

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

     return shapes

@torch.jit.ignore
def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase		, __UpperCamelCase)      ->					Optional[Any]:
     a     =				[]
     for d in reversed(_a):
          idx.append(flat_idx % d)
          a     =				flat_idx // d

     return tuple(reversed(_a))

@torch.jit.ignore
def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase		, __UpperCamelCase		, __UpperCamelCase		, __UpperCamelCase = None		, __UpperCamelCase = None		, )      ->					Tuple:

     # start_edges and end_edges both indicate whether, starting from any given
     # dimension, the start/end index is at the top/bottom edge of the
     # corresponding tensor, modeled as a tree
     def reduce_edge_list(__UpperCamelCase) -> None:
          a     =				True
          for i in range(len(_a)):
               a     =				-1 * (i + 1)
               l[reversed_idx] &= tally
               a     =				l[reversed_idx]

     if start_edges is None:
          a     =				[s == 0 for s in start]
          reduce_edge_list(_a)
     if end_edges is None:
          a     =				[e == (d - 1) for e, d in zip(_a		, _a)]
          reduce_edge_list(_a)

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

     a     =				[]
     a     =				[]

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

     a     =				tuple(_a)
     a     =				len(_a)

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

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

          a     =				start[divergence_idx]
          return tuple(
              path + (slice(_a		, 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     =				end[divergence_idx]
          return tuple(
              path + (slice(_a		, 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     =				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  SCREAMING_SNAKE_CASE							(       __UpperCamelCase		, __UpperCamelCase		, __UpperCamelCase		, __UpperCamelCase)      ->					Union[str, Any]:
     a     =				t.shape[:no_batch_dims]
     a     =				list(_flat_idx_to_idx(_a		, _a))
     # _get_minimal_slice_set is inclusive
     a     =				list(_flat_idx_to_idx(flat_end - 1		, _a))

     # Get an ordered list of slices to perform
     a     =				_get_minimal_slice_set(
         _a		, _a		, _a		, )

     a     =				[t[s] for s in slices]

     return torch.cat([s.view((-1,) + t.shape[no_batch_dims:]) for s in sliced_tensors])

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase		, __UpperCamelCase		, __UpperCamelCase		, __UpperCamelCase		, __UpperCamelCase = False		, __UpperCamelCase = None		, __UpperCamelCase = False		, )      ->					Dict:
     if not (len(_a) > 0):
          raise ValueError("Must provide at least one input")

     a     =				[shape[:no_batch_dims] for shape in _fetch_dims(_a)]
     a     =				tuple([max(_a) for s in zip(*_a)])

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

     a     =				tensor_tree_map(_prep_inputs		, _a)
     a     =				None
     if _out is not None:
          a     =				tensor_tree_map(lambda __UpperCamelCase: t.view([-1] + list(t.shape[no_batch_dims:]))		, _out)

     a     =				1
     for d in orig_batch_dims:
          flat_batch_dim *= d

     a     =				flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

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

     a     =				0
     a     =				prepped_outputs
     for _ in range(_a):
          # Chunk the input
          if not low_mem:
               a     =				_select_chunk
          else:
               a     =				partial(
                   _chunk_slice		, flat_start=_a		, flat_end=min(_a		, i + chunk_size)		, no_batch_dims=len(_a)		, )

          a     =				tensor_tree_map(_a		, _a)

          # Run the layer on the chunk
          a     =				layer(**_a)

          # Allocate space for the output
          if out is None:
               a     =				tensor_tree_map(lambda __UpperCamelCase: t.new_zeros((flat_batch_dim,) + t.shape[1:])		, _a)

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

               def assign(__UpperCamelCase		, __UpperCamelCase) -> None:
                    for k, v in da.items():
                         if isinstance(_a		, _a):
                              assign(_a		, da[k])
                         else:
                              if _add_into_out:
                                   v[i : i + chunk_size] += da[k]
                              else:
                                   a     =				da[k]

               assign(_a		, _a)
          elif isinstance(_a		, _a):
               for xa, xa in zip(_a		, _a):
                    if _add_into_out:
                         xa[i : i + chunk_size] += xa
                    else:
                         a     =				xa
          elif isinstance(_a		, torch.Tensor):
               if _add_into_out:
                    out[i : i + chunk_size] += output_chunk
               else:
                    a     =				output_chunk
          else:
               raise ValueError("Not supported")

          i += chunk_size

     a     =				tensor_tree_map(lambda __UpperCamelCase: t.view(orig_batch_dims + t.shape[1:])		, _a)

     return out





class       a__	:







     def __init__(     self  ,		A = 512  ,		)  ->   List[Any]:



