



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      __snake_case	(			_UpperCAmelCase				):
    __a						       =				[]
    if isinstance(_UpperCAmelCase   , _UpperCAmelCase				):
        for v in tree.values():
            shapes.extend(_fetch_dims(_UpperCAmelCase				)				)
    elif isinstance(_UpperCAmelCase   , (list, tuple)				):
        for t in tree:
            shapes.extend(_fetch_dims(_UpperCAmelCase				)				)
    elif isinstance(_UpperCAmelCase   , torch.Tensor				):
        shapes.append(tree.shape				)
    else:
        raise ValueError('''Not supported'''				)

    return shapes





@torch.jit.ignore
def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase				):
    __a						       =				[]
    for d in reversed(_UpperCAmelCase				):
        idx.append(flat_idx % d				)
        __a						       =				flat_idx // d

    return tuple(reversed(_UpperCAmelCase				)				)





@torch.jit.ignore
def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase = None   , _UpperCAmelCase = None   , ):

    # 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(_UpperCAmelCase				)				):
            __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(_UpperCAmelCase				)
    if end_edges is None:
        __a						       =				[e == (d - 1) for e, d in zip(_UpperCAmelCase   , _UpperCAmelCase				)]
        reduce_edge_list(_UpperCAmelCase				)

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

    __a						       =				tuple(_UpperCAmelCase				)
    __a						       =				len(_UpperCAmelCase				)

    # start == end, and we're done
    if divergence_idx == len(_UpperCAmelCase				):
        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(_UpperCAmelCase   , 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(_UpperCAmelCase   , 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      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase				):
    __a						       =				t.shape[:no_batch_dims]
    __a						       =				list(_flat_idx_to_idx(_UpperCAmelCase   , _UpperCAmelCase				)				)
    # _get_minimal_slice_set is inclusive
    __a						       =				list(_flat_idx_to_idx(flat_end - 1   , _UpperCAmelCase				)				)

    # Get an ordered list of slices to perform
    __a						       =				_get_minimal_slice_set(
        _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , )

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

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





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase = False   , _UpperCAmelCase = None   , _UpperCAmelCase = False   , ):
    if not (len(_UpperCAmelCase				) > 0):
        raise ValueError('''Must provide at least one input'''				)

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

    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   , _UpperCAmelCase				)
    __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(_UpperCAmelCase				):
        # Chunk the input
        if not low_mem:
            __a						       =				_select_chunk
        else:
            __a						       =				partial(
                _chunk_slice   , flat_start=_UpperCAmelCase   , flat_end=min(_UpperCAmelCase   , i + chunk_size				)   , no_batch_dims=len(_UpperCAmelCase				)   , )

        __a						       =				tensor_tree_map(_UpperCAmelCase   , _UpperCAmelCase				)

        # Run the layer on the chunk
        __a						       =				layer(**_UpperCAmelCase				)

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

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

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

            assign(_UpperCAmelCase   , _UpperCAmelCase				)
        elif isinstance(_UpperCAmelCase   , _UpperCAmelCase				):
            for xa, xa in zip(_UpperCAmelCase   , _UpperCAmelCase				):
                if _add_into_out:
                    xa[i : i + chunk_size] += xa
                else:
                    __a						       =				xa
        elif isinstance(_UpperCAmelCase   , 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:]				)   , _UpperCAmelCase				)

    return out

class     _A       :



       def __init__(		self							:     List[str]     ,		__SCREAMING_SNAKE_CASE							:     int = 512     ,		):


           '''simple docstring'''

           __a						       =				max_chunk_size
           __a						       =				None
           __a						       =				None



       def 		_lowerCamelCase			(		self							:     Tuple     ,		__SCREAMING_SNAKE_CASE							:     Callable     ,		__SCREAMING_SNAKE_CASE							:     tuple     ,		__SCREAMING_SNAKE_CASE							:     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(__SCREAMING_SNAKE_CASE							:     int) -> 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							:     Union[str, Any]     ,		__SCREAMING_SNAKE_CASE							:     Iterable     ,		__SCREAMING_SNAKE_CASE							:     Iterable):


           '''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 __SCREAMING_SNAKE_CASE: x[0])]
                   __a						       =				[v for _, v in sorted(aa.items()     ,		key=lambda __SCREAMING_SNAKE_CASE: x[0])]
                   consistent &= self._compare_arg_caches(__SCREAMING_SNAKE_CASE     ,		__SCREAMING_SNAKE_CASE)
               else:
                   consistent &= aa == aa

           return consistent





       def 		_lowerCamelCase			(		self							:     List[Any]     ,		__SCREAMING_SNAKE_CASE							:     Callable     ,		__SCREAMING_SNAKE_CASE							:     tuple     ,		__SCREAMING_SNAKE_CASE							:     int     ,		):


           '''simple docstring'''

           __a						       =				True
           __a						       =				tree_map(lambda __SCREAMING_SNAKE_CASE: 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











"""simple docstring"""






from __future__ import annotations

from collections.abc import Iterator
from typing import Any






class lowerCAmelCase__	:






