

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 						UpperCamelCase					(lowercase_: Union[dict, list, tuple, torch.Tensor]					)     ->      List[Tuple[int, ...]]:
	A__							:    int        =		[]
	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 						UpperCamelCase					(lowercase_: int    ,      lowercase_: Tuple[int, ...]					)     ->      Tuple[int, ...]:
	A__							:    Optional[int]        =		[]
	for d in reversed(lowercase_					):
		idx.append(flat_idx % d					)
		A__							:    List[str]        =		flat_idx // d

	return tuple(reversed(lowercase_					)					)

@torch.jit.ignore
def 						UpperCamelCase					(lowercase_: Sequence[int]    ,      lowercase_: Sequence[int]    ,      lowercase_: Sequence[int]    ,      lowercase_: Optional[Sequence[bool]] = None    ,      lowercase_: Optional[Sequence[bool]] = 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(lowercase_: List[bool]					) -> None:
		A__							:    str        =		True
		for i in range(len(lowercase_					)					):
			A__							:    Union[str, Any]        =		-1 * (i + 1)
			l[reversed_idx] &= tally
			A__							:    List[str]        =		l[reversed_idx]

	if start_edges is None:
		A__							:    Optional[int]        =		[s == 0 for s in start]
		reduce_edge_list(lowercase_					)
	if end_edges is None:
		A__							:    Optional[int]        =		[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					),)]

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

	# 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

	A__							:    Tuple[slice, ...]        =		tuple(lowercase_					)
	A__							:    Any        =		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

		A__							:    Tuple        =		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

		A__							:    Optional[Any]        =		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()					)
		A__							:    Tuple        =		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 						UpperCamelCase					(lowercase_: torch.Tensor    ,      lowercase_: int    ,      lowercase_: int    ,      lowercase_: int					)     ->      torch.Tensor:
	A__							:    Tuple        =		t.shape[:no_batch_dims]
	A__							:    Dict        =		list(_flat_idx_to_idx(lowercase_    ,      lowercase_					)					)
	# _get_minimal_slice_set is inclusive
	A__							:    Optional[int]        =		list(_flat_idx_to_idx(flat_end - 1    ,      lowercase_					)					)

	# Get an ordered list of slices to perform
	A__							:    Optional[Any]        =		_get_minimal_slice_set(
	    lowercase_    ,      lowercase_    ,      lowercase_    ,      )

	A__							:    int        =		[t[s] for s in slices]

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

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

	A__							:    str        =		[shape[:no_batch_dims] for shape in _fetch_dims(lowercase_					)]
	A__							:    Optional[int]        =		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:
				A__							:    str        =		t.expand(orig_batch_dims + t.shape[no_batch_dims:]					)
			A__							:    List[Any]        =		t.reshape(-1    ,      *t.shape[no_batch_dims:]					)
		else:
			A__							:    Optional[Any]        =		t.expand(orig_batch_dims + t.shape[no_batch_dims:]					)
		return t

	A__							:    Dict[str, Any]        =		tensor_tree_map(_prep_inputs    ,      lowercase_					)
	A__							:    List[Any]        =		None
	if _out is not None:
		A__							:    List[str]        =		tensor_tree_map(lambda lowercase_					: t.view([-1] + list(t.shape[no_batch_dims:]					)					)    ,      _out					)

	A__							:    Tuple        =		1
	for d in orig_batch_dims:
		flat_batch_dim *= d

	A__							:    Any        =		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

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

		A__							:    Dict[str, Any]        =		tensor_tree_map(lowercase_    ,      lowercase_					)

		# Run the layer on the chunk
		A__							:    Dict        =		layer(**lowercase_					)

		# Allocate space for the output
		if out is None:
			A__							:    Any        =		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:
							A__							:    str        =		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:
					A__							:    Optional[Any]        =		xa
		elif isinstance(lowercase_    ,      torch.Tensor					):
			if _add_into_out:
				out[i : i + chunk_size] += output_chunk
			else:
				A__							:    Tuple        =		output_chunk
		else:
			raise ValueError("""Not supported"""					)

		i += chunk_size

	A__							:    int        =		tensor_tree_map(lambda lowercase_					: t.view(orig_batch_dims + t.shape[1:]					)    ,      lowercase_					)

	return out



class     _a						:


					'''simple docstring'''






					def __init__( self    ,       A__ = 512    ,       ):
						A__							:    List[str]        =		max_chunk_size
						A__							:    Optional[int]        =		None
						A__							:    Optional[tuple]        =		None






					def   __A			( self    ,       A__    ,       A__    ,       A__			):
						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[Any]        =		[c for c in candidates if c > min_chunk_size]
						A__							:    Any        =		[min_chunk_size] + candidates
						candidates[-1] += 4

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

						A__							:    Optional[Any]        =		0
						A__							:    Tuple        =		len(A__			) - 1
						while i > min_viable_chunk_size_index:
							A__							:    Union[str, Any]        =		test_chunk_size(candidates[i]			)
							if not viable:
								A__							:    Union[str, Any]        =		(min_viable_chunk_size_index + i) // 2
							else:
								A__							:    Union[str, Any]        =		i
								A__							:    int        =		(i + len(A__			) - 1) // 2

						return candidates[min_viable_chunk_size_index]






					def   __A			( self    ,       A__    ,       A__			):
						A__							:    Dict        =		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__			):
								A__							:    List[Any]        =		[v for _, v in sorted(aa.items()    ,       key=lambda A__			: x[0]			)]
								A__							:    Tuple        =		[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    ,       A__    ,       A__    ,       A__    ,       ):
						A__							:    Tuple        =		True
						A__							:    tuple        =		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__			)
							A__							:    Optional[int]        =		self._compare_arg_caches(self.cached_arg_data    ,       A__			)
						else:
							# Otherwise, we can reuse the precomputed value
							A__							:    int        =		False

						if not consistent:
							A__							:    Optional[int]        =		self._determine_favorable_chunk_size(
							    A__    ,       A__    ,       A__    ,       )
							A__							:    Any        =		arg_data

						assert self.cached_chunk_size is not None

						return self.cached_chunk_size






import string

def 						UpperCamelCase					(lowercase_: str					)     ->      None:
	for key in range(len(string.ascii_uppercase					)					):
		A__							:    Dict        =		""""""
		for symbol in message:
			if symbol in string.ascii_uppercase:
				A__							:    Dict        =		string.ascii_uppercase.find(lowercase_					)
				A__							:    Optional[int]        =		num - key
				if num < 0:
					A__							:    Optional[int]        =		num + len(string.ascii_uppercase					)
				A__							:    Any        =		translated + string.ascii_uppercase[num]
			else:
				A__							:    Optional[Any]        =		translated + symbol
		print(f"""Decryption using Key #{key}: {translated}"""					)

def 						UpperCamelCase					()     ->      None:
	A__							:    Optional[Any]        =		input("""Encrypted message: """					)
	A__							:    Optional[Any]        =		message.upper()
	decrypt(lowercase_					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()



