



def    lowerCamelCase_(lowerCamelCase_ = 600_851_475_143    ) ->       int:

						try:
												UpperCAmelCase         =     int(lowerCamelCase_    )
						except (TypeError, ValueError):
												raise TypeError("Parameter n must be int or castable to int."    )
						if n <= 0:
												raise ValueError("Parameter n must be greater than or equal to one."    )
						UpperCAmelCase         =     1
						UpperCAmelCase         =     2
						while i * i <= n:
												while n % i == 0:
																		UpperCAmelCase         =     i
																		n //= i
												i += 1
						if n > 1:
												UpperCAmelCase         =     n
						return int(lowerCamelCase_    )


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








from dataclasses import dataclass
from typing import Dict, Optional, Tuple, Union

import torch
import torch.nn as nn

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, apply_forward_hook
from .attention_processor import AttentionProcessor, AttnProcessor
from .modeling_utils import ModelMixin
from .vae import Decoder, DecoderOutput, DiagonalGaussianDistribution, Encoder





@dataclass
class  __magic_name__   (							A__						):
		lowercase      :       "DiagonalGaussianDistribution"





class  __magic_name__   (							A__,  A__						):
		lowercase      :       Union[str, Any]          =True






		@register_to_config
		def __init__(						self      :     List[str]				,		UpperCamelCase__      :     int = 3				,		UpperCamelCase__      :     int = 3				,		UpperCamelCase__      :     Tuple[str] = ("DownEncoderBlock2D",)				,		UpperCamelCase__      :     Tuple[str] = ("UpDecoderBlock2D",)				,		UpperCamelCase__      :     Tuple[int] = (64,)				,		UpperCamelCase__      :     int = 1				,		UpperCamelCase__      :     str = "silu"				,		UpperCamelCase__      :     int = 4				,		UpperCamelCase__      :     int = 32				,		UpperCamelCase__      :     int = 32				,		UpperCamelCase__      :     float = 0.1_82_15				,		)				->					List[str]:
								'''simple docstring'''







								super().__init__()

								# pass init params to Encoder
								UpperCAmelCase         =     Encoder(
								    in_channels=UpperCamelCase__				,		out_channels=UpperCamelCase__				,		down_block_types=UpperCamelCase__				,		block_out_channels=UpperCamelCase__				,		layers_per_block=UpperCamelCase__				,		act_fn=UpperCamelCase__				,		norm_num_groups=UpperCamelCase__				,		double_z=UpperCamelCase__				,		)

								# pass init params to Decoder
								UpperCAmelCase         =     Decoder(
								    in_channels=UpperCamelCase__				,		out_channels=UpperCamelCase__				,		up_block_types=UpperCamelCase__				,		block_out_channels=UpperCamelCase__				,		layers_per_block=UpperCamelCase__				,		norm_num_groups=UpperCamelCase__				,		act_fn=UpperCamelCase__				,		)

								UpperCAmelCase         =     nn.Convad(2 * latent_channels				,		2 * latent_channels				,		1      )
								UpperCAmelCase         =     nn.Convad(UpperCamelCase__				,		UpperCamelCase__				,		1      )

								UpperCAmelCase         =     False
								UpperCAmelCase         =     False

								# only relevant if vae tiling is enabled
								UpperCAmelCase         =     self.config.sample_size
								UpperCAmelCase         =     (
								    self.config.sample_size[0]
								    if isinstance(self.config.sample_size				,		(list, tuple)      )
								    else self.config.sample_size
								)
								UpperCAmelCase         =     int(sample_size / (2 ** (len(self.config.block_out_channels      ) - 1))      )
								UpperCAmelCase         =     0.25






		def SCREAMING_SNAKE_CASE_			(						self      :     Dict				,		UpperCamelCase__      :     Optional[int]				,		UpperCamelCase__      :     int=False      )				->					Optional[int]:
								'''simple docstring'''







								if isinstance(UpperCamelCase__				,		(Encoder, Decoder)      ):
														UpperCAmelCase         =     value






		def SCREAMING_SNAKE_CASE_			(						self      :     Optional[int]				,		UpperCamelCase__      :     bool = True      )				->					Tuple:
								'''simple docstring'''







