





"""simple docstring"""




import logging
import math
from functools import partial
from typing import Any, Callable, Dict, Iterable, List, Optional, Sequence, Tuple, Union

import torch

from .tensor_utils import tensor_tree_map, tree_map
def 					_A	(		SCREAMING_SNAKE_CASE					:       Union[dict, list, tuple, torch.Tensor]						):





  """simple docstring"""



  a__     : List[str]  =[]
  if isinstance(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						):
    for v in tree.values():
      shapes.extend(_fetch_dims(SCREAMING_SNAKE_CASE						)						)
  elif isinstance(SCREAMING_SNAKE_CASE	,	(list, tuple)						):
    for t in tree:
      shapes.extend(_fetch_dims(SCREAMING_SNAKE_CASE						)						)
  elif isinstance(SCREAMING_SNAKE_CASE	,	torch.Tensor						):
    shapes.append(tree.shape						)
  else:
    raise ValueError("Not supported"						)

  return shapes
@torch.jit.ignore
def 					_A	(		SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       Tuple[int, ...]						):





  """simple docstring"""



  a__     : List[Any]  =[]
  for d in reversed(SCREAMING_SNAKE_CASE						):
    idx.append(flat_idx % d						)
    a__     : Dict  =flat_idx // d

  return tuple(reversed(SCREAMING_SNAKE_CASE						)						)
@torch.jit.ignore
def 					_A	(		SCREAMING_SNAKE_CASE					:       Sequence[int]	,	SCREAMING_SNAKE_CASE					:       Sequence[int]	,	SCREAMING_SNAKE_CASE					:       Sequence[int]	,	SCREAMING_SNAKE_CASE					:       Optional[Sequence[bool]] = None	,	SCREAMING_SNAKE_CASE					:       Optional[Sequence[bool]] = None	,	):





  """simple docstring"""



  def reduce_edge_list(SCREAMING_SNAKE_CASE					:       List[bool]						) -> None:
    a__     : int  =True
    for i in range(len(SCREAMING_SNAKE_CASE						)						):
      a__     : List[Any]  =-1 * (i + 1)
      l[reversed_idx] &= tally
      a__     : List[str]  =l[reversed_idx]

  if start_edges is None:
    a__     : Dict  =[s == 0 for s in start]
    reduce_edge_list(SCREAMING_SNAKE_CASE						)
  if end_edges is None:
    a__     : Optional[int]  =[e == (d - 1) for e, d in zip(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)]
    reduce_edge_list(SCREAMING_SNAKE_CASE						)

  # Base cases. Either start/end are empty and we're done, or the final,
  # one-dimensional tensor can be simply sliced
  if len(SCREAMING_SNAKE_CASE						) == 0:
    return [()]
  elif len(SCREAMING_SNAKE_CASE						) == 1:
    return [(slice(start[0]	,	end[0] + 1						),)]

  a__     : List[Tuple[slice, ...]]  =[]
  a__     : List[slice]  =[]

  # Dimensions common to start and end can be selected directly
  for s, e in zip(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						):
    if s == e:
      path_list.append(slice(SCREAMING_SNAKE_CASE	,	s + 1						)						)
    else:
      break

  a__     : Tuple[slice, ...]  =tuple(SCREAMING_SNAKE_CASE						)
  a__     : int  =len(SCREAMING_SNAKE_CASE						)

  # start == end, and we're done
  if divergence_idx == len(SCREAMING_SNAKE_CASE						):
    return [path]

  def upper() -> Tuple[Tuple[slice, ...], ...]:
    assert start_edges is not None
    assert end_edges is not None

    a__     : Union[str, Any]  =start[divergence_idx]
    return tuple(
        path + (slice(SCREAMING_SNAKE_CASE	,	sdi + 1						),) + s
        for s in _get_minimal_slice_set(
            start[divergence_idx + 1 :]	,	[d - 1 for d in dims[divergence_idx + 1 :]]	,	dims[divergence_idx + 1 :]	,	start_edges=start_edges[divergence_idx + 1 :]	,	end_edges=[True for _ in end_edges[divergence_idx + 1 :]]	,	)						)

