






from copy import deepcopy

import torch
import torch.nn.functional as F
from torch.optim import AdamW
from torch.optim.lr_scheduler import LambdaLR
from torch.utils.data import DataLoader

from accelerate.accelerator import Accelerator
from accelerate.state import GradientState
from accelerate.test_utils import RegressionDataset, RegressionModel
from accelerate.utils import DistributedType, is_torch_version, set_seed






def 							lowerCamelCase__ (       __lowerCamelCase     :	Tuple    ,						__lowerCamelCase     :	Dict    ,						__lowerCamelCase     :	int    ,						__lowerCamelCase     :	Any						):
  for param, grad_param in zip(model_a.parameters()    ,						model_b.parameters()						):
    if not param.requires_grad:
      continue
    if not did_step:
      # Grads should not be in sync
      assert (
          torch.allclose(param.grad    ,						grad_param.grad						) is False
      ), f"""Gradients in sync when they should not be at iteration {iteration}:\nmodel_a grad ({param.grad}) == model_b grad ({grad_param.grad})"""
    else:
      # Grads should be in sync
      assert (
          torch.allclose(param.grad    ,						grad_param.grad						) is True
      ), f"""Gradients not in sync when they should be at iteration {iteration}:\nmodel_a grad ({param.grad}) != model_b grad ({grad_param.grad})"""






def 							lowerCamelCase__ (       __lowerCamelCase     :	List[Any]    ,						__lowerCamelCase     :	Any    ,						__lowerCamelCase     :	Dict    ,						__lowerCamelCase     :	Optional[Any]    ,						__lowerCamelCase     :	Union[str, Any]=True						):
  model.train()
  __UpperCAmelCase				:      Tuple	 =    model(__lowerCamelCase						)
  __UpperCAmelCase				:      Optional[int]	 =    F.mse_loss(__lowerCamelCase    ,						target.to(output.device						)						)
  if not do_backward:
    loss /= accelerator.gradient_accumulation_steps
    loss.backward()
  else:
    accelerator.backward(__lowerCamelCase						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	Union[str, Any]    ,						__lowerCamelCase     :	str=False						):
  set_seed(42						)
  __UpperCAmelCase				:      Optional[int]	 =    RegressionModel()
  __UpperCAmelCase				:      Tuple	 =    deepcopy(__lowerCamelCase						)
  __UpperCAmelCase				:      Tuple	 =    RegressionDataset(length=80						)
  __UpperCAmelCase				:      Dict	 =    DataLoader(__lowerCamelCase    ,						batch_size=16						)
  model.to(accelerator.device						)
  if sched:
    __UpperCAmelCase				:      Optional[Any]	 =    AdamW(params=model.parameters()    ,						lr=1E-3						)
    __UpperCAmelCase				:      Union[str, Any]	 =    AdamW(params=ddp_model.parameters()    ,						lr=1E-3						)
    __UpperCAmelCase				:      Any	 =    LambdaLR(__lowerCamelCase    ,						lr_lambda=lambda __lowerCamelCase						: epoch**0.6_5						)
    __UpperCAmelCase				:      str	 =    LambdaLR(__lowerCamelCase    ,						lr_lambda=lambda __lowerCamelCase						: epoch**0.6_5						)
  # Make a copy of `model`
  if sched:
    __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				:      Optional[Any]	 =    accelerator.prepare(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
  else:
    __UpperCAmelCase ,					__UpperCAmelCase				:      Tuple	 =    accelerator.prepare(__lowerCamelCase    ,						__lowerCamelCase						)
  if sched:
    return (model, opt, sched, dataloader, ddp_model, ddp_opt, ddp_sched)
  return model, ddp_model, dataloader






def 							lowerCamelCase__ (       __lowerCamelCase     :	Optional[int]						):
  # Test when on a single CPU or GPU that the context manager does nothing
  __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				:      Optional[int]	 =    get_training_setup(__lowerCamelCase						)
  # Use a single batch
  __UpperCAmelCase ,					__UpperCAmelCase				:      Optional[Any]	 =    next(iter(__lowerCamelCase						)						).values()
  for iteration in range(3						):
    # Gather the distributed inputs and targs for the base model
    __UpperCAmelCase ,					__UpperCAmelCase				:      Tuple	 =    accelerator.gather((ddp_input, ddp_target)						)
    __UpperCAmelCase ,					__UpperCAmelCase				:      Any	 =    input.to(accelerator.device						), target.to(accelerator.device						)
    # Perform our initial ground truth step in non "DDP"
    step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
    # Do "gradient accumulation" (noop)
    if iteration % 2 == 0:
      # Accumulate grads locally
      with accelerator.no_sync(__lowerCamelCase						):
        step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
    else:
      # Sync grads
      step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)