								UpperCAmelCase         =     use_tiling






		def SCREAMING_SNAKE_CASE_			(						self      :     List[Any]      )				->					Tuple:
								'''simple docstring'''







								self.enable_tiling(UpperCamelCase__      )






		def SCREAMING_SNAKE_CASE_			(						self      :     Any      )				->					Tuple:
								'''simple docstring'''







								UpperCAmelCase         =     True






		def SCREAMING_SNAKE_CASE_			(						self      :     Dict      )				->					List[str]:
								'''simple docstring'''







								UpperCAmelCase         =     False






		@property
		# Copied from diffusers.models.unet_2d_condition.UNet2DConditionModel.attn_processors
		def SCREAMING_SNAKE_CASE_			(						self      :     str      )				->					Dict[str, AttentionProcessor]:
								'''simple docstring'''







								UpperCAmelCase         =     {}

								def fn_recursive_add_processors(UpperCamelCase__      :     str				,		UpperCamelCase__      :     torch.nn.Module				,		UpperCamelCase__      :     Dict[str, AttentionProcessor]      ):
														if hasattr(UpperCamelCase__				,		"set_processor"      ):
																				UpperCAmelCase         =     module.processor

														for sub_name, child in module.named_children():
																				fn_recursive_add_processors(F'{name}.{sub_name}'				,		UpperCamelCase__				,		UpperCamelCase__      )

														return processors

								for name, module in self.named_children():
														fn_recursive_add_processors(UpperCamelCase__				,		UpperCamelCase__				,		UpperCamelCase__      )

								return processors






		def SCREAMING_SNAKE_CASE_			(						self      :     Union[str, Any]				,		UpperCamelCase__      :     Union[AttentionProcessor, Dict[str, AttentionProcessor]]      )				->					List[Any]:
								'''simple docstring'''







								UpperCAmelCase         =     len(self.attn_processors.keys()      )

								if isinstance(UpperCamelCase__				,		UpperCamelCase__      ) and len(UpperCamelCase__      ) != count:
														raise ValueError(
														    F'A dict of processors was passed, but the number of processors {len(UpperCamelCase__      )} does not match the'
														    F' number of attention layers: {count}. Please make sure to pass {count} processor classes.'      )

								def fn_recursive_attn_processor(UpperCamelCase__      :     str				,		UpperCamelCase__      :     torch.nn.Module				,		UpperCamelCase__      :     List[Any]      ):
														if hasattr(UpperCamelCase__				,		"set_processor"      ):
																				if not isinstance(UpperCamelCase__				,		UpperCamelCase__      ):
																										module.set_processor(UpperCamelCase__      )
																				else:
																										module.set_processor(processor.pop(F'{name}.processor'      )      )

														for sub_name, child in module.named_children():
																				fn_recursive_attn_processor(F'{name}.{sub_name}'				,		UpperCamelCase__				,		UpperCamelCase__      )

								for name, module in self.named_children():
														fn_recursive_attn_processor(UpperCamelCase__				,		UpperCamelCase__				,		UpperCamelCase__      )






		def SCREAMING_SNAKE_CASE_			(						self      :     Dict      )				->					Dict:
								'''simple docstring'''







								self.set_attn_processor(AttnProcessor()      )






		@apply_forward_hook
		def SCREAMING_SNAKE_CASE_			(						self      :     Any				,		UpperCamelCase__      :     torch.FloatTensor				,		UpperCamelCase__      :     bool = True      )				->					AutoencoderKLOutput:
								'''simple docstring'''







								if self.use_tiling and (x.shape[-1] > self.tile_sample_min_size or x.shape[-2] > self.tile_sample_min_size):
														return self.tiled_encode(UpperCamelCase__				,		return_dict=UpperCamelCase__      )

								if self.use_slicing and x.shape[0] > 1:
														UpperCAmelCase         =     [self.encoder(UpperCamelCase__      ) for x_slice in x.split(1      )]
														UpperCAmelCase         =     torch.cat(UpperCamelCase__      )
								else:
														UpperCAmelCase         =     self.encoder(UpperCamelCase__      )