          '''simple docstring'''



          a     =				max_chunk_size
          a     =				None
          a     =				None







     def       lowerCAmelCase_    (     self  ,		A  ,		A  ,		A			)  ->   int:



          '''simple docstring'''



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

          if min_chunk_size >= self.max_chunk_size:
               return min_chunk_size

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

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

          a     =				0
          a     =				len(_SCREAMING_SNAKE_CASE			) - 1
          while i > min_viable_chunk_size_index:
               a     =				test_chunk_size(candidates[i]			)
               if not viable:
                    a     =				(min_viable_chunk_size_index + i) // 2
               else:
                    a     =				i
                    a     =				(i + len(_SCREAMING_SNAKE_CASE			) - 1) // 2

          return candidates[min_viable_chunk_size_index]







     def       lowerCAmelCase_    (     self  ,		A  ,		A			)  ->   bool:



          '''simple docstring'''



          a     =				True
          for aa, aa in zip(_SCREAMING_SNAKE_CASE  ,		_SCREAMING_SNAKE_CASE			):
               assert type(_SCREAMING_SNAKE_CASE			) == type(_SCREAMING_SNAKE_CASE			)
               if isinstance(_SCREAMING_SNAKE_CASE  ,		(list, tuple)			):
                    consistent &= self._compare_arg_caches(_SCREAMING_SNAKE_CASE  ,		_SCREAMING_SNAKE_CASE			)
               elif isinstance(_SCREAMING_SNAKE_CASE  ,		_SCREAMING_SNAKE_CASE			):
                    a     =				[v for _, v in sorted(aa.items()  ,		key=lambda A			: x[0]			)]
                    a     =				[v for _, v in sorted(aa.items()  ,		key=lambda A			: x[0]			)]
                    consistent &= self._compare_arg_caches(_SCREAMING_SNAKE_CASE  ,		_SCREAMING_SNAKE_CASE			)
               else:
                    consistent &= aa == aa

          return consistent







     def       lowerCAmelCase_    (     self  ,		A  ,		A  ,		A  ,		)  ->   int:



          '''simple docstring'''



          a     =				True
          a     =				tree_map(lambda A			: a.shape if isinstance(_SCREAMING_SNAKE_CASE  ,		torch.Tensor			) else a  ,		_SCREAMING_SNAKE_CASE  ,		_SCREAMING_SNAKE_CASE			)
          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(_SCREAMING_SNAKE_CASE			)
               a     =				self._compare_arg_caches(self.cached_arg_data  ,		_SCREAMING_SNAKE_CASE			)
          else:
               # Otherwise, we can reuse the precomputed value
               a     =				False

          if not consistent:
               a     =				self._determine_favorable_chunk_size(
                   _SCREAMING_SNAKE_CASE  ,		_SCREAMING_SNAKE_CASE  ,		_SCREAMING_SNAKE_CASE  ,		)
               a     =				arg_data

          assert self.cached_chunk_size is not None

          return self.cached_chunk_size







import math
import sys

def  SCREAMING_SNAKE_CASE							(       __UpperCamelCase)      ->					int:
     if number != int(__UpperCamelCase):
          raise ValueError("the value of input must be a natural number")
     if number < 0:
          raise ValueError("the value of input must not be a negative number")
     if number == 0:
          return 1
     a     =				[-1] * (number + 1)
     a     =				0
     for i in range(1		, number + 1):
          a     =				sys.maxsize
          a     =				int(math.sqrt(__UpperCamelCase))
          for j in range(1		, root + 1):
               a     =				1 + answers[i - (j**2)]
               a     =				min(__UpperCamelCase		, __UpperCamelCase)
          a     =				answer
     return answers[number]


if __name__ == "__main__":
   import doctest

   doctest.testmod()