    # Since `no_sync` is a noop, `ddp_model` and `model` grads should always be in sync
    check_model_parameters(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
    for param, ddp_param in zip(model.parameters()    ,						ddp_model.parameters()						):
      if not param.requires_grad:
        continue
      assert torch.allclose(
          param.grad    ,						ddp_param.grad						), f"""Gradients not in sync when they should be:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"""

    # Shuffle ddp_input on each iteration
    torch.manual_seed(1337 + iteration						)
    __UpperCAmelCase				:      Optional[Any]	 =    ddp_input[torch.randperm(len(__lowerCamelCase						)						)]






def 							lowerCamelCase__ (       __lowerCamelCase     :	Any						):
  # Test on distributed setup that context manager behaves properly
  __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				:      List[str]	 =    get_training_setup(__lowerCamelCase						)
  # Use a single batch
  __UpperCAmelCase ,					__UpperCAmelCase				:      Union[str, Any]	 =    next(iter(__lowerCamelCase						)						).values()
  for iteration in range(3						):
    # Gather the distributed inputs and targs for the base model
    __UpperCAmelCase ,					__UpperCAmelCase				:      Tuple	 =    accelerator.gather((ddp_input, ddp_target)						)
    __UpperCAmelCase ,					__UpperCAmelCase				:      Tuple	 =    input.to(accelerator.device						), target.to(accelerator.device						)
    # Perform our initial ground truth step in non "DDP"
    step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
    # Do "gradient accumulation" (noop)
    if iteration % 2 == 0:
      # Accumulate grads locally
      with accelerator.no_sync(__lowerCamelCase						):
        step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
    else:
      # Sync grads
      step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)

    # DDP model and model should only be in sync when not (iteration % 2 == 0)
    for param, ddp_param in zip(model.parameters()    ,						ddp_model.parameters()						):
      if not param.requires_grad:
        continue
      if iteration % 2 == 0:
        # Grads should not be in sync
        assert (
            torch.allclose(param.grad    ,						ddp_param.grad						) is False
        ), f"""Gradients in sync when they should not be:\nModel grad ({param.grad}) == DDP grad ({ddp_param.grad})"""
      else:
        # Grads should be in sync
        assert (
            torch.allclose(param.grad    ,						ddp_param.grad						) is True
        ), f"""Gradients not in sync when they should be:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"""

        # Shuffle ddp_input on each iteration
    torch.manual_seed(1337 + iteration						)
    __UpperCAmelCase				:      str	 =    ddp_input[torch.randperm(len(__lowerCamelCase						)						)]






def 							lowerCamelCase__ (       __lowerCamelCase     :	Dict=False    ,						__lowerCamelCase     :	List[Any]=False						):
  __UpperCAmelCase				:      Tuple	 =    Accelerator(
      split_batches=__lowerCamelCase    ,						dispatch_batches=__lowerCamelCase    ,						gradient_accumulation_steps=2						)
  # Test that context manager behaves properly
  __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				:      str	 =    get_training_setup(__lowerCamelCase						)
  for iteration, batch in enumerate(__lowerCamelCase						):
    __UpperCAmelCase ,					__UpperCAmelCase				:      List[str]	 =    batch.values()
    # Gather the distributed inputs and targs for the base model
    __UpperCAmelCase ,					__UpperCAmelCase				:      List[str]	 =    accelerator.gather((ddp_input, ddp_target)						)
    __UpperCAmelCase ,					__UpperCAmelCase				:      List[str]	 =    input.to(accelerator.device						), target.to(accelerator.device						)
    # Perform our initial ground truth step in non "DDP"
    step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
    # Do "gradient accumulation" (noop)
    with accelerator.accumulate(__lowerCamelCase						):
      step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)

    # DDP model and model should only be in sync when not (iteration % 2 == 0)
    for param, ddp_param in zip(model.parameters()    ,						ddp_model.parameters()						):
      if not param.requires_grad:
        continue
      if ((iteration + 1) % 2 == 0) or (iteration == len(__lowerCamelCase						) - 1):
        # Grads should be in sync
        assert (
            torch.allclose(param.grad    ,						ddp_param.grad						) is True
        ), f"""Gradients not in sync when they should be at iteration {iteration}:\nModel grad ({param.grad}) != DDP grad ({ddp_param.grad})"""
      else:
        # Grads should not be in sync
        assert (
            torch.allclose(param.grad    ,						ddp_param.grad						) is False
        ), f"""Gradients in sync when they should not be at iteration {iteration}:\nModel grad ({param.grad}) == DDP grad ({ddp_param.grad})"""

        # Shuffle ddp_input on each iteration
    torch.manual_seed(1337 + iteration						)
    __UpperCAmelCase				:      Dict	 =    ddp_input[torch.randperm(len(__lowerCamelCase						)						)]
  GradientState._reset_state()






def 							lowerCamelCase__ (       __lowerCamelCase     :	List[str]=False    ,						__lowerCamelCase     :	Union[str, Any]=False						):
  __UpperCAmelCase				:      Optional[int]	 =    Accelerator(
      split_batches=__lowerCamelCase    ,						dispatch_batches=__lowerCamelCase    ,						gradient_accumulation_steps=2						)
  # Test that context manager behaves properly
  __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				:      Union[str, Any]	 =    get_training_setup(__lowerCamelCase    ,						__lowerCamelCase						)
  for iteration, batch in enumerate(__lowerCamelCase						):
    __UpperCAmelCase ,					__UpperCAmelCase				:      str	 =    batch.values()
    # Gather the distributed inputs and targs for the base model
    __UpperCAmelCase ,					__UpperCAmelCase				:      Optional[Any]	 =    accelerator.gather((ddp_input, ddp_target)						)
    __UpperCAmelCase ,					__UpperCAmelCase				:      Tuple	 =    input.to(accelerator.device						), target.to(accelerator.device						)
    # Perform our initial ground truth step in non "DDP"
    model.train()
    ddp_model.train()
    step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
    opt.step()

    if ((iteration + 1) % 2 == 0) or ((iteration + 1) == len(__lowerCamelCase						)):
      if split_batches:
        sched.step()
      else:
        for _ in range(accelerator.num_processes						):
          sched.step()
    opt.zero_grad()
    # Perform gradient accumulation under wrapper
    with accelerator.accumulate(__lowerCamelCase						):
      step_model(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
      ddp_opt.step()
      ddp_sched.step()
      ddp_opt.zero_grad()

    # Learning rates should be the same
    assert (
        opt.param_groups[0]["lr"] == ddp_opt.param_groups[0]["lr"]
    ), f"""Learning rates found in each optimizer did not align\nopt: {opt.param_groups[0]["lr"]}\nDDP opt: {ddp_opt.param_groups[0]["lr"]}\n"""
    __UpperCAmelCase				:      Optional[Any]	 =    (((iteration + 1) % 2) == 0) or ((iteration + 1) == len(__lowerCamelCase						))
    if accelerator.num_processes > 1:
      check_model_parameters(__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase    ,						__lowerCamelCase						)
    # Shuffle ddp_input on each iteration
    torch.manual_seed(1337 + iteration						)
  GradientState._reset_state()






def 							lowerCamelCase__ (       ):
  __UpperCAmelCase				:      List[str]	 =    Accelerator()

  __UpperCAmelCase				:      Optional[Any]	 =    RegressionDataset(length=80						)
  __UpperCAmelCase				:      Any	 =    DataLoader(__lowerCamelCase    ,						batch_size=16						)
  __UpperCAmelCase				:      Optional[Any]	 =    RegressionDataset(length=96						)
  __UpperCAmelCase				:      Union[str, Any]	 =    DataLoader(__lowerCamelCase    ,						batch_size=16						)
  __UpperCAmelCase ,					__UpperCAmelCase				:      Union[str, Any]	 =    accelerator.prepare(__lowerCamelCase    ,						__lowerCamelCase						)
  assert accelerator.gradient_state.active_dataloader is None
  for iteration, _ in enumerate(__lowerCamelCase						):
    assert id(accelerator.gradient_state.active_dataloader						) == id(__lowerCamelCase						)
    if iteration < len(__lowerCamelCase						) - 1:
      assert not accelerator.gradient_state.end_of_dataloader
      if iteration == 1:
        for batch_num, _ in enumerate(__lowerCamelCase						):
          assert id(accelerator.gradient_state.active_dataloader						) == id(__lowerCamelCase						)
          if batch_num < len(__lowerCamelCase						) - 1:
            assert not accelerator.gradient_state.end_of_dataloader
          else:
            assert accelerator.gradient_state.end_of_dataloader
    else:
      assert accelerator.gradient_state.end_of_dataloader
  assert accelerator.gradient_state.active_dataloader is None