								UpperCAmelCase         =     self.quant_conv(UpperCamelCase__      )
								UpperCAmelCase         =     DiagonalGaussianDistribution(UpperCamelCase__      )

								if not return_dict:
														return (posterior,)

								return AutoencoderKLOutput(latent_dist=UpperCamelCase__      )






		def SCREAMING_SNAKE_CASE_			(						self      :     List[str]				,		UpperCamelCase__      :     torch.FloatTensor				,		UpperCamelCase__      :     bool = True      )				->					Union[DecoderOutput, torch.FloatTensor]:
								'''simple docstring'''







								if self.use_tiling and (z.shape[-1] > self.tile_latent_min_size or z.shape[-2] > self.tile_latent_min_size):
														return self.tiled_decode(UpperCamelCase__				,		return_dict=UpperCamelCase__      )

								UpperCAmelCase         =     self.post_quant_conv(UpperCamelCase__      )
								UpperCAmelCase         =     self.decoder(UpperCamelCase__      )

								if not return_dict:
														return (dec,)

								return DecoderOutput(sample=UpperCamelCase__      )






		@apply_forward_hook
		def SCREAMING_SNAKE_CASE_			(						self      :     Any				,		UpperCamelCase__      :     torch.FloatTensor				,		UpperCamelCase__      :     bool = True      )				->					Union[DecoderOutput, torch.FloatTensor]:
								'''simple docstring'''







								if self.use_slicing and z.shape[0] > 1:
														UpperCAmelCase         =     [self._decode(UpperCamelCase__      ).sample for z_slice in z.split(1      )]
														UpperCAmelCase         =     torch.cat(UpperCamelCase__      )
								else:
														UpperCAmelCase         =     self._decode(UpperCamelCase__      ).sample

								if not return_dict:
														return (decoded,)

								return DecoderOutput(sample=UpperCamelCase__      )






		def SCREAMING_SNAKE_CASE_			(						self      :     Dict				,		UpperCamelCase__      :     Any				,		UpperCamelCase__      :     Tuple				,		UpperCamelCase__      :     Tuple      )				->					List[Any]:
								'''simple docstring'''







								UpperCAmelCase         =     min(a.shape[2]				,		b.shape[2]				,		UpperCamelCase__      )
								for y in range(UpperCamelCase__      ):
														UpperCAmelCase         =     a[:, :, -blend_extent + y, :] * (1 - y / blend_extent) + b[:, :, y, :] * (y / blend_extent)
								return b






		def SCREAMING_SNAKE_CASE_			(						self      :     str				,		UpperCamelCase__      :     Optional[Any]				,		UpperCamelCase__      :     Union[str, Any]				,		UpperCamelCase__      :     int      )				->					List[str]:
								'''simple docstring'''







								UpperCAmelCase         =     min(a.shape[3]				,		b.shape[3]				,		UpperCamelCase__      )
								for x in range(UpperCamelCase__      ):
														UpperCAmelCase         =     a[:, :, :, -blend_extent + x] * (1 - x / blend_extent) + b[:, :, :, x] * (x / blend_extent)
								return b






		def SCREAMING_SNAKE_CASE_			(						self      :     str				,		UpperCamelCase__      :     torch.FloatTensor				,		UpperCamelCase__      :     bool = True      )				->					AutoencoderKLOutput:
								'''simple docstring'''







								UpperCAmelCase         =     int(self.tile_sample_min_size * (1 - self.tile_overlap_factor)      )
								UpperCAmelCase         =     int(self.tile_latent_min_size * self.tile_overlap_factor      )
								UpperCAmelCase         =     self.tile_latent_min_size - blend_extent

								# Split the image into 512x512 tiles and encode them separately.
								UpperCAmelCase         =     []
								for i in range(0				,		x.shape[2]				,		UpperCamelCase__      ):
														UpperCAmelCase         =     []
														for j in range(0				,		x.shape[3]				,		UpperCamelCase__      ):
																				UpperCAmelCase         =     x[:, :, i : i + self.tile_sample_min_size, j : j + self.tile_sample_min_size]
																				UpperCAmelCase         =     self.encoder(UpperCamelCase__      )
																				UpperCAmelCase         =     self.quant_conv(UpperCamelCase__      )
																				row.append(UpperCamelCase__      )
														rows.append(UpperCamelCase__      )
								UpperCAmelCase         =     []
								for i, row in enumerate(UpperCamelCase__      ):
														UpperCAmelCase         =     []
														for j, tile in enumerate(UpperCamelCase__      ):
																				# blend the above tile and the left tile
																				# to the current tile and add the current tile to the result row
																				if i > 0:
																										UpperCAmelCase         =     self.blend_v(rows[i - 1][j]				,		UpperCamelCase__				,		UpperCamelCase__      )
																				if j > 0:
																										UpperCAmelCase         =     self.blend_h(row[j - 1]				,		UpperCamelCase__				,		UpperCamelCase__      )
																				result_row.append(tile[:, :, :row_limit, :row_limit]      )
														result_rows.append(torch.cat(UpperCamelCase__				,		dim=3      )      )