  def lower() -> Tuple[Tuple[slice, ...], ...]:
    assert start_edges is not None
    assert end_edges is not None

    a__     : Union[str, Any]  =end[divergence_idx]
    return tuple(
        path + (slice(SCREAMING_SNAKE_CASE	,	edi + 1						),) + s
        for s in _get_minimal_slice_set(
            [0 for _ in start[divergence_idx + 1 :]]	,	end[divergence_idx + 1 :]	,	dims[divergence_idx + 1 :]	,	start_edges=[True for _ in start_edges[divergence_idx + 1 :]]	,	end_edges=end_edges[divergence_idx + 1 :]	,	)						)

  # If both start and end are at the edges of the subtree rooted at
  # divergence_idx, we can just select the whole subtree at once
  if start_edges[divergence_idx] and end_edges[divergence_idx]:
    slices.append(path + (slice(start[divergence_idx]	,	end[divergence_idx] + 1						),)						)
  # If just start is at the edge, we can grab almost all of the subtree,
  # treating only the ragged bottom edge as an edge case
  elif start_edges[divergence_idx]:
    slices.append(path + (slice(start[divergence_idx]	,	end[divergence_idx]						),)						)
    slices.extend(lower()						)
  # Analogous to the previous case, but the top is ragged this time
  elif end_edges[divergence_idx]:
    slices.extend(upper()						)
    slices.append(path + (slice(start[divergence_idx] + 1	,	end[divergence_idx] + 1						),)						)
  # If both sides of the range are ragged, we need to handle both sides
  # separately. If there's contiguous meat in between them, we can index it
  # in one big chunk
  else:
    slices.extend(upper()						)
    a__     : List[Any]  =end[divergence_idx] - start[divergence_idx]
    if middle_ground > 1:
      slices.append(path + (slice(start[divergence_idx] + 1	,	end[divergence_idx]						),)						)
    slices.extend(lower()						)

  return slices
@torch.jit.ignore
def 					_A	(		SCREAMING_SNAKE_CASE					:       torch.Tensor	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       int						):





  """simple docstring"""



  a__     : Optional[int]  =t.shape[:no_batch_dims]
  a__     : Dict  =list(_flat_idx_to_idx(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)						)
  # _get_minimal_slice_set is inclusive
  a__     : Union[str, Any]  =list(_flat_idx_to_idx(flat_end - 1	,	SCREAMING_SNAKE_CASE						)						)

  # Get an ordered list of slices to perform
  a__     : int  =_get_minimal_slice_set(
      SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE	,	)

  a__     : Any  =[t[s] for s in slices]

  return torch.cat([s.view((-1,) + t.shape[no_batch_dims:]						) for s in sliced_tensors]						)
def 					_A	(		SCREAMING_SNAKE_CASE					:       Callable	,	SCREAMING_SNAKE_CASE					:       Dict[str, Any]	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       int	,	SCREAMING_SNAKE_CASE					:       bool = False	,	SCREAMING_SNAKE_CASE					:       Any = None	,	SCREAMING_SNAKE_CASE					:       bool = False	,	):





  """simple docstring"""



  if not (len(SCREAMING_SNAKE_CASE						) > 0):
    raise ValueError("Must provide at least one input"						)

  a__     : str  =[shape[:no_batch_dims] for shape in _fetch_dims(SCREAMING_SNAKE_CASE						)]
  a__     : Optional[int]  =tuple([max(SCREAMING_SNAKE_CASE						) for s in zip(*SCREAMING_SNAKE_CASE						)]						)

  def _prep_inputs(SCREAMING_SNAKE_CASE					:       torch.Tensor						) -> torch.Tensor:
    if not low_mem:
      if not sum(t.shape[:no_batch_dims]						) == no_batch_dims:
        a__     : List[Any]  =t.expand(orig_batch_dims + t.shape[no_batch_dims:]						)
      a__     : Any  =t.reshape(-1	,	*t.shape[no_batch_dims:]						)
    else:
      a__     : Any  =t.expand(orig_batch_dims + t.shape[no_batch_dims:]						)
    return t

