






'''simple docstring'''



from __future__ import annotations



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	tuple[int, int],					SCREAMING_SNAKE_CASE__:	int    )  ->			list[tuple[int, int]]:

   """simple docstring"""
   __a     ,			__a				     =    position
   __a				     =    [
       (y + 1, x + 2),
       (y - 1, x + 2),
       (y + 1, x - 2),
       (y - 1, x - 2),
       (y + 2, x + 1),
       (y + 2, x - 1),
       (y - 2, x + 1),
       (y - 2, x - 1),
   ]
   __a				     =    []

   for position in positions:
      __a     ,			__a				     =    position
      if 0 <= y_test < n and 0 <= x_test < n:
         permissible_positions.append(SCREAMING_SNAKE_CASE__    )

   return permissible_positions



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	list[list[int]]    )  ->			bool:

   """simple docstring"""
   return not any(elem == 0 for row in board for elem in row    )



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	list[list[int]],					SCREAMING_SNAKE_CASE__:	tuple[int, int],					SCREAMING_SNAKE_CASE__:	int    )  ->			bool:

   """simple docstring"""

   if is_complete(SCREAMING_SNAKE_CASE__    ):
      return True

   for position in get_valid_pos(SCREAMING_SNAKE_CASE__,					len(SCREAMING_SNAKE_CASE__    )    ):
      __a     ,			__a				     =    position

      if board[y][x] == 0:
         __a				     =    curr + 1
         if open_knight_tour_helper(SCREAMING_SNAKE_CASE__,					SCREAMING_SNAKE_CASE__,					curr + 1    ):
            return True
         __a				     =    0

   return False



def    __UpperCAmelCase	(				SCREAMING_SNAKE_CASE__:	int    )  ->			list[list[int]]:

   """simple docstring"""
   __a				     =    [[0 for i in range(SCREAMING_SNAKE_CASE__    )] for j in range(SCREAMING_SNAKE_CASE__    )]

   for i in range(SCREAMING_SNAKE_CASE__    ):
      for j in range(SCREAMING_SNAKE_CASE__    ):
         __a				     =    1
         if open_knight_tour_helper(SCREAMING_SNAKE_CASE__,					(i, j),					1    ):
            return board
         __a				     =    0

   __a				     =    f"""Open Kight Tour cannot be performed on a board of size {n}"""
   raise ValueError(SCREAMING_SNAKE_CASE__    )


if __name__ == "__main__":
 import doctest

 doctest.testmod()







'''simple docstring'''



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	(				SCREAMING_SNAKE_CASE__:	List[Any]    )  ->			Dict:

   """simple docstring"""
   __a     ,			__a				     =    image.size
   __a     ,			__a				     =    (x - x % 32 for x in (w, h))  # resize to integer multiple of 32
   __a				     =    image.resize((w, h),					resample=PIL_INTERPOLATION['lanczos']    )
   __a				     =    np.array(SCREAMING_SNAKE_CASE__    ).astype(np.floataa    ) / 2_5_5.0
   __a				     =    image[None].transpose(0,					3,					1,					2    )
   __a				     =    torch.from_numpy(SCREAMING_SNAKE_CASE__    )
   return 2.0 * image - 1.0



class 							__SCREAMING_SNAKE_CASE       (							_lowerCAmelCase     ):




      def __init__(  self ,   lowerCamelCase ,   lowerCamelCase ,   lowerCamelCase ,   )							->Dict:



         '''simple docstring'''
         super().__init__()
         self.register_modules(vqvae=lowerCamelCase ,   unet=lowerCamelCase ,   scheduler=lowerCamelCase      )






      @torch.no_grad()
      def __call__(  self ,   lowerCamelCase = None ,   lowerCamelCase = 1 ,   lowerCamelCase = 100 ,   lowerCamelCase = 0.0 ,   lowerCamelCase = None ,   lowerCamelCase = "pil" ,   lowerCamelCase = True ,   )							->Union[Tuple, ImagePipelineOutput]:



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

         if isinstance(lowerCamelCase ,   PIL.Image.Image      ):
            __a				     =    preprocess(lowerCamelCase      )

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

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

         __a				     =    randn_tensor(lowerCamelCase ,   generator=lowerCamelCase ,   device=self.device ,   dtype=lowerCamelCase      )

         __a				     =    image.to(device=self.device ,   dtype=lowerCamelCase      )

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

         # scale the initial noise by the standard deviation required by the scheduler
         __a				     =    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]
         __a				     =    'eta' in set(inspect.signature(self.scheduler.step      ).parameters.keys()      )
         __a				     =    {}
         if accepts_eta:
            __a				     =    eta

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

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

         if output_type == "pil":
            __a				     =    self.numpy_to_pil(lowerCamelCase      )

         if not return_dict:
            return (image,)

         return ImagePipelineOutput(images=lowerCamelCase      )