





import sys

__UpperCAmelCase	:       Optional[int]    	=							(
    "73167176531330624919225119674426574742355349194934"
    "96983520312774506326239578318016984801869478851843"
    "85861560789112949495459501737958331952853208805511"
    "12540698747158523863050715693290963295227443043557"
    "66896648950445244523161731856403098711121722383113"
    "62229893423380308135336276614282806444486645238749"
    "30358907296290491560440772390713810515859307960866"
    "70172427121883998797908792274921901699720888093776"
    "65727333001053367881220235421809751254540594752243"
    "52584907711670556013604839586446706324415722155397"
    "53697817977846174064955149290862569321978468622482"
    "83972241375657056057490261407972968652414535100474"
    "82166370484403199890008895243450658541227588666881"
    "16427171479924442928230863465674813919123162824586"
    "17866458359124566529476545682848912883142607690042"
    "24219022671055626321111109370544217506941658960408"
    "07198403850962455444362981230987879927244284909188"
    "84580156166097919133875499200524063689912560717606"
    "05886116467109405077541002256983155200055935729725"
    "71636269561882670428252483600823257530420752963450"
)







def       A__							(   SCREAMING_SNAKE_CASE__)       ->   int:
  __snake_case:						Dict			  =						1
  for digit in s:
    product *= int(SCREAMING_SNAKE_CASE__)
  return product







def       A__							(   SCREAMING_SNAKE_CASE__ = N)       ->   int:
  __snake_case:						Optional[int]			  =						-sys.maxsize - 1
  __snake_case:						Optional[Any]			  =						n[:13]
  __snake_case:						str			  =						13
  while cur_index < len(SCREAMING_SNAKE_CASE__) - 13:
    if int(n[cur_index]) >= int(substr[0]):
      __snake_case:						Optional[Any]			  =						substr[1:] + n[cur_index]
      cur_index += 1
    else:
      __snake_case:						int			  =						max(SCREAMING_SNAKE_CASE__ , str_eval(SCREAMING_SNAKE_CASE__))
      __snake_case:						Dict			  =						n[cur_index : cur_index + 13]
      cur_index += 13
  return largest_product


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    __snake_case	(							__lowerCamelCase      ):





       '''simple docstring'''







       lowerCAmelCase__						=					42







class    __snake_case	(							__lowerCamelCase       ,      __lowerCamelCase      ):





       '''simple docstring'''







       lowerCAmelCase__						=					True




       @register_to_config
       def __init__(  self			:   Union[str, Any]							,    A			:   int = 3							,    A			:   int = 3							,    A			:   Tuple[str] = ("DownEncoderBlock2D",)							,    A			:   Tuple[str] = ("UpDecoderBlock2D",)							,    A			:   Tuple[int] = (64,)							,    A			:   int = 1							,    A			:   str = "silu"							,    A			:   int = 4							,    A			:   int = 32							,    A			:   int = 32							,    A			:   float = 0.1_8215							,    ):
         super().__init__()

         # pass init params to Encoder
         __snake_case:						Any			  =						Encoder(
             in_channels=A							,    out_channels=A							,    down_block_types=A							,    block_out_channels=A							,    layers_per_block=A							,    act_fn=A							,    norm_num_groups=A							,    double_z=A							,    )

         # pass init params to Decoder
         __snake_case:						int			  =						Decoder(
             in_channels=A							,    out_channels=A							,    up_block_types=A							,    block_out_channels=A							,    layers_per_block=A							,    norm_num_groups=A							,    act_fn=A							,    )

         __snake_case:						Dict			  =						nn.Convad(2 * latent_channels							,    2 * latent_channels							,    1		)
         __snake_case:						int			  =						nn.Convad(A							,    A							,    1		)

