


"""simple docstring"""




def       a_ (	lowercase__ :Dict,			lowercase__ :Optional[int],			lowercase__ :List[Any],			lowercase__ :Tuple,			lowercase__ :Union[str, Any],			lowercase__ :Dict     ):
			if index == r:
						for j in range(lowercase__     ):
									print(data[j],			end=""" """     )
						print(""" """     )
						return
			#  When no more elements are there to put in data[]
			if i >= n:
						return
			# current is included, put next at next location
			__lowerCamelCase          =      arr[i]
			combination_util(lowercase__,			lowercase__,			lowercase__,			index + 1,			lowercase__,			i + 1     )
			# current is excluded, replace it with
			# next (Note that i+1 is passed, but
			# index is not changed)
			combination_util(lowercase__,			lowercase__,			lowercase__,			lowercase__,			lowercase__,			i + 1     )
			# The main function that prints all combinations
			# of size r in arr[] of size n. This function
			# mainly uses combinationUtil()





def       a_ (	lowercase__ :str,			lowercase__ :str,			lowercase__ :Dict     ):
			# A temporary array to store all combination one by one
			__lowerCamelCase          =      [0] * r
			# Print all combination using temporary array 'data[]'
			combination_util(lowercase__,			lowercase__,			lowercase__,			0,			lowercase__,			0     )


if __name__ == "__main__":
					# Driver code to check the function above
					__magic_name__						: Dict    =				[1_0, 2_0, 3_0, 4_0, 5_0]
					print_combination(arr, len(arr), 3)
					# This code is contributed by Ambuj sahu








"""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_ (	lowercase__ :Union[dict, list, tuple, torch.Tensor]     ):
			__lowerCamelCase          =      []
			if isinstance(lowercase__,			lowercase__     ):
						for v in tree.values():
									shapes.extend(_fetch_dims(lowercase__     )     )
			elif isinstance(lowercase__,			(list, tuple)     ):
						for t in tree:
									shapes.extend(_fetch_dims(lowercase__     )     )
			elif isinstance(lowercase__,			torch.Tensor     ):
						shapes.append(tree.shape     )
			else:
						raise ValueError("""Not supported"""     )

			return shapes





@torch.jit.ignore
def       a_ (	lowercase__ :int,			lowercase__ :Tuple[int, ...]     ):
			__lowerCamelCase          =      []
			for d in reversed(lowercase__     ):
						idx.append(flat_idx % d     )
						__lowerCamelCase          =      flat_idx // d

			return tuple(reversed(lowercase__     )     )





@torch.jit.ignore
def       a_ (	lowercase__ :Sequence[int],			lowercase__ :Sequence[int],			lowercase__ :Sequence[int],			lowercase__ :Optional[Sequence[bool]] = None,			lowercase__ :Optional[Sequence[bool]] = 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(lowercase__ :List[bool]     ) -> None:
						__lowerCamelCase          =      True
						for i in range(len(lowercase__     )     ):
									__lowerCamelCase          =      -1 * (i + 1)
									l[reversed_idx] &= tally
									__lowerCamelCase          =      l[reversed_idx]

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

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

			__lowerCamelCase          =      []
			__lowerCamelCase          =      []

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

			__lowerCamelCase          =      tuple(lowercase__     )
			__lowerCamelCase          =      len(lowercase__     )

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

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

						__lowerCamelCase          =      start[divergence_idx]
						return tuple(
						    path + (slice(lowercase__,			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

						__lowerCamelCase          =      end[divergence_idx]
						return tuple(
						    path + (slice(lowercase__,			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()     )
						__lowerCamelCase          =      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_ (	lowercase__ :torch.Tensor,			lowercase__ :int,			lowercase__ :int,			lowercase__ :int     ):
			__lowerCamelCase          =      t.shape[:no_batch_dims]
			__lowerCamelCase          =      list(_flat_idx_to_idx(lowercase__,			lowercase__     )     )
			# _get_minimal_slice_set is inclusive
			__lowerCamelCase          =      list(_flat_idx_to_idx(flat_end - 1,			lowercase__     )     )

			# Get an ordered list of slices to perform
			__lowerCamelCase          =      _get_minimal_slice_set(
			    lowercase__,			lowercase__,			lowercase__,			)

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

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





def       a_ (	lowercase__ :Callable,			lowercase__ :Dict[str, Any],			lowercase__ :int,			lowercase__ :int,			lowercase__ :bool = False,			lowercase__ :Any = None,			lowercase__ :bool = False,			):
			if not (len(lowercase__     ) > 0):
						raise ValueError("""Must provide at least one input"""     )

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

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

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

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

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

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

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

						__lowerCamelCase          =      tensor_tree_map(lowercase__,			lowercase__     )

						# Run the layer on the chunk
						__lowerCamelCase          =      layer(**lowercase__     )

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

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

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

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

						i += chunk_size

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

			return out




class 			__snake_case   :




							def __init__(     self:    Union[str, Any]     ,							A_:    int = 5_12     ,							):
										__lowerCamelCase          =      max_chunk_size
										__lowerCamelCase          =      None
										__lowerCamelCase          =      None




							def   __a   (     self:    Tuple     ,							A_:    Callable     ,							A_:    tuple     ,							A_:    int   ):
										logging.info("""Tuning chunk size..."""   )

										if min_chunk_size >= self.max_chunk_size:
													return min_chunk_size

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

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

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

										return candidates[min_viable_chunk_size_index]




							def   __a   (     self:    Tuple     ,							A_:    Iterable     ,							A_:    Iterable   ):
										__lowerCamelCase          =      True
										for aa, aa in zip(A_     ,							A_   ):
													assert type(A_   ) == type(A_   )
													if isinstance(A_     ,							(list, tuple)   ):
																consistent &= self._compare_arg_caches(A_     ,							A_   )
													elif isinstance(A_     ,							A_   ):
																__lowerCamelCase          =      [v for _, v in sorted(aa.items()     ,							key=lambda A_   : x[0]   )]
																__lowerCamelCase          =      [v for _, v in sorted(aa.items()     ,							key=lambda A_   : x[0]   )]
																consistent &= self._compare_arg_caches(A_     ,							A_   )
													else:
																consistent &= aa == aa

										return consistent




							def   __a   (     self:    str     ,							A_:    Callable     ,							A_:    tuple     ,							A_:    int     ,							):
										__lowerCamelCase          =      True
										__lowerCamelCase          =      tree_map(lambda A_   : a.shape if isinstance(A_     ,							torch.Tensor   ) else a     ,							A_     ,							A_   )
										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(A_   )
													__lowerCamelCase          =      self._compare_arg_caches(self.cached_arg_data     ,							A_   )
										else:
													# Otherwise, we can reuse the precomputed value
													__lowerCamelCase          =      False

										if not consistent:
													__lowerCamelCase          =      self._determine_favorable_chunk_size(
													    A_     ,							A_     ,							A_     ,							)
													__lowerCamelCase          =      arg_data

										assert self.cached_chunk_size is not None

										return self.cached_chunk_size




