


"""simple docstring"""


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

import torch
from transformers import CLIPImageProcessor, CLIPTextModel, CLIPTokenizer

from diffusers import DiffusionPipeline
from diffusers.models import AutoencoderKL, UNetaDConditionModel
from diffusers.pipelines.stable_diffusion import StableDiffusionPipelineOutput
from diffusers.pipelines.stable_diffusion.safety_checker import StableDiffusionSafetyChecker
from diffusers.schedulers import DDIMScheduler, LMSDiscreteScheduler, PNDMScheduler
from diffusers.utils import logging


A  :     Dict    					=    logging.get_logger(__name__)  # pylint: disable=invalid-name
class 						_UpperCamelCase						(     lowerCAmelCase__	):
							'''simple docstring'''







							def __init__(  self					,     __a					,     __a					,     __a					,     __a					,     __a					,     __a					,     __a					,     ):
										super().__init__()
										self.register_modules(
										    vae=__a					,     text_encoder=__a					,     tokenizer=__a					,     unet=__a					,     scheduler=__a					,     safety_checker=__a					,     feature_extractor=__a					,     )

							def     snake_case       (  self					,     __a = "auto"			):
										if slice_size == "auto":
													# half the attention head size is usually a good trade-off between
													# speed and memory
													__lowerCAmelCase       					=    self.unet.config.attention_head_dim // 2
										self.unet.set_attention_slice(__a			)

							def     snake_case       (  self			):
										self.enable_attention_slicing(__a			)



							@torch.no_grad()
							def __call__(  self					,     __a					,     __a = 5_12					,     __a = 5_12					,     __a = 50					,     __a = 7.5					,     __a = None					,     __a = 1					,     __a = 0.0					,     __a = None					,     __a = None					,     __a = "pil"					,     __a = True					,     __a = None					,     __a = 1					,     __a = None					,     **__a					,     ):

										if isinstance(__a					,     __a			):
													__lowerCAmelCase       					=    1
										elif isinstance(__a					,     __a			):
													__lowerCAmelCase       					=    len(__a			)
										else:
													raise ValueError(f"`prompt` has to be of type `str` or `list` but is {type(__a			)}"			)

										if height % 8 != 0 or width % 8 != 0:
													raise ValueError(f"`height` and `width` have to be divisible by 8 but are {height} and {width}."			)

										if (callback_steps is None) or (
										    callback_steps is not None and (not isinstance(__a					,     __a			) or callback_steps <= 0)
										):
													raise ValueError(
													    f"`callback_steps` has to be a positive integer but is {callback_steps} of type"
													    f" {type(__a			)}."			)

										# get prompt text embeddings
										__lowerCAmelCase       					=    self.tokenizer(
										    __a					,     padding="max_length"					,     max_length=self.tokenizer.model_max_length					,     return_tensors="pt"					,     )
										__lowerCAmelCase       					=    text_inputs.input_ids

										if text_input_ids.shape[-1] > self.tokenizer.model_max_length:
													__lowerCAmelCase       					=    self.tokenizer.batch_decode(text_input_ids[:, self.tokenizer.model_max_length :]			)
													logger.warning(
													    "The following part of your input was truncated because CLIP can only handle sequences up to"
													    f" {self.tokenizer.model_max_length} tokens: {removed_text}"			)
													__lowerCAmelCase       					=    text_input_ids[:, : self.tokenizer.model_max_length]

										if text_embeddings is None:
													__lowerCAmelCase       					=    self.text_encoder(text_input_ids.to(self.device			)			)[0]

										# duplicate text embeddings for each generation per prompt, using mps friendly method
										__lowerCAmelCase					,			__lowerCAmelCase					,			__lowerCAmelCase       					=    text_embeddings.shape
										__lowerCAmelCase       					=    text_embeddings.repeat(1					,     __a					,     1			)
										__lowerCAmelCase       					=    text_embeddings.view(bs_embed * num_images_per_prompt					,     __a					,     -1			)

										# here `guidance_scale` is defined analog to the guidance weight `w` of equation (2)
										# of the Imagen paper: https://arxiv.org/pdf/2205.11487.pdf . `guidance_scale = 1`
										# corresponds to doing no classifier free guidance.
										__lowerCAmelCase       					=    guidance_scale > 1.0
										# get unconditional embeddings for classifier free guidance
										if do_classifier_free_guidance:
													__lowerCAmelCase       					=    42
													if negative_prompt is None:
																__lowerCAmelCase       					=    [""]
													elif type(__a			) is not type(__a			):
																raise TypeError(
																    f"`negative_prompt` should be the same type to `prompt`, but got {type(__a			)} !="
																    f" {type(__a			)}."			)
													elif isinstance(__a					,     __a			):
																__lowerCAmelCase       					=    [negative_prompt]
													elif batch_size != len(__a			):
																raise ValueError(
																    f"`negative_prompt`: {negative_prompt} has batch size {len(__a			)}, but `prompt`:"
																    f" {prompt} has batch size {batch_size}. Please make sure that passed `negative_prompt` matches"
																    " the batch size of `prompt`."			)
													else:
																__lowerCAmelCase       					=    negative_prompt

													__lowerCAmelCase       					=    text_input_ids.shape[-1]
													__lowerCAmelCase       					=    self.tokenizer(
													    __a					,     padding="max_length"					,     max_length=__a					,     truncation=__a					,     return_tensors="pt"					,     )
													__lowerCAmelCase       					=    self.text_encoder(uncond_input.input_ids.to(self.device			)			)[0]

													# duplicate unconditional embeddings for each generation per prompt, using mps friendly method
													__lowerCAmelCase       					=    uncond_embeddings.shape[1]
													__lowerCAmelCase       					=    uncond_embeddings.repeat(__a					,     __a					,     1			)
													__lowerCAmelCase       					=    uncond_embeddings.view(batch_size * num_images_per_prompt					,     __a					,     -1			)

													# For classifier free guidance, we need to do two forward passes.
													# Here we concatenate the unconditional and text embeddings into a single batch
													# to avoid doing two forward passes
													__lowerCAmelCase       					=    torch.cat([uncond_embeddings, text_embeddings]			)

										# get the initial random noise unless the user supplied it

										# Unlike in other pipelines, latents need to be generated in the target device
										# for 1-to-1 results reproducibility with the CompVis implementation.
										# However this currently doesn't work in `mps`.
										__lowerCAmelCase       					=    (batch_size * num_images_per_prompt, self.unet.config.in_channels, height // 8, width // 8)
										__lowerCAmelCase       					=    (batch_size * num_images_per_prompt, self.unet.config.in_channels, 64, 64)
										__lowerCAmelCase       					=    text_embeddings.dtype
										if latents is None:
													if self.device.type == "mps":
																# randn does not exist on mps
																__lowerCAmelCase       					=    torch.randn(
																    __a					,     generator=__a					,     device="cpu"					,     dtype=__a			).to(self.device			)
																__lowerCAmelCase       					=    torch.randn(__a					,     generator=__a					,     device="cpu"					,     dtype=__a			).to(
																    self.device			)
													else:
																__lowerCAmelCase       					=    torch.randn(
																    __a					,     generator=__a					,     device=self.device					,     dtype=__a			)
																__lowerCAmelCase       					=    torch.randn(__a					,     generator=__a					,     device=self.device					,     dtype=__a			)
										else:
													if latents_reference.shape != latents_shape:
																raise ValueError(f"Unexpected latents shape, got {latents.shape}, expected {latents_shape}"			)
													__lowerCAmelCase       					=    latents_reference.to(self.device			)
													__lowerCAmelCase       					=    latents.to(self.device			)

