






from typing import List, Optional, Union

import numpy as np
import PIL
import torch
from PIL import Image

from ...models import UNetaDConditionModel, VQModel
from ...pipelines import DiffusionPipeline
from ...pipelines.pipeline_utils import ImagePipelineOutput
from ...schedulers import DDPMScheduler
from ...utils import (
    is_accelerate_available,
    is_accelerate_version,
    logging,
    randn_tensor,
    replace_example_docstring,
)


A_	:	Optional[Any]				=				logging.get_logger(__name__)  # pylint: disable=invalid-name

A_	:	Any				=				'\n    Examples:\n        ```py\n        >>> import torch\n        >>> import numpy as np\n\n        >>> from diffusers import KandinskyV22PriorEmb2EmbPipeline, KandinskyV22ControlnetImg2ImgPipeline\n        >>> from transformers import pipeline\n        >>> from diffusers.utils import load_image\n\n\n        >>> def make_hint(image, depth_estimator):\n        ...     image = depth_estimator(image)["depth"]\n        ...     image = np.array(image)\n        ...     image = image[:, :, None]\n        ...     image = np.concatenate([image, image, image], axis=2)\n        ...     detected_map = torch.from_numpy(image).float() / 255.0\n        ...     hint = detected_map.permute(2, 0, 1)\n        ...     return hint\n\n\n        >>> depth_estimator = pipeline("depth-estimation")\n\n        >>> pipe_prior = KandinskyV22PriorEmb2EmbPipeline.from_pretrained(\n        ...     "kandinsky-community/kandinsky-2-2-prior", torch_dtype=torch.float16\n        ... )\n        >>> pipe_prior = pipe_prior.to("cuda")\n\n        >>> pipe = KandinskyV22ControlnetImg2ImgPipeline.from_pretrained(\n        ...     "kandinsky-community/kandinsky-2-2-controlnet-depth", torch_dtype=torch.float16\n        ... )\n        >>> pipe = pipe.to("cuda")\n\n        >>> img = load_image(\n        ...     "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main"\n        ...     "/kandinsky/cat.png"\n        ... ).resize((768, 768))\n\n\n        >>> hint = make_hint(img, depth_estimator).unsqueeze(0).half().to("cuda")\n\n        >>> prompt = "A robot, 4k photo"\n        >>> negative_prior_prompt = "lowres, text, error, cropped, worst quality, low quality, jpeg artifacts, ugly, duplicate, morbid, mutilated, out of frame, extra fingers, mutated hands, poorly drawn hands, poorly drawn face, mutation, deformed, blurry, dehydrated, bad anatomy, bad proportions, extra limbs, cloned face, disfigured, gross proportions, malformed limbs, missing arms, missing legs, extra arms, extra legs, fused fingers, too many fingers, long neck, username, watermark, signature"\n\n        >>> generator = torch.Generator(device="cuda").manual_seed(43)\n\n        >>> img_emb = pipe_prior(prompt=prompt, image=img, strength=0.85, generator=generator)\n        >>> negative_emb = pipe_prior(prompt=negative_prior_prompt, image=img, strength=1, generator=generator)\n\n        >>> images = pipe(\n        ...     image=img,\n        ...     strength=0.5,\n        ...     image_embeds=img_emb.image_embeds,\n        ...     negative_image_embeds=negative_emb.image_embeds,\n        ...     hint=hint,\n        ...     num_inference_steps=50,\n        ...     generator=generator,\n        ...     height=768,\n        ...     width=768,\n        ... ).images\n\n        >>> images[0].save("robot_cat.png")\n        ```\n'

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__			,					UpperCAmelCase__=8						) ->       Any:
  UpperCamelCase_:      Union[str, Any]					   =       height // scale_factor**2
  if height % scale_factor**2 != 0:
    new_height += 1
  UpperCamelCase_:      Union[str, Any]					   =       width // scale_factor**2
  if width % scale_factor**2 != 0:
    new_width += 1
  return new_height * scale_factor, new_width * scale_factor

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__=5_1_2			,					UpperCAmelCase__=5_1_2						) ->       int:
  UpperCamelCase_:      List[str]					   =       pil_image.resize((w, h)			,					resample=Image.BICUBIC			,					reducing_gap=1						)
  UpperCamelCase_:      Union[str, Any]					   =       np.array(pil_image.convert('RGB'						)						)
  UpperCamelCase_:      str					   =       arr.astype(np.floataa						) / 127.5 - 1
  UpperCamelCase_:      Optional[Any]					   =       np.transpose(_A			,					[2, 0, 1]						)
  UpperCamelCase_:      List[str]					   =       torch.from_numpy(_A						).unsqueeze(0						)
  return image


class        _lowerCAmelCase( lowerCamelCase__      ):





       """simple docstring"""







       def __init__(      self						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    ):
         super().__init__()

         self.register_modules(
             unet=lowercase_						,    scheduler=lowercase_						,    movq=lowercase_						,    )
         UpperCamelCase_:      Dict					   =       2 ** (len(self.movq.config.block_out_channels							) - 1)





       def     _a					(      self						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase							):
         UpperCamelCase_:      Optional[int]					   =       min(int(num_inference_steps * strength							)						,    lowercase_							)

         UpperCamelCase_:      List[str]					   =       max(num_inference_steps - init_timestep						,    0							)
         UpperCamelCase_:      int					   =       self.scheduler.timesteps[t_start:]

         return timesteps, num_inference_steps - t_start





       def     _a					(      self						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase=None							):






         if not isinstance(lowercase_						,    (torch.Tensor, PIL.Image.Image, list)							):
           raise ValueError(
               f'''`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(lowercase_							)}'''							)

         UpperCamelCase_:      Dict					   =       image.to(device=lowercase_						,    dtype=lowercase_							)

         UpperCamelCase_:      List[Any]					   =       batch_size * num_images_per_prompt

         if image.shape[1] == 4:
           UpperCamelCase_:      Any					   =       image

         else:
           if isinstance(lowercase_						,    lowercase_							) and len(lowercase_							) != batch_size:
             raise ValueError(
                 f'''You have passed a list of generators of length {len(lowercase_							)}, but requested an effective batch'''
                 f''' size of {batch_size}. Make sure the batch size matches the length of the generators.'''							)

           elif isinstance(lowercase_						,    lowercase_							):
             UpperCamelCase_:      List[Any]					   =       [
                 self.movq.encode(image[i : i + 1]							).latent_dist.sample(generator[i]							) for i in range(lowercase_							)
             ]
             UpperCamelCase_:      List[Any]					   =       torch.cat(lowercase_						,    dim=0							)
           else:
             UpperCamelCase_:      Any					   =       self.movq.encode(lowercase_							).latent_dist.sample(lowercase_							)

           UpperCamelCase_:      List[Any]					   =       self.movq.config.scaling_factor * init_latents

         UpperCamelCase_:      List[Any]					   =       torch.cat([init_latents]						,    dim=0							)

         UpperCamelCase_:      Optional[Any]					   =       init_latents.shape
         UpperCamelCase_:      Dict					   =       randn_tensor(lowercase_						,    generator=lowercase_						,    device=lowercase_						,    dtype=lowercase_							)

         # get latents
         UpperCamelCase_:      List[str]					   =       self.scheduler.add_noise(lowercase_						,    lowercase_						,    lowercase_							)

         UpperCamelCase_:      Optional[Any]					   =       init_latents

         return latents





       def     _a					(      self						,    _lowerCamelCase=0							):






         if is_accelerate_available():
           from accelerate import cpu_offload
         else:
           raise ImportError('Please install accelerate via `pip install accelerate`'							)

         UpperCamelCase_:      Optional[Any]					   =       torch.device(f'''cuda:{gpu_id}'''							)

         UpperCamelCase_:      Union[str, Any]					   =       [
             self.unet,
             self.movq,
         ]
         for cpu_offloaded_model in models:
           if cpu_offloaded_model is not None:
             cpu_offload(lowercase_						,    lowercase_							)





       def     _a					(      self						,    _lowerCamelCase=0							):






         if is_accelerate_available() and is_accelerate_version('>='						,    '0.17.0.dev0'							):
           from accelerate import cpu_offload_with_hook
         else:
           raise ImportError('`enable_model_cpu_offload` requires `accelerate v0.17.0` or higher.'							)

         UpperCamelCase_:      Any					   =       torch.device(f'''cuda:{gpu_id}'''							)

         if self.device.type != "cpu":
           self.to('cpu'						,    silence_dtype_warnings=lowercase_							)
           torch.cuda.empty_cache()  # otherwise we don't see the memory savings (but they probably exist)

         UpperCamelCase_:      Tuple					   =       None
         for cpu_offloaded_model in [self.unet, self.movq]:
           UpperCamelCase_   ,UpperCamelCase_:      Optional[int]					   =       cpu_offload_with_hook(lowercase_						,    lowercase_						,    prev_module_hook=lowercase_							)

         # We'll offload the last model manually.
         UpperCamelCase_:      Any					   =       hook





       @property
       # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._execution_device
       def     _a					(      self							):






         if not hasattr(self.unet						,    '_hf_hook'							):
           return self.device
         for module in self.unet.modules():
           if (
               hasattr(lowercase_						,    '_hf_hook'							)
               and hasattr(module._hf_hook						,    'execution_device'							)
               and module._hf_hook.execution_device is not None
           ):
             return torch.device(module._hf_hook.execution_device							)
         return self.device





       @torch.no_grad()
       @replace_example_docstring(lowercase_							)
       def __call__(      self						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase						,    _lowerCamelCase = 5_1_2						,    _lowerCamelCase = 5_1_2						,    _lowerCamelCase = 1_0_0						,    _lowerCamelCase = 4.0						,    _lowerCamelCase = 0.3						,    _lowerCamelCase = 1						,    _lowerCamelCase = None						,    _lowerCamelCase = "pil"						,    _lowerCamelCase = True						,    ):
         UpperCamelCase_:      Optional[int]					   =       self._execution_device

         UpperCamelCase_:      Union[str, Any]					   =       guidance_scale > 1.0

         if isinstance(lowercase_						,    lowercase_							):
           UpperCamelCase_:      Union[str, Any]					   =       torch.cat(lowercase_						,    dim=0							)
         if isinstance(lowercase_						,    lowercase_							):
           UpperCamelCase_:      Any					   =       torch.cat(lowercase_						,    dim=0							)
         if isinstance(lowercase_						,    lowercase_							):
           UpperCamelCase_:      Union[str, Any]					   =       torch.cat(lowercase_						,    dim=0							)

         UpperCamelCase_:      List[Any]					   =       image_embeds.shape[0]

         if do_classifier_free_guidance:
           UpperCamelCase_:      Dict					   =       image_embeds.repeat_interleave(lowercase_						,    dim=0							)
           UpperCamelCase_:      Tuple					   =       negative_image_embeds.repeat_interleave(lowercase_						,    dim=0							)
           UpperCamelCase_:      Any					   =       hint.repeat_interleave(lowercase_						,    dim=0							)

         UpperCamelCase_:      Dict					   =       torch.cat([negative_image_embeds, image_embeds]						,    dim=0							).to(dtype=self.unet.dtype						,    device=lowercase_							)
         UpperCamelCase_:      int					   =       torch.cat([hint, hint]						,    dim=0							).to(dtype=self.unet.dtype						,    device=lowercase_							)

         if not isinstance(lowercase_						,    lowercase_							):
           UpperCamelCase_:      Union[str, Any]					   =       [image]
         if not all(isinstance(lowercase_						,    (PIL.Image.Image, torch.Tensor)							) for i in image							):
           raise ValueError(
               f'''Input is in incorrect format: {[type(lowercase_							) for i in image]}. Currently, we only support  PIL image and pytorch tensor'''							)

         UpperCamelCase_:      List[Any]					   =       torch.cat([prepare_image(lowercase_						,    lowercase_						,    lowercase_							) for i in image]						,    dim=0							)
         UpperCamelCase_:      int					   =       image.to(dtype=image_embeds.dtype						,    device=lowercase_							)

         UpperCamelCase_:      Optional[Any]					   =       self.movq.encode(lowercase_							)['latents']
         UpperCamelCase_:      int					   =       latents.repeat_interleave(lowercase_						,    dim=0							)
         self.scheduler.set_timesteps(lowercase_						,    device=lowercase_							)
         UpperCamelCase_   ,UpperCamelCase_:      Dict					   =       self.get_timesteps(lowercase_						,    lowercase_						,    lowercase_							)
         UpperCamelCase_:      Optional[Any]					   =       timesteps[:1].repeat(batch_size * num_images_per_prompt							)
         UpperCamelCase_   ,UpperCamelCase_:      Union[str, Any]					   =       downscale_height_and_width(lowercase_						,    lowercase_						,    self.movq_scale_factor							)
         UpperCamelCase_:      Tuple					   =       self.prepare_latents(
             lowercase_						,    lowercase_						,    lowercase_						,    lowercase_						,    image_embeds.dtype						,    lowercase_						,    lowercase_							)
         for i, t in enumerate(self.progress_bar(lowercase_							)							):
           # expand the latents if we are doing classifier free guidance
           UpperCamelCase_:      Tuple					   =       torch.cat([latents] * 2							) if do_classifier_free_guidance else latents

           UpperCamelCase_:      Dict					   =       {'image_embeds': image_embeds, 'hint': hint}
           UpperCamelCase_:      Any					   =       self.unet(
               sample=lowercase_						,    timestep=lowercase_						,    encoder_hidden_states=lowercase_						,    added_cond_kwargs=lowercase_						,    return_dict=lowercase_						,    )[0]

           if do_classifier_free_guidance:
             UpperCamelCase_   ,UpperCamelCase_:      Dict					   =       noise_pred.split(latents.shape[1]						,    dim=1							)
             UpperCamelCase_   ,UpperCamelCase_:      List[Any]					   =       noise_pred.chunk(2							)
             UpperCamelCase_   ,UpperCamelCase_:      Any					   =       variance_pred.chunk(2							)
             UpperCamelCase_:      Any					   =       noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
             UpperCamelCase_:      Tuple					   =       torch.cat([noise_pred, variance_pred_text]						,    dim=1							)

           if not (
               hasattr(self.scheduler.config						,    'variance_type'							)
               and self.scheduler.config.variance_type in ["learned", "learned_range"]
           ):
             UpperCamelCase_   ,UpperCamelCase_:      int					   =       noise_pred.split(latents.shape[1]						,    dim=1							)

           # compute the previous noisy sample x_t -> x_t-1

           UpperCamelCase_:      int					   =       self.scheduler.step(
               lowercase_						,    lowercase_						,    lowercase_						,    generator=lowercase_						,    )[0]

         # post-processing
         UpperCamelCase_:      int					   =       self.movq.decode(lowercase_						,    force_not_quantize=lowercase_							)['sample']

         if output_type not in ["pt", "np", "pil"]:
           raise ValueError(f'''Only the output types `pt`, `pil` and `np` are supported not output_type={output_type}'''							)

         if output_type in ["np", "pil"]:
           UpperCamelCase_:      Union[str, Any]					   =       image * 0.5 + 0.5
           UpperCamelCase_:      List[Any]					   =       image.clamp(0						,    1							)
           UpperCamelCase_:      Optional[Any]					   =       image.cpu().permute(0						,    2						,    3						,    1							).float().numpy()

         if output_type == "pil":
           UpperCamelCase_:      Tuple					   =       self.numpy_to_pil(lowercase_							)

         if not return_dict:
           return (image,)

         return ImagePipelineOutput(images=lowercase_							)







from math import factorial

def 						snake_case      (UpperCAmelCase__			,					UpperCAmelCase__						) ->       Dict:
  return factorial(UpperCAmelCase__						) / (factorial(UpperCAmelCase__						) * factorial(n - r						))

def 						snake_case      () ->       Optional[Any]:
  UpperCamelCase_:      int					   =       0

  for i in range(1			,					1_0_1						):
    for j in range(1			,					i + 1						):
      if combinations(UpperCAmelCase__			,					UpperCAmelCase__						) > 1E6:
        total += 1
  return total


if __name__ == "__main__":
   print(solution())