  a__     : Dict[str, Any]  =tensor_tree_map(_prep_inputs	,	SCREAMING_SNAKE_CASE						)
  a__     : Optional[int]  =None
  if _out is not None:
    a__     : Dict  =tensor_tree_map(lambda SCREAMING_SNAKE_CASE						: t.view([-1] + list(t.shape[no_batch_dims:]						)						)	,	_out						)

  a__     : Dict  =1
  for d in orig_batch_dims:
    flat_batch_dim *= d

  a__     : Union[str, Any]  =flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

  def _select_chunk(SCREAMING_SNAKE_CASE					:       torch.Tensor						) -> torch.Tensor:
    return t[i : i + chunk_size] if t.shape[0] != 1 else t

  a__     : Dict  =0
  a__     : Any  =prepped_outputs
  for _ in range(SCREAMING_SNAKE_CASE						):
    # Chunk the input
    if not low_mem:
      a__     : List[str]  =_select_chunk
    else:
      a__     : int  =partial(
          _chunk_slice	,	flat_start=SCREAMING_SNAKE_CASE	,	flat_end=min(SCREAMING_SNAKE_CASE	,	i + chunk_size						)	,	no_batch_dims=len(SCREAMING_SNAKE_CASE						)	,	)

    a__     : Dict[str, Any]  =tensor_tree_map(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)

    # Run the layer on the chunk
    a__     : List[Any]  =layer(**SCREAMING_SNAKE_CASE						)

    # Allocate space for the output
    if out is None:
      a__     : Union[str, Any]  =tensor_tree_map(lambda SCREAMING_SNAKE_CASE						: t.new_zeros((flat_batch_dim,) + t.shape[1:]						)	,	SCREAMING_SNAKE_CASE						)

    # Put the chunk in its pre-allocated space
    if isinstance(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						):

      def assign(SCREAMING_SNAKE_CASE					:       dict	,	SCREAMING_SNAKE_CASE					:       dict						) -> None:
        for k, v in da.items():
          if isinstance(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						):
            assign(SCREAMING_SNAKE_CASE	,	da[k]						)
          else:
            if _add_into_out:
              v[i : i + chunk_size] += da[k]
            else:
              a__     : Tuple  =da[k]

      assign(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						)
    elif isinstance(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						):
      for xa, xa in zip(SCREAMING_SNAKE_CASE	,	SCREAMING_SNAKE_CASE						):
        if _add_into_out:
          xa[i : i + chunk_size] += xa
        else:
          a__     : int  =xa
    elif isinstance(SCREAMING_SNAKE_CASE	,	torch.Tensor						):
      if _add_into_out:
        out[i : i + chunk_size] += output_chunk
      else:
        a__     : Union[str, Any]  =output_chunk
    else:
      raise ValueError("Not supported"						)

    i += chunk_size

  a__     : List[Any]  =tensor_tree_map(lambda SCREAMING_SNAKE_CASE						: t.view(orig_batch_dims + t.shape[1:]						)	,	SCREAMING_SNAKE_CASE						)

  return out







class     __lowerCAmelCase	:







      def __init__(   self		,				lowerCAmelCase__ = 5_1_2		,				)       ->						str:



        '''simple docstring'''




        a__     : Any  =max_chunk_size
        a__     : Optional[int]  =None
        a__     : Optional[tuple]  =None







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__							)       ->						Any:



