

"""simple docstring"""


import math



def   _A					(	_a	:						int				):



      """simple docstring"""






      A				  =		[]
      A				  =		2
      A				  =		int(math.sqrt(_a				)				)  # Size of every segment
      A				  =		[True] * (end + 1)
      A				  =		[]

      while start <= end:
            if temp[start] is True:
                  in_prime.append(_a				)
                  for i in range(start * start     ,   end + 1     ,   _a				):
                        A				  =		False
            start += 1
      prime += in_prime

      A				  =		end + 1
      A				  =		min(2 * end     ,   _a				)

      while low <= n:
            A				  =		[True] * (high - low + 1)
            for each in in_prime:
                  A				  =		math.floor(low / each				) * each
                  if t < low:
                        t += each

                  for j in range(_a     ,   high + 1     ,   _a				):
                        A				  =		False

            for j in range(len(_a				)				):
                  if temp[j] is True:
                        prime.append(j + low				)

            A				  =		high + 1
            A				  =		min(high + end     ,   _a				)

      return prime





print(sieve(10**6))







"""simple docstring"""


import functools
import gc
import inspect

import torch

from .imports import is_npu_available, is_xpu_available



def   _A					(	*_a	:						int				):



      """simple docstring"""






      if not isinstance(_a     ,   _a				):
            A				  =		list(_a				)
      for i in range(len(_a				)				):
            A				  =		None
      gc.collect()
      if is_xpu_available():
            torch.xpu.empty_cache()
      elif is_npu_available():
            torch.npu.empty_cache()
      else:
            torch.cuda.empty_cache()
      return objects



def   _A					(	_a	:						Exception				):



      """simple docstring"""






      A				  =		[
          """CUDA out of memory.""",  # CUDA OOM
          """cuDNN error: CUDNN_STATUS_NOT_SUPPORTED.""",  # CUDNN SNAFU
          """DefaultCPUAllocator: can't allocate memory""",  # CPU OOM
      ]
      if isinstance(_a     ,   _a				) and len(exception.args				) == 1:
            return any(err in exception.args[0] for err in _statements				)
      return False





def   _A					(	_a	:						callable = None     ,   _a	:						int = 1_2_8				):



      """simple docstring"""






      if function is None:
            return functools.partial(_a     ,   starting_batch_size=_a				)

      A				  =		starting_batch_size

      def decorator(*_a	:						Union[str, Any]     ,   **_a	:						List[Any]				):
            nonlocal batch_size
            gc.collect()
            if is_xpu_available():
                  torch.xpu.empty_cache()
            elif is_npu_available():
                  torch.npu.empty_cache()
            else:
                  torch.cuda.empty_cache()
            A				  =		list(inspect.signature(_a				).parameters.keys()				)
            # Guard against user error
            if len(_a				) < (len(_a				) + 1):
                  A				  =		""", """.join([f'{arg}={value}' for arg, value in zip(params[1:]     ,   args[1:]				)]				)
                  raise TypeError(
                      f'Batch size was passed into `{function.__name__}` as the first argument when called.'
                      f'Remove this as the decorator already does so: `{function.__name__}({arg_str})`'				)
            while True:
                  if batch_size == 0:
                        raise RuntimeError("""No executable batch size found, reached zero."""				)
                  try:
                        return function(_a     ,   *_a     ,   **_a				)
                  except Exception as e:
                        if should_reduce_batch_size(_a				):
                              gc.collect()
                              if is_xpu_available():
                                    torch.xpu.empty_cache()
                              elif is_npu_available():
                                    torch.npu.empty_cache()
                              else:
                                    torch.cuda.empty_cache()
                              batch_size //= 2
                        else:
                              raise

      return decorator