def 							lowerCamelCase__ (       ):
  __UpperCAmelCase				:      int	 =    Accelerator()
  __UpperCAmelCase				:      Dict	 =    accelerator.state
  if state.local_process_index == 0:
    print("""**Test `accumulate` gradient accumulation with dataloader break**"""						)
  test_dataloader_break()
  if state.distributed_type == DistributedType.NO:
    if state.local_process_index == 0:
      print("""**Test NOOP `no_sync` context manager**"""						)
    test_noop_sync(__lowerCamelCase						)
  if state.distributed_type in (DistributedType.MULTI_GPU, DistributedType.MULTI_CPU):
    if state.local_process_index == 0:
      print("""**Test Distributed `no_sync` context manager**"""						)
    test_distributed_sync(__lowerCamelCase						)
  if state.distributed_type == DistributedType.MULTI_GPU:
    for split_batch in [True, False]:
      for dispatch_batches in [True, False]:
        if state.local_process_index == 0:
          print(
              """**Test `accumulate` gradient accumulation, """    ,						f"""`split_batches={split_batch}` and `dispatch_batches={dispatch_batches}`**"""    ,						)
        test_gradient_accumulation(__lowerCamelCase    ,						__lowerCamelCase						)

    # Currently will break on torch 2.0 +, need to investigate why
  if is_torch_version("""<"""    ,						"""2.0"""						) or state.distributed_type == DistributedType.NO:
    if state.local_process_index == 0:
      print(
          """**Test `accumulate` gradient accumulation with optimizer and scheduler, """    ,						"""`split_batches=False`, `dispatch_batches=False`**"""    ,						)
    test_gradient_accumulation_with_opt_and_scheduler()
    if state.distributed_type == DistributedType.MULTI_GPU:
      for split_batch in [True, False]:
        for dispatch_batches in [True, False]:
          if not split_batch and not dispatch_batches:
            continue
          if state.local_process_index == 0:
            print(
                """**Test `accumulate` gradient accumulation with optimizer and scheduler, """    ,						f"""`split_batches={split_batch}` and `dispatch_batches={dispatch_batches}`**"""    ,						)
          test_gradient_accumulation_with_opt_and_scheduler(__lowerCamelCase    ,						__lowerCamelCase						)






def 							lowerCamelCase__ (       __lowerCamelCase     :	int						):
  # For xla_spawn (TPUs)
  main()


if __name__ == "__main__":
       main()






from __future__ import annotations

import math
def 	_UpperCamelCase					(    lowerCAmelCase_ )    ->bool:

   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(lowerCAmelCase_ ) + 1 )	,    6 ):
      if number % i == 0 or number % (i + 2) == 0:
         return False
   return True


__a	 =      [num for num in range(3, 10_0001, 2) if not is_prime(num)]
def 	_UpperCamelCase					(    lowerCAmelCase_ )    ->list[int]:
   if not isinstance(lowerCAmelCase_	,    lowerCAmelCase_ ):
      raise ValueError("""n must be an integer""" )
   if n <= 0:
      raise ValueError("""n must be >= 0""" )

   UpperCAmelCase      					=  []
   for num in range(len(lowerCAmelCase_ ) ):
      UpperCAmelCase      					=  0
      while 2 * i * i <= odd_composites[num]:
         UpperCAmelCase      					=  odd_composites[num] - 2 * i * i
         if is_prime(lowerCAmelCase_ ):
            break
         i += 1
      else:
         list_nums.append(odd_composites[num] )
         if len(lowerCAmelCase_ ) == n:
            return list_nums

   return []
def 	_UpperCamelCase					(    )    ->int:
   return compute_nums(1 )[0]


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