			'''simple docstring'''



			def __init__(  self  ,      lowercase  ):
							_lowerCamelCase     :			Any    =    data
							_lowerCamelCase     :			Node | None    =    None






class lowerCAmelCase__	:






			'''simple docstring'''



			def __init__(  self  ):
							_lowerCamelCase     :			str    =    None
							_lowerCamelCase     :			str    =    None
			def __iter__(  self  ):
							_lowerCamelCase     :			List[str]    =    self.head
							while self.head:
											yield node.data
											_lowerCamelCase     :			Optional[int]    =    node.next
											if node == self.head:
															break
			def __len__(  self  ):
							return sum(1 for _ in self  )
			def __repr__(  self  ):
							return "->".join(str(lowercase  ) for item in iter(self  )  )
			def 					A_    (  self  ,      lowercase  ):
							self.insert_nth(len(self  )  ,      lowercase  )
			def 					A_    (  self  ,      lowercase  ):
							self.insert_nth(0  ,      lowercase  )
			def 					A_    (  self  ,      lowercase  ,      lowercase  ):
							if index < 0 or index > len(self  ):
											raise IndexError('list index out of range.'  )
							_lowerCamelCase     :			List[Any]    =    Node(lowercase  )
							if self.head is None:
											_lowerCamelCase     :			str    =    new_node  # first node points itself
											_lowerCamelCase     :			Union[str, Any]    =    new_node
							elif index == 0:  # insert at head
											_lowerCamelCase     :			List[str]    =    self.head
											_lowerCamelCase     :			str    =    new_node
							else:
											_lowerCamelCase     :			Union[str, Any]    =    self.head
											for _ in range(index - 1  ):
															_lowerCamelCase     :			List[Any]    =    temp.next
											_lowerCamelCase     :			Union[str, Any]    =    temp.next
											_lowerCamelCase     :			List[str]    =    new_node
											if index == len(self  ) - 1:  # insert at tail
															_lowerCamelCase     :			Any    =    new_node
			def 					A_    (  self  ):
							return self.delete_nth(0  )
			def 					A_    (  self  ):
							return self.delete_nth(len(self  ) - 1  )
			def 					A_    (  self  ,      lowercase = 0  ):
							if not 0 <= index < len(self  ):
											raise IndexError('list index out of range.'  )
							_lowerCamelCase     :			Any    =    self.head
							if self.head == self.tail:  # just one node
											_lowerCamelCase     :			List[str]    =    None
							elif index == 0:  # delete head node
											_lowerCamelCase     :			List[str]    =    self.tail.next.next
											_lowerCamelCase     :			Optional[int]    =    self.head.next
							else:
											_lowerCamelCase     :			Dict    =    self.head
											for _ in range(index - 1  ):
															_lowerCamelCase     :			List[Any]    =    temp.next
											_lowerCamelCase     :			int    =    temp.next
											_lowerCamelCase     :			Optional[int]    =    temp.next.next
											if index == len(self  ) - 1:  # delete at tail
															_lowerCamelCase     :			List[Any]    =    temp
							return delete_node.data






			def 					A_    (  self  ):
							return len(self  ) == 0







def      _snake_case			(				):
				_lowerCamelCase     :			Union[str, Any]    =    CircularLinkedList()
				assert len(lowercase__		) == 0
				assert circular_linked_list.is_empty() is True
				assert str(lowercase__		) == ""

				try:
								circular_linked_list.delete_front()
								raise AssertionError  # This should not happen
				except IndexError:
								assert True  # This should happen

				try:
								circular_linked_list.delete_tail()
								raise AssertionError  # This should not happen
				except IndexError:
								assert True  # This should happen

				try:
								circular_linked_list.delete_nth(-1		)
								raise AssertionError
				except IndexError:
								assert True

				try:
								circular_linked_list.delete_nth(0		)
								raise AssertionError
				except IndexError:
								assert True

				assert circular_linked_list.is_empty() is True
				for i in range(5		):
								assert len(lowercase__		) == i
								circular_linked_list.insert_nth(lowercase__							,    i + 1		)
				assert str(lowercase__		) == "->".join(str(lowercase__		) for i in range(1							,    6		)		)

				circular_linked_list.insert_tail(6		)
				assert str(lowercase__		) == "->".join(str(lowercase__		) for i in range(1							,    7		)		)
				circular_linked_list.insert_head(0		)
				assert str(lowercase__		) == "->".join(str(lowercase__		) for i in range(0							,    7		)		)

				assert circular_linked_list.delete_front() == 0
				assert circular_linked_list.delete_tail() == 6
				assert str(lowercase__		) == "->".join(str(lowercase__		) for i in range(1							,    6		)		)
				assert circular_linked_list.delete_nth(2		) == 3

				circular_linked_list.insert_nth(2							,    3		)
				assert str(lowercase__		) == "->".join(str(lowercase__		) for i in range(1							,    6		)		)

				assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
			import doctest

			doctest.testmod()