
from math import factorial

_UpperCAmelCase :			Optional[int]              =	{str(d): factorial(d) for d in range(10)}


def 				A	( lowercase			)       ->  int:
		'''simple docstring'''

		return sum(DIGIT_FACTORIAL[d] for d in str(lowercase			)			)


def 				A	( )       ->  int:
		'''simple docstring'''

		UpperCamelCase          =					7 * factorial(9			) + 1
		return sum(i for i in range(3   ,	lowercase			) if sum_of_digit_factorial(lowercase			) == i			)


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


from dataclasses import dataclass
from typing import Optional

import numpy as np
import torch
import torch.nn as nn

from ..utils import BaseOutput, is_torch_version, randn_tensor
from .attention_processor import SpatialNorm
from .unet_ad_blocks import UNetMidBlockaD, get_down_block, get_up_block


@dataclass
class     lowercase (		_SCREAMING_SNAKE_CASE       ):
		__lowercase	:	torch.FloatTensor






class     lowercase (		nn.Module       ):



		def __init__(			self    ,				A_=3    ,				A_=3    ,				A_=("DownEncoderBlock2D",)    ,				A_=(64,)    ,				A_=2    ,				A_=32    ,				A_="silu"    ,				A_=True    ,				)  -> List[Any]:
				"""simple docstring"""
				super().__init__()
				UpperCamelCase          =					layers_per_block

				UpperCamelCase          =					torch.nn.Convad(
				    A_    ,				block_out_channels[0]    ,				kernel_size=3    ,				stride=1    ,				padding=1    ,				)

				UpperCamelCase          =					None
				UpperCamelCase          =					nn.ModuleList([]	)

				# down
				UpperCamelCase          =					block_out_channels[0]
				for i, down_block_type in enumerate(A_	):
						UpperCamelCase          =					output_channel
						UpperCamelCase          =					block_out_channels[i]
						UpperCamelCase          =					i == len(A_	) - 1

						UpperCamelCase          =					get_down_block(
						    A_    ,				num_layers=self.layers_per_block    ,				in_channels=A_    ,				out_channels=A_    ,				add_downsample=not is_final_block    ,				resnet_eps=1e-6    ,				downsample_padding=0    ,				resnet_act_fn=A_    ,				resnet_groups=A_    ,				attention_head_dim=A_    ,				temb_channels=A_    ,				)
						self.down_blocks.append(A_	)

				# mid
				UpperCamelCase          =					UNetMidBlockaD(
				    in_channels=block_out_channels[-1]    ,				resnet_eps=1e-6    ,				resnet_act_fn=A_    ,				output_scale_factor=1    ,				resnet_time_scale_shift='default'    ,				attention_head_dim=block_out_channels[-1]    ,				resnet_groups=A_    ,				temb_channels=A_    ,				)

				# out
				UpperCamelCase          =					nn.GroupNorm(num_channels=block_out_channels[-1]    ,				num_groups=A_    ,				eps=1e-6	)
				UpperCamelCase          =					nn.SiLU()

				UpperCamelCase          =					2 * out_channels if double_z else out_channels
				UpperCamelCase          =					nn.Convad(block_out_channels[-1]    ,				A_    ,				3    ,				padding=1	)

				UpperCamelCase          =					False



		def __UpperCamelCase			(			self    ,				A_	)  -> Optional[Any]:
				"""simple docstring"""
				UpperCamelCase          =					x
				UpperCamelCase          =					self.conv_in(A_	)

				if self.training and self.gradient_checkpointing:

						def create_custom_forward(A_	):
								def custom_forward(*A_	):
										return module(*A_	)

								return custom_forward

						# down
						if is_torch_version('>='    ,				'1.11.0'	):
								for down_block in self.down_blocks:
										UpperCamelCase          =					torch.utils.checkpoint.checkpoint(
										    create_custom_forward(A_	)    ,				A_    ,				use_reentrant=A_	)
								# middle
								UpperCamelCase          =					torch.utils.checkpoint.checkpoint(
								    create_custom_forward(self.mid_block	)    ,				A_    ,				use_reentrant=A_	)
						else:
								for down_block in self.down_blocks:
										UpperCamelCase          =					torch.utils.checkpoint.checkpoint(create_custom_forward(A_	)    ,				A_	)
								# middle
								UpperCamelCase          =					torch.utils.checkpoint.checkpoint(create_custom_forward(self.mid_block	)    ,				A_	)

				else:
						# down
						for down_block in self.down_blocks:
								UpperCamelCase          =					down_block(A_	)