										# This is the key part of the pipeline where we
										# try to ensure that the generated images w/ the same seed
										# but different sizes actually result in similar images
										__lowerCAmelCase       					=    (latents_shape[3] - latents_shape_reference[3]) // 2
										__lowerCAmelCase       					=    (latents_shape[2] - latents_shape_reference[2]) // 2
										__lowerCAmelCase       					=    latents_shape_reference[3] if dx >= 0 else latents_shape_reference[3] + 2 * dx
										__lowerCAmelCase       					=    latents_shape_reference[2] if dy >= 0 else latents_shape_reference[2] + 2 * dy
										__lowerCAmelCase       					=    0 if dx < 0 else dx
										__lowerCAmelCase       					=    0 if dy < 0 else dy
										__lowerCAmelCase       					=    max(-dx					,     0			)
										__lowerCAmelCase       					=    max(-dy					,     0			)
										# import pdb
										# pdb.set_trace()
										__lowerCAmelCase       					=    latents_reference[:, :, dy : dy + h, dx : dx + w]

										# set timesteps
										self.scheduler.set_timesteps(__a			)

										# Some schedulers like PNDM have timesteps as arrays
										# It's more optimized to move all timesteps to correct device beforehand
										__lowerCAmelCase       					=    self.scheduler.timesteps.to(self.device			)

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

										for i, t in enumerate(self.progress_bar(__a			)			):
													# expand the latents if we are doing classifier free guidance
													__lowerCAmelCase       					=    torch.cat([latents] * 2			) if do_classifier_free_guidance else latents
													__lowerCAmelCase       					=    self.scheduler.scale_model_input(__a					,     __a			)

													# predict the noise residual
													__lowerCAmelCase       					=    self.unet(__a					,     __a					,     encoder_hidden_states=__a			).sample

													# perform guidance
													if do_classifier_free_guidance:
																__lowerCAmelCase					,			__lowerCAmelCase       					=    noise_pred.chunk(2			)
																__lowerCAmelCase       					=    noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)

													# compute the previous noisy sample x_t -> x_t-1
													__lowerCAmelCase       					=    self.scheduler.step(__a					,     __a					,     __a					,     **__a			).prev_sample

													# call the callback, if provided
													if callback is not None and i % callback_steps == 0:
																callback(__a					,     __a					,     __a			)

										__lowerCAmelCase       					=    1 / 0.1_8_2_1_5 * latents
										__lowerCAmelCase       					=    self.vae.decode(__a			).sample

										__lowerCAmelCase       					=    (image / 2 + 0.5).clamp(0					,     1			)

										# we always cast to float32 as this does not cause significant overhead and is compatible with bfloat16
										__lowerCAmelCase       					=    image.cpu().permute(0					,     2					,     3					,     1			).float().numpy()

										if self.safety_checker is not None:
													__lowerCAmelCase       					=    self.feature_extractor(self.numpy_to_pil(__a			)					,     return_tensors="pt"			).to(
													    self.device			)
													__lowerCAmelCase					,			__lowerCAmelCase       					=    self.safety_checker(
													    images=__a					,     clip_input=safety_checker_input.pixel_values.to(text_embeddings.dtype			)			)
										else:
													__lowerCAmelCase       					=    None

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

										if not return_dict:
													return (image, has_nsfw_concept)

										return StableDiffusionPipelineOutput(images=__a					,     nsfw_content_detected=__a			)








"""simple docstring"""


from itertools import product


def _lowerCamelCase			(	_UpperCamelCase					,				_UpperCamelCase   ):

			'''simple docstring'''




			__lowerCAmelCase       					=    sides_number
			__lowerCAmelCase       					=    max_face_number * dice_number
			__lowerCAmelCase       					=    [0] * (max_total + 1)

			__lowerCAmelCase       					=    1
			__lowerCAmelCase       					=    range(_UpperCamelCase					,				max_face_number + 1   )
			for dice_numbers in product(_UpperCamelCase					,				repeat=_UpperCamelCase   ):
						__lowerCAmelCase       					=    sum(_UpperCamelCase   )
						totals_frequencies[total] += 1

			return totals_frequencies


def _lowerCