
'''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 				SCREAMING_SNAKE_CASE__	(   __A	)       ->	List[Tuple[int, ...]]:
	_snake_case   						=		[]
	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__	(   __A			,				__A	)       ->	Tuple[int, ...]:
	_snake_case   						=		[]
	for d in reversed(__A	):
		idx.append(flat_idx % d	)
		_snake_case   						=		flat_idx // d

	return tuple(reversed(__A	)	)







@torch.jit.ignore
def 				SCREAMING_SNAKE_CASE__	(   __A			,				__A			,				__A			,				__A = None			,				__A = None			,				)       ->	List[Tuple[slice, ...]]:

	# 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(__A	) -> None:
		_snake_case   						=		True
		for i in range(len(__A	)	):
			_snake_case   						=		-1 * (i + 1)
			l[reversed_idx] &= tally
			_snake_case   						=		l[reversed_idx]

	if start_edges is None:
		_snake_case   						=		[s == 0 for s in start]
		reduce_edge_list(__A	)
	if end_edges is None:
		_snake_case   						=		[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	),)]

	_snake_case   						=		[]
	_snake_case   						=		[]

	# 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

	_snake_case   						=		tuple(__A	)
	_snake_case   						=		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

		_snake_case   						=		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

		_snake_case   						=		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()	)
		_snake_case   						=		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__	(   __A			,				__A			,				__A			,				__A	)       ->	torch.Tensor:
	_snake_case   						=		t.shape[:no_batch_dims]
	_snake_case   						=		list(_flat_idx_to_idx(__A			,				__A	)	)
	# _get_minimal_slice_set is inclusive
	_snake_case   						=		list(_flat_idx_to_idx(flat_end - 1			,				__A	)	)

	# Get an ordered list of slices to perform
	_snake_case   						=		_get_minimal_slice_set(
	    __A			,				__A			,				__A			,				)

	_snake_case   						=		[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__	(   __A			,				__A			,				__A			,				__A			,				__A = False			,				__A = None			,				__A = False			,				)       ->	Any:
	if not (len(__A	) > 0):
		raise ValueError('Must provide at least one input'	)

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

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

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

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

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

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

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

		_snake_case   						=		tensor_tree_map(__A			,				__A	)

		# Run the layer on the chunk
		_snake_case   						=		layer(**__A	)

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

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

			def assign(__A			,				__A	) -> 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:
							_snake_case   						=		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:
					_snake_case   						=		xa
		elif isinstance(__A			,				torch.Tensor	):
			if _add_into_out:
				out[i : i + chunk_size] += output_chunk
			else:
				_snake_case   						=		output_chunk
		else:
			raise ValueError('Not supported'	)

		i += chunk_size

	_snake_case   						=		tensor_tree_map(lambda __A	: t.view(orig_batch_dims + t.shape[1:]	)			,				__A	)

	return out





class 						__UpperCAmelCase      :


							def __init__(       self    ,   lowerCAmelCase_ = 5_12    ,   ):





								"""simple docstring"""






								_snake_case   						=		max_chunk_size
								_snake_case   						=		None
								_snake_case   						=		None


							def  lowerCamelCase				(       self    ,   lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_  ):





								"""simple docstring"""






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

								if min_chunk_size >= self.max_chunk_size:
									return min_chunk_size

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

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

								return candidates[min_viable_chunk_size_index]


							def  lowerCamelCase				(       self    ,   lowerCAmelCase_    ,   lowerCAmelCase_  ):





								"""simple docstring"""






								_snake_case   						=		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_  ):
										_snake_case   						=		[v for _, v in sorted(aa.items()    ,   key=lambda lowerCAmelCase_  : x[0]  )]
										_snake_case   						=		[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  lowerCamelCase				(       self    ,   lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_    ,   ):





								"""simple docstring"""






								_snake_case   						=		True
								_snake_case   						=		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_  )
									_snake_case   						=		self._compare_arg_caches(self.cached_arg_data    ,   lowerCAmelCase_  )
								else:
									# Otherwise, we can reuse the precomputed value
									_snake_case   						=		False

								if not consistent:
									_snake_case   						=		self._determine_favorable_chunk_size(
									    lowerCAmelCase_    ,   lowerCAmelCase_    ,   lowerCAmelCase_    ,   )
									_snake_case   						=		arg_data

								assert self.cached_chunk_size is not None

								return self.cached_chunk_size



'''simple docstring'''







def 				SCREAMING_SNAKE_CASE__	(   __A = 100	)       ->	int:
	_snake_case   						=		n * (n + 1) * (2 * n + 1) / 6
	_snake_case   						=		(n * (n + 1) / 2) ** 2
	return int(square_of_sum - sum_of_squares	)


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

