





'''simple docstring'''

import math





def lowerCamelCase						(     __lowerCamelCase :    int    )						->bool:
    _SCREAMING_SNAKE_CASE									=			math.loga(math.sqrt(4 * positive_integer + 1    ) / 2 + 1 / 2    )

    return exponent == int(__lowerCamelCase    )





def lowerCamelCase						(     __lowerCamelCase :    float = 1 / 1_2345    )						->int:
    _SCREAMING_SNAKE_CASE									=			0
    _SCREAMING_SNAKE_CASE									=			0

    _SCREAMING_SNAKE_CASE									=			3
    while True:
        _SCREAMING_SNAKE_CASE									=			(integer**2 - 1) / 4
        # if candidate is an integer, then there is a partition for k
        if partition_candidate == int(__lowerCamelCase    ):
            _SCREAMING_SNAKE_CASE									=			int(__lowerCamelCase    )
            total_partitions += 1
            if check_partition_perfect(__lowerCamelCase    ):
                perfect_partitions += 1
        if perfect_partitions > 0:
            if perfect_partitions / total_partitions < max_proportion:
                return int(__lowerCamelCase    )
        integer += 1


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







from dataclasses import dataclass
from typing import 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 .modeling_utils import ModelMixin
from .vae import Decoder, DecoderOutput, Encoder, VectorQuantizer





@dataclass
class       A    (   A_ ):
							UpperCamelCase_   :							torch.FloatTensor





class       A    (   A_					,				A_ ):


							@register_to_config
							def __init__(self      ,				lowerCAmelCase = 3      ,				lowerCAmelCase = 3      ,				lowerCAmelCase = ("DownEncoderBlock2D",)      ,				lowerCAmelCase = ("UpDecoderBlock2D",)      ,				lowerCAmelCase = (6_4,)      ,				lowerCAmelCase = 1      ,				lowerCAmelCase = "silu"      ,				lowerCAmelCase = 3      ,				lowerCAmelCase = 3_2      ,				lowerCAmelCase = 2_5_6      ,				lowerCAmelCase = 3_2      ,				lowerCAmelCase = None      ,				lowerCAmelCase = 0.1_82_15      ,				lowerCAmelCase = "group"      ,				):
									super().__init__()

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

									__lowercase=			vq_embed_dim if vq_embed_dim is not None else latent_channels

									__lowercase=			nn.Convad(lowerCAmelCase      ,				lowerCAmelCase      ,				1					)
									__lowercase=			VectorQuantizer(lowerCAmelCase      ,				lowerCAmelCase      ,				beta=0.25      ,				remap=lowerCAmelCase      ,				sane_index_shape=lowerCAmelCase					)
									__lowercase=			nn.Convad(lowerCAmelCase      ,				lowerCAmelCase      ,				1					)

									# pass init params to Decoder
									__lowercase=			Decoder(
									    in_channels=lowerCAmelCase      ,				out_channels=lowerCAmelCase      ,				up_block_types=lowerCAmelCase      ,				block_out_channels=lowerCAmelCase      ,				layers_per_block=lowerCAmelCase      ,				act_fn=lowerCAmelCase      ,				norm_num_groups=lowerCAmelCase      ,				norm_type=lowerCAmelCase      ,				)


							@apply_forward_hook
							def 			_A       (self      ,				lowerCAmelCase      ,				lowerCAmelCase = True					):
									__lowercase=			self.encoder(lowerCAmelCase					)
									__lowercase=			self.quant_conv(lowerCAmelCase					)

									if not return_dict:
											return (h,)

									return VQEncoderOutput(latents=lowerCAmelCase					)


							@apply_forward_hook
							def 			_A       (self      ,				lowerCAmelCase      ,				lowerCAmelCase = False      ,				lowerCAmelCase = True					):
									# also go through quantization layer
									if not force_not_quantize:
											__lowercase,							__lowercase,							__lowercase=			self.quantize(lowerCAmelCase					)
									else:
											__lowercase=			h
									__lowercase=			self.post_quant_conv(lowerCAmelCase					)
									__lowercase=			self.decoder(lowerCAmelCase      ,				quant if self.config.norm_type == 'spatial' else None					)

									if not return_dict:
											return (dec,)

									return DecoderOutput(sample=lowerCAmelCase					)







							def 			_A       (self      ,				lowerCAmelCase      ,				lowerCAmelCase = True					):
									__lowercase=			sample
									__lowercase=			self.encode(lowerCAmelCase					).latents
									__lowercase=			self.decode(lowerCAmelCase					).sample

									if not return_dict:
											return (dec,)

									return DecoderOutput(sample=lowerCAmelCase					)