						# middle
						UpperCamelCase          =					self.mid_block(A_	)

				# post-process
				UpperCamelCase          =					self.conv_norm_out(A_	)
				UpperCamelCase          =					self.conv_act(A_	)
				UpperCamelCase          =					self.conv_out(A_	)

				return sample






class     lowercase (		nn.Module       ):



		def __init__(			self    ,				A_=3    ,				A_=3    ,				A_=("UpDecoderBlock2D",)    ,				A_=(64,)    ,				A_=2    ,				A_=32    ,				A_="silu"    ,				A_="group"    ,				)  -> Tuple:
				"""simple docstring"""
				super().__init__()
				UpperCamelCase          =					layers_per_block

				UpperCamelCase          =					nn.Convad(
				    A_    ,				block_out_channels[-1]    ,				kernel_size=3    ,				stride=1    ,				padding=1    ,				)

				UpperCamelCase          =					None
				UpperCamelCase          =					nn.ModuleList([]	)

				UpperCamelCase          =					in_channels if norm_type == 'spatial' else None

				# mid
				UpperCamelCase          =					UNetMidBlockaD(
				    in_channels=block_out_channels[-1]    ,				resnet_eps=1e-6    ,				resnet_act_fn=A_    ,				output_scale_factor=1    ,				resnet_time_scale_shift='default' if norm_type == 'group' else norm_type    ,				attention_head_dim=block_out_channels[-1]    ,				resnet_groups=A_    ,				temb_channels=A_    ,				)

				# up
				UpperCamelCase          =					list(reversed(A_	)	)
				UpperCamelCase          =					reversed_block_out_channels[0]
				for i, up_block_type in enumerate(A_	):
						UpperCamelCase          =					output_channel
						UpperCamelCase          =					reversed_block_out_channels[i]

						UpperCamelCase          =					i == len(A_	) - 1

						UpperCamelCase          =					get_up_block(
						    A_    ,				num_layers=self.layers_per_block + 1    ,				in_channels=A_    ,				out_channels=A_    ,				prev_output_channel=A_    ,				add_upsample=not is_final_block    ,				resnet_eps=1e-6    ,				resnet_act_fn=A_    ,				resnet_groups=A_    ,				attention_head_dim=A_    ,				temb_channels=A_    ,				resnet_time_scale_shift=A_    ,				)
						self.up_blocks.append(A_	)
						UpperCamelCase          =					output_channel

				# out
				if norm_type == "spatial":
						UpperCamelCase          =					SpatialNorm(block_out_channels[0]    ,				A_	)
				else:
						UpperCamelCase          =					nn.GroupNorm(num_channels=block_out_channels[0]    ,				num_groups=A_    ,				eps=1e-6	)
				UpperCamelCase          =					nn.SiLU()
				UpperCamelCase          =					nn.Convad(block_out_channels[0]    ,				A_    ,				3    ,				padding=1	)

				UpperCamelCase          =					False



		def __UpperCamelCase			(			self    ,				A_    ,				A_=None	)  -> Dict:
				"""simple docstring"""
				UpperCamelCase          =					z
				UpperCamelCase          =					self.conv_in(A_	)

				UpperCamelCase          =					next(iter(self.up_blocks.parameters()	)	).dtype
				if self.training and self.gradient_checkpointing:

						def create_custom_forward(A_	):
								def custom_forward(*A_	):
										return module(*A_	)

								return custom_forward

						if is_torch_version('>='    ,				'1.11.0'	):
								# middle
								UpperCamelCase          =					torch.utils.checkpoint.checkpoint(
								    create_custom_forward(self.mid_block	)    ,				A_    ,				A_    ,				use_reentrant=A_	)
								UpperCamelCase          =					sample.to(A_	)

								# up
								for up_block in self.up_blocks:
										UpperCamelCase          =					torch.utils.checkpoint.checkpoint(
										    create_custom_forward(A_	)    ,				A_    ,				A_    ,				use_reentrant=A_	)
						else:
								# middle
								UpperCamelCase          =					torch.utils.checkpoint.checkpoint(
								    create_custom_forward(self.mid_block	)    ,				A_    ,				A_	)
								UpperCamelCase          =					sample.to(A_	)