        '''simple docstring'''




        logging.info("Tuning chunk size..."							)

        if min_chunk_size >= self.max_chunk_size:
          return min_chunk_size

        a__     : List[int]  =[2**l for l in range(int(math.log(self.max_chunk_size		,				2							)							) + 1							)]
        a__     : List[str]  =[c for c in candidates if c > min_chunk_size]
        a__     : int  =[min_chunk_size] + candidates
        candidates[-1] += 4

        def test_chunk_size(lowerCAmelCase__							) -> bool:
          try:
            with torch.no_grad():
              fn(*__lowerCamelCase		,				chunk_size=__lowerCamelCase							)
            return True
          except RuntimeError:
            return False

        a__     : Dict  =0
        a__     : Dict  =len(__lowerCamelCase							) - 1
        while i > min_viable_chunk_size_index:
          a__     : str  =test_chunk_size(candidates[i]							)
          if not viable:
            a__     : List[str]  =(min_viable_chunk_size_index + i) // 2
          else:
            a__     : List[Any]  =i
            a__     : Dict  =(i + len(__lowerCamelCase							) - 1) // 2

        return candidates[min_viable_chunk_size_index]







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__							)       ->						List[Any]:



        '''simple docstring'''




        a__     : Dict  =True
        for aa, aa in zip(__lowerCamelCase		,				__lowerCamelCase							):
          assert type(__lowerCamelCase							) == type(__lowerCamelCase							)
          if isinstance(__lowerCamelCase		,				(list, tuple)							):
            consistent &= self._compare_arg_caches(__lowerCamelCase		,				__lowerCamelCase							)
          elif isinstance(__lowerCamelCase		,				__lowerCamelCase							):
            a__     : Optional[int]  =[v for _, v in sorted(aa.items()		,				key=lambda lowerCAmelCase__							: x[0]							)]
            a__     : int  =[v for _, v in sorted(aa.items()		,				key=lambda lowerCAmelCase__							: x[0]							)]
            consistent &= self._compare_arg_caches(__lowerCamelCase		,				__lowerCamelCase							)
          else:
            consistent &= aa == aa

        return consistent







      def        _lowercase  (   self		,				lowerCAmelCase__		,				lowerCAmelCase__		,				lowerCAmelCase__		,				)       ->						Dict:



        '''simple docstring'''




        a__     : Optional[Any]  =True
        a__     : tuple  =tree_map(lambda lowerCAmelCase__							: a.shape if isinstance(__lowerCamelCase		,				torch.Tensor							) else a		,				__lowerCamelCase		,				__lowerCamelCase							)
        if self.cached_arg_data is not None:
          # If args have changed shape/value, we need to re-tune
          assert len(self.cached_arg_data							) == len(__lowerCamelCase							)
          a__     : Union[str, Any]  =self._compare_arg_caches(self.cached_arg_data		,				__lowerCamelCase							)
        else:
          # Otherwise, we can reuse the precomputed value
          a__     : Any  =False

        if not consistent:
          a__     : List[str]  =self._determine_favorable_chunk_size(
              __lowerCamelCase		,				__lowerCamelCase		,				__lowerCamelCase		,				)
          a__     : Dict  =arg_data

        assert self.cached_chunk_size is not None

        return self.cached_chunk_size













from __future__ import annotations

import math
def 					_A	(		SCREAMING_SNAKE_CASE					:       int						):





  """simple docstring"""



  if num <= 0:
    a__     : List[str]  =f'''{num}: Invalid input, please enter a positive integer.'''
    raise ValueError(SCREAMING_SNAKE_CASE						)

  a__     : Union[str, Any]  =[True] * (num + 1)
  a__     : Union[str, Any]  =[]
  a__     : str  =2
  a__     : Any  =int(math.sqrt(SCREAMING_SNAKE_CASE						)						)

  while start <= end:
    # If start is a prime
    if sieve[start] is True:
      prime.append(SCREAMING_SNAKE_CASE						)

      # Set multiples of start be False
      for i in range(start * start	,	num + 1	,	SCREAMING_SNAKE_CASE						):
        if sieve[i] is True:
          a__     : Optional[int]  =False

    start += 1

  for j in range(end + 1	,	num + 1						):
    if sieve[j] is True:
      prime.append(SCREAMING_SNAKE_CASE						)

  return prime


if __name__ == "__main__":
     print(prime_sieve(int(input("""Enter a positive integer: """).strip())))






