






import inspect
from typing import List, Optional, Tuple, Union

import numpy as np
import PIL
import torch
import torch.utils.checkpoint

from ...models import UNetaDModel, VQModel
from ...schedulers import (
    DDIMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    LMSDiscreteScheduler,
    PNDMScheduler,
)
from ...utils import PIL_INTERPOLATION, randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput

def _UpperCAmelCase   (	a						:	Tuple ):
							snake_case__  , snake_case__	  =       image.size
							snake_case__  , snake_case__	  =       (x - x % 32 for x in (w, h))  # resize to integer multiple of 32
							snake_case__	  =       image.resize((w, h)  ,					resample=PIL_INTERPOLATION["""lanczos"""] )
							snake_case__	  =       np.array(a ).astype(np.floataa ) / 255.0
							snake_case__	  =       image[None].transpose(0  ,					3  ,					1  ,					2 )
							snake_case__	  =       torch.from_numpy(a )
							return 2.0 * image - 1.0



class    _lowerCAmelCase			(		lowercase_      ):



				"""simple docstring"""



				def __init__(      self    :    Optional[int]			,		UpperCamelCase__    :    VQModel			,		UpperCamelCase__    :    UNetaDModel			,		UpperCamelCase__    :    Union[
				        DDIMScheduler,
				        PNDMScheduler,
				        LMSDiscreteScheduler,
				        EulerDiscreteScheduler,
				        EulerAncestralDiscreteScheduler,
				        DPMSolverMultistepScheduler,
				    ]			,		):






											'''simple docstring'''







											super().__init__()
											self.register_modules(vqvae=UpperCamelCase__			,		unet=UpperCamelCase__			,		scheduler=UpperCamelCase__)



				@torch.no_grad()
				def __call__(      self    :    int			,		UpperCamelCase__    :    Union[torch.Tensor, PIL.Image.Image] = None			,		UpperCamelCase__    :    Optional[int] = 1			,		UpperCamelCase__    :    Optional[int] = 1_0_0			,		UpperCamelCase__    :    Optional[float] = 0.0			,		UpperCamelCase__    :    Optional[Union[torch.Generator, List[torch.Generator]]] = None			,		UpperCamelCase__    :    Optional[str] = "pil"			,		UpperCamelCase__    :    bool = True			,		):






											'''simple docstring'''







											if isinstance(UpperCamelCase__			,		PIL.Image.Image):
																		snake_case__	  =       1
											elif isinstance(UpperCamelCase__			,		torch.Tensor):
																		snake_case__	  =       image.shape[0]
											else:
																		raise ValueError(F'''`image` has to be of type `PIL.Image.Image` or `torch.Tensor` but is {type(UpperCamelCase__)}''')

											if isinstance(UpperCamelCase__			,		PIL.Image.Image):
																		snake_case__	  =       preprocess(UpperCamelCase__)

											snake_case__  , snake_case__	  =       image.shape[-2:]

											# in_channels should be 6: 3 for latents, 3 for low resolution image
											snake_case__	  =       (batch_size, self.unet.config.in_channels // 2, height, width)
											snake_case__	  =       next(self.unet.parameters()).dtype

											snake_case__	  =       randn_tensor(UpperCamelCase__			,		generator=UpperCamelCase__			,		device=self.device			,		dtype=UpperCamelCase__)

											snake_case__	  =       image.to(device=self.device			,		dtype=UpperCamelCase__)

											# set timesteps and move to the correct device
											self.scheduler.set_timesteps(UpperCamelCase__			,		device=self.device)
											snake_case__	  =       self.scheduler.timesteps

											# scale the initial noise by the standard deviation required by the scheduler
											snake_case__	  =       latents * self.scheduler.init_noise_sigma

											# prepare extra kwargs for the scheduler step, since not all schedulers have the same signature.
											# eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
											# eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
											# and should be between [0, 1]
											snake_case__	  =       """eta""" in set(inspect.signature(self.scheduler.step).parameters.keys())
											snake_case__	  =       {}
											if accepts_eta:
																		snake_case__	  =       eta

											for t in self.progress_bar(UpperCamelCase__):
																		# concat latents and low resolution image in the channel dimension.
																		snake_case__	  =       torch.cat([latents, image]			,		dim=1)
																		snake_case__	  =       self.scheduler.scale_model_input(UpperCamelCase__			,		UpperCamelCase__)
																		# predict the noise residual
																		snake_case__	  =       self.unet(UpperCamelCase__			,		UpperCamelCase__).sample
																		# compute the previous noisy sample x_t -> x_t-1
																		snake_case__	  =       self.scheduler.step(UpperCamelCase__			,		UpperCamelCase__			,		UpperCamelCase__			,		**UpperCamelCase__).prev_sample

											# decode the image latents with the VQVAE
											snake_case__	  =       self.vqvae.decode(UpperCamelCase__).sample
											snake_case__	  =       torch.clamp(UpperCamelCase__			,		-1.0			,		1.0)
											snake_case__	  =       image / 2 + 0.5
											snake_case__	  =       image.cpu().permute(0			,		2			,		3			,		1).numpy()

											if output_type == "pil":
																		snake_case__	  =       self.numpy_to_pil(UpperCamelCase__)

											if not return_dict:
																		return (image,)

											return ImagePipelineOutput(images=UpperCamelCase__)








def _UpperCAmelCase   (	a						:	int = 1000 ):
							snake_case__  , snake_case__	  =       1, 1
							snake_case__	  =       2
							while True:
														snake_case__	  =       0
														snake_case__	  =       fa + fa
														snake_case__  , snake_case__	  =       fa, f
														index += 1
														for _ in str(a ):
																					i += 1
														if i == n:
																					break
							return index


if __name__ == "__main__":
	print(solution(int(str(input()).strip())))