								# up
								for up_block in self.up_blocks:
										UpperCamelCase          =					torch.utils.checkpoint.checkpoint(create_custom_forward(A_	)    ,				A_    ,				A_	)
				else:
						# middle
						UpperCamelCase          =					self.mid_block(A_    ,				A_	)
						UpperCamelCase          =					sample.to(A_	)

						# up
						for up_block in self.up_blocks:
								UpperCamelCase          =					up_block(A_    ,				A_	)

        # post-process
				if latent_embeds is None:
						UpperCamelCase          =					self.conv_norm_out(A_	)
				else:
						UpperCamelCase          =					self.conv_norm_out(A_    ,				A_	)
				UpperCamelCase          =					self.conv_act(A_	)
				UpperCamelCase          =					self.conv_out(A_	)

				return sample






class     lowercase (		nn.Module       ):



		def __init__(			self    ,				A_    ,				A_    ,				A_    ,				A_=None    ,				A_="random"    ,				A_=False    ,				A_=True	)  -> Tuple:
				"""simple docstring"""
				super().__init__()
				UpperCamelCase          =					n_e
				UpperCamelCase          =					vq_embed_dim
				UpperCamelCase          =					beta
				UpperCamelCase          =					legacy

				UpperCamelCase          =					nn.Embedding(self.n_e    ,				self.vq_embed_dim	)
				self.embedding.weight.data.uniform_(-1.0 / self.n_e    ,				1.0 / self.n_e	)

				UpperCamelCase          =					remap
				if self.remap is not None:
						self.register_buffer('used'    ,				torch.tensor(np.load(self.remap	)	)	)
						UpperCamelCase          =					self.used.shape[0]
						UpperCamelCase          =					unknown_index  # "random" or "extra" or integer
						if self.unknown_index == "extra":
								UpperCamelCase          =					self.re_embed
								UpperCamelCase          =					self.re_embed + 1
						print(
						    F'''Remapping {self.n_e} indices to {self.re_embed} indices. '''
						    F'''Using {self.unknown_index} for unknown indices.'''	)
				else:
						UpperCamelCase          =					n_e

				UpperCamelCase          =					sane_index_shape



		def __UpperCamelCase			(			self    ,				A_	)  -> Dict:
				"""simple docstring"""
				UpperCamelCase          =					inds.shape
				assert len(A_	) > 1
				UpperCamelCase          =					inds.reshape(ishape[0]    ,				-1	)
				UpperCamelCase          =					self.used.to(A_	)
				UpperCamelCase          =					(inds[:, :, None] == used[None, None, ...]).long()
				UpperCamelCase          =					match.argmax(-1	)
				UpperCamelCase          =					match.sum(2	) < 1
				if self.unknown_index == "random":
						UpperCamelCase          =					torch.randint(0    ,				self.re_embed    ,				size=new[unknown].shape	).to(device=new.device	)
				else:
						UpperCamelCase          =					self.unknown_index
				return new.reshape(A_	)



		def __UpperCamelCase			(			self    ,				A_	)  -> List[str]:
				"""simple docstring"""
				UpperCamelCase          =					inds.shape
				assert len(A_	) > 1
				UpperCamelCase          =					inds.reshape(ishape[0]    ,				-1	)
				UpperCamelCase          =					self.used.to(A_	)
				if self.re_embed > self.used.shape[0]:  # extra token
						UpperCamelCase          =					0  # simply set to zero
				UpperCamelCase          =					torch.gather(used[None, :][inds.shape[0] * [0], :]    ,				1    ,				A_	)
				return back.reshape(A_	)



		def __UpperCamelCase			(			self    ,				A_	)  -> List[str]:
				"""simple docstring"""
				# reshape z -> (batch, height, width, channel) and flatten
				UpperCamelCase          =					z.permute(0    ,				2    ,				3    ,				1	).contiguous()
				UpperCamelCase          =					z.view(-1    ,				self.vq_embed_dim	)

				# distances from z to embeddings e_j (z - e)^2 = z^2 + e^2 - 2 e * z
				UpperCamelCase          =					torch.argmin(torch.cdist(A_    ,				self.embedding.weight	)    ,				dim=1	)

				UpperCamelCase          =					self.embedding(A_	).view(z.shape	)
				UpperCamelCase          =					None
				UpperCamelCase          =					None

				# compute loss for embedding
				if not self.legacy:
						UpperCamelCase          =					self.beta * torch.mean((z_q.detach() - z) ** 2	) + torch.mean((z_q - z.detach()) ** 2	)
				else:
						UpperCamelCase          =					torch.mean((z_q.detach() - z) ** 2	) + self.beta * torch.mean((z_q - z.detach()) ** 2	)

				# preserve gradients
				UpperCamelCase          =					z + (z_q - z).detach()

				# reshape back to match original input shape
				UpperCamelCase          =					z_q.permute(0    ,				3    ,				1    ,				2	).contiguous()

				if self.remap is not None:
						UpperCamelCase          =					min_encoding_indices.reshape(z.shape[0]    ,				-1	)  # add batch axis
						UpperCamelCase          =					self.remap_to_used(A_	)
						UpperCamelCase          =					min_encoding_indices.reshape(-1    ,				1	)  # flatten

				if self.sane_index_shape:
						UpperCamelCase          =					min_encoding_indices.reshape(z_q.shape[0]    ,				z_q.shape[2]    ,				z_q.shape[3]	)

				return z_q, loss, (perplexity, min_encodings, min_encoding_indices)



		def __UpperCamelCase			(			self    ,				A_    ,				A_	)  -> Optional[int]:
				"""simple docstring"""
				# shape specifying (batch, height, width, channel)
				if self.remap is not None:
						UpperCamelCase          =					indices.reshape(shape[0]    ,				-1	)  # add batch axis
						UpperCamelCase          =					self.unmap_to_all(A_	)
						UpperCamelCase          =					indices.reshape(-1	)  # flatten again

				# get quantized latent vectors
				UpperCamelCase          =					self.embedding(A_	)

				if shape is not None:
						UpperCamelCase          =					z_q.view(A_	)
						# reshape back to match original input shape
						UpperCamelCase          =					z_q.permute(0    ,				3    ,				1    ,				2	).contiguous()

				return z_q






class     lowercase (		_SCREAMING_SNAKE_CASE       ):



		def __init__(			self    ,				A_    ,				A_=False	)  -> Any:
				"""simple docstring"""
				UpperCamelCase          =					parameters
				UpperCamelCase     ,  UpperCamelCase          =					torch.chunk(A_    ,				2    ,				dim=1	)
				UpperCamelCase          =					torch.clamp(self.logvar    ,				-30.0    ,				20.0	)
				UpperCamelCase          =					deterministic
				UpperCamelCase          =					torch.exp(0.5 * self.logvar	)
				UpperCamelCase          =					torch.exp(self.logvar	)
				if self.deterministic:
						UpperCamelCase          =					UpperCamelCase          =					torch.zeros_like(
						    self.mean    ,				device=self.parameters.device    ,				dtype=self.parameters.dtype	)



		def __UpperCamelCase			(			self    ,				A_ = None	)  -> torch.FloatTensor:
				"""simple docstring"""
				# make sure sample is on the same device as the parameters and has same dtype
				UpperCamelCase          =					randn_tensor(
				    self.mean.shape    ,				generator=A_    ,				device=self.parameters.device    ,				dtype=self.parameters.dtype	)
				UpperCamelCase          =					self.mean + self.std * sample
				return x



		def __UpperCamelCase			(			self    ,				A_=None	)  -> Tuple:
				"""simple docstring"""
				if self.deterministic:
						return torch.Tensor([0.0]	)
				else:
						if other is None:
								return 0.5 * torch.sum(torch.pow(self.mean    ,				2	) + self.var - 1.0 - self.logvar    ,				dim=[1, 2, 3]	)
						else:
								return 0.5 * torch.sum(
								    torch.pow(self.mean - other.mean    ,				2	) / other.var
								    + self.var / other.var
								    - 1.0
								    - self.logvar
								    + other.logvar    ,				dim=[1, 2, 3]    ,				)



		def __UpperCamelCase			(			self    ,				A_    ,				A_=[1, 2, 3]	)  -> Optional[Any]:
				"""simple docstring"""
				if self.deterministic:
						return torch.Tensor([0.0]	)
				UpperCamelCase          =					np.log(2.0 * np.pi	)
				return 0.5 * torch.sum(logtwopi + self.logvar + torch.pow(sample - self.mean    ,				2	) / self.var    ,				dim=A_	)



		def __UpperCamelCase			(			self	)  -> Union[str, Any]:
				"""simple docstring"""
				return self.mean