								UpperCAmelCase         =     torch.cat(UpperCamelCase__				,		dim=2      )
								UpperCAmelCase         =     DiagonalGaussianDistribution(UpperCamelCase__      )

								if not return_dict:
														return (posterior,)

								return AutoencoderKLOutput(latent_dist=UpperCamelCase__      )






		def SCREAMING_SNAKE_CASE_			(						self      :     List[Any]				,		UpperCamelCase__      :     torch.FloatTensor				,		UpperCamelCase__      :     bool = True      )				->					Union[DecoderOutput, torch.FloatTensor]:
								'''simple docstring'''







								UpperCAmelCase         =     int(self.tile_latent_min_size * (1 - self.tile_overlap_factor)      )
								UpperCAmelCase         =     int(self.tile_sample_min_size * self.tile_overlap_factor      )
								UpperCAmelCase         =     self.tile_sample_min_size - blend_extent

								# Split z into overlapping 64x64 tiles and decode them separately.
								# The tiles have an overlap to avoid seams between tiles.
								UpperCAmelCase         =     []
								for i in range(0				,		z.shape[2]				,		UpperCamelCase__      ):
														UpperCAmelCase         =     []
														for j in range(0				,		z.shape[3]				,		UpperCamelCase__      ):
																				UpperCAmelCase         =     z[:, :, i : i + self.tile_latent_min_size, j : j + self.tile_latent_min_size]
																				UpperCAmelCase         =     self.post_quant_conv(UpperCamelCase__      )
																				UpperCAmelCase         =     self.decoder(UpperCamelCase__      )
																				row.append(UpperCamelCase__      )
														rows.append(UpperCamelCase__      )
								UpperCAmelCase         =     []
								for i, row in enumerate(UpperCamelCase__      ):
														UpperCAmelCase         =     []
														for j, tile in enumerate(UpperCamelCase__      ):
																				# blend the above tile and the left tile
																				# to the current tile and add the current tile to the result row
																				if i > 0:
																										UpperCAmelCase         =     self.blend_v(rows[i - 1][j]				,		UpperCamelCase__				,		UpperCamelCase__      )
																				if j > 0:
																										UpperCAmelCase         =     self.blend_h(row[j - 1]				,		UpperCamelCase__				,		UpperCamelCase__      )
																				result_row.append(tile[:, :, :row_limit, :row_limit]      )
														result_rows.append(torch.cat(UpperCamelCase__				,		dim=3      )      )

								UpperCAmelCase         =     torch.cat(UpperCamelCase__				,		dim=2      )
								if not return_dict:
														return (dec,)

								return DecoderOutput(sample=UpperCamelCase__      )







		def SCREAMING_SNAKE_CASE_			(						self      :     List[str]				,		UpperCamelCase__      :     torch.FloatTensor				,		UpperCamelCase__      :     bool = False				,		UpperCamelCase__      :     bool = True				,		UpperCamelCase__      :     Optional[torch.Generator] = None				,		)				->					Union[DecoderOutput, torch.FloatTensor]:
								'''simple docstring'''







								UpperCAmelCase         =     sample
								UpperCAmelCase         =     self.encode(UpperCamelCase__      ).latent_dist
								if sample_posterior:
														UpperCAmelCase         =     posterior.sample(generator=UpperCamelCase__      )
								else:
														UpperCAmelCase         =     posterior.mode()
								UpperCAmelCase         =     self.decode(UpperCamelCase__      ).sample

								if not return_dict:
														return (dec,)

								return DecoderOutput(sample=UpperCamelCase__      )



