0
 a		  =      0
 a		  =      primes[prime_index]

 while (last_prime**2) <= limit:
  a		  =      primes[prime_index + 1]

  a		  =      last_prime**2
  a		  =      next_prime**2

  # Get numbers divisible by lps(current)
  a		  =      lower_bound + last_prime
  while upper_bound > current <= limit:
   matches_sum += current
   current += last_prime

  # Reset the upper_bound
  while (upper_bound - next_prime) > limit:
   upper_bound -= next_prime

  # Add the numbers divisible by ups(current)
  a		  =      upper_bound - next_prime
  while current > lower_bound:
   matches_sum += current
   current -= next_prime

  # Remove the numbers divisible by both ups and lps
  a		  =      0
  while upper_bound > current <= limit:
   if current <= lower_bound:
    # Increment the current number
    current += last_prime * next_prime
    continue

   if current > limit:
    break

   # Remove twice since it was added by both ups and lps
   matches_sum -= current * 2

   # Increment the current number
   current += last_prime * next_prime

  # Setup for next pair
  a		  =      next_prime
  prime_index += 1

 return matches_sum


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