         __snake_case:						List[str]			  =						False
         __snake_case:						Optional[int]			  =						False

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




       def 							UpperCAmelCase__			(  self			:   int							,    A			:   List[str]							,    A			:   Optional[Any]=False		):
         if isinstance(A							,    (Encoder, Decoder)		):
           __snake_case:						str			  =						value




       def 							UpperCAmelCase__			(  self			:   str							,    A			:   bool = True		):
         __snake_case:						Union[str, Any]			  =						use_tiling




       def 							UpperCAmelCase__			(  self			:   Optional[int]		):
         self.enable_tiling(A		)




       def 							UpperCAmelCase__			(  self			:   List[Any]		):
         __snake_case:						List[str]			  =						True




       def 							UpperCAmelCase__			(  self			:   List[str]		):
         __snake_case:						List[str]			  =						False




       @property
       # Copied from diffusers.models.unet_2d_condition.UNet2DConditionModel.attn_processors
       def 							UpperCAmelCase__			(  self			:   Tuple		):
         __snake_case:						Any			  =						{}

         def fn_recursive_add_processors(A			:   str							,    A			:   torch.nn.Module							,    A			:   Dict[str, AttentionProcessor]		):
           if hasattr(A							,    """set_processor"""		):
             __snake_case:						List[Any]			  =						module.processor

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

           return processors

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

         return processors




       def 							UpperCAmelCase__			(  self			:   Optional[int]							,    A			:   Union[AttentionProcessor, Dict[str, AttentionProcessor]]		):
         __snake_case:						Any			  =						len(self.attn_processors.keys()		)

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

         def fn_recursive_attn_processor(A			:   str							,    A			:   torch.nn.Module							,    A			:   Optional[Any]		):
           if hasattr(A							,    """set_processor"""		):
             if not isinstance(A							,    A		):
               module.set_processor(A		)
             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}'''							,    A							,    A		)

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




       def 							UpperCAmelCase__			(  self			:   List[str]		):
         self.set_attn_processor(AttnProcessor()		)




       @apply_forward_hook
       def 							UpperCAmelCase__			(  self			:   Optional[Any]							,    A			:   torch.FloatTensor							,    A			:   bool = True		):
         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(A							,    return_dict=A		)

         if self.use_slicing and x.shape[0] > 1:
           __snake_case:						List[Any]			  =						[self.encoder(A		) for x_slice in x.split(1		)]
           __snake_case:						Optional[Any]			  =						torch.cat(A		)
         else:
           __snake_case:						str			  =						self.encoder(A		)

         __snake_case:						Any			  =						self.quant_conv(A		)
         __snake_case:						Tuple			  =						DiagonalGaussianDistribution(A		)

         if not return_dict:
           return (posterior,)

         return AutoencoderKLOutput(latent_dist=A		)




       def 							UpperCAmelCase__			(  self			:   Tuple							,    A			:   torch.FloatTensor							,    A			:   bool = True		):
         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(A							,    return_dict=A		)

         __snake_case:						Optional[int]			  =						self.post_quant_conv(A		)
         __snake_case:						Union[str, Any]			  =						self.decoder(A		)

         if not return_dict:
           return (dec,)

         return DecoderOutput(sample=A		)




       @apply_forward_hook
       def 							UpperCAmelCase__			(  self			:   Tuple							,    A			:   torch.FloatTensor							,    A			:   bool = True		):
         if self.use_slicing and z.shape[0] > 1:
           __snake_case:						Union[str, Any]			  =						[self._decode(A		).sample for z_slice in z.split(1		)]
           __snake_case:						List[str]			  =						torch.cat(A		)
         else:
           __snake_case:						int			  =						self._decode(A		).sample

         if not return_dict:
           return (decoded,)

         return DecoderOutput(sample=A		)




       def 							UpperCAmelCase__			(  self			:   Any							,    A			:   Tuple							,    A			:   int							,    A			:   List[Any]		):
         __snake_case:						int			  =						min(a.shape[2]							,    b.shape[2]							,    A		)
         for y in range(A		):
           __snake_case:						Dict			  =						a[:, :, -blend_extent + y, :] * (1 - y / blend_extent) + b[:, :, y, :] * (y / blend_extent)
         return b




       def 							UpperCAmelCase__			(  self			:   Union[str, Any]							,    A			:   Optional[Any]							,    A			:   List[str]							,    A			:   List[str]		):
         __snake_case:						Dict			  =						min(a.shape[3]							,    b.shape[3]							,    A		)
         for x in range(A		):
           __snake_case:						Tuple			  =						a[:, :, :, -blend_extent + x] * (1 - x / blend_extent) + b[:, :, :, x] * (x / blend_extent)
         return b




       def 							UpperCAmelCase__			(  self			:   int							,    A			:   torch.FloatTensor							,    A			:   bool = True		):
         __snake_case:						List[str]			  =						int(self.tile_sample_min_size * (1 - self.tile_overlap_factor)		)
         __snake_case:						Dict			  =						int(self.tile_latent_min_size * self.tile_overlap_factor		)
         __snake_case:						Dict			  =						self.tile_latent_min_size - blend_extent

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

         __snake_case:						Tuple			  =						torch.cat(A							,    dim=2		)
         __snake_case:						Optional[int]			  =						DiagonalGaussianDistribution(A		)

         if not return_dict:
           return (posterior,)

         return AutoencoderKLOutput(latent_dist=A		)




       def 							UpperCAmelCase__			(  self			:   Union[str, Any]							,    A			:   torch.FloatTensor							,    A			:   bool = True		):
         __snake_case:						Optional[Any]			  =						int(self.tile_latent_min_size * (1 - self.tile_overlap_factor)		)
         __snake_case:						str			  =						int(self.tile_sample_min_size * self.tile_overlap_factor		)
         __snake_case:						int			  =						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.
         __snake_case:						List[Any]			  =						[]
         for i in range(0							,    z.shape[2]							,    A		):
           __snake_case:						Optional[Any]			  =						[]
           for j in range(0							,    z.shape[3]							,    A		):
             __snake_case:						Dict			  =						z[:, :, i : i + self.tile_latent_min_size, j : j + self.tile_latent_min_size]
             __snake_case:						Any			  =						self.post_quant_conv(A		)
             __snake_case:						Optional[Any]			  =						self.decoder(A		)
             row.append(A		)
           rows.append(A		)
         __snake_case:						Optional[Any]			  =						[]
         for i, row in enumerate(A		):
           __snake_case:						Optional[Any]			  =						[]
           for j, tile in enumerate(A		):
             # blend the above tile and the left tile
             # to the current tile and add the current tile to the result row
             if i > 0:
               __snake_case:						Tuple			  =						self.blend_v(rows[i - 1][j]							,    A							,    A		)
             if j > 0:
               __snake_case:						List[str]			  =						self.blend_h(row[j - 1]							,    A							,    A		)
             result_row.append(tile[:, :, :row_limit, :row_limit]		)
           result_rows.append(torch.cat(A							,    dim=3		)		)

         __snake_case:						Dict			  =						torch.cat(A							,    dim=2		)
         if not return_dict:
           return (dec,)

         return DecoderOutput(sample=A		)






       def 							UpperCAmelCase__			(  self			:   List[Any]							,    A			:   torch.FloatTensor							,    A			:   bool = False							,    A			:   bool = True							,    A			:   Optional[torch.Generator] = None							,    ):
         __snake_case:						Optional[Any]			  =						sample
         __snake_case:						Union[str, Any]			  =						self.encode(A		).latent_dist
         if sample_posterior:
           __snake_case:						Optional[Any]			  =						posterior.sample(generator=A		)
         else:
           __snake_case:						Dict			  =						posterior.mode()
         __snake_case:						Any			  =						self.decode(A		).sample

         if not return_dict:
           return (dec,)

         return DecoderOutput(sample=A		)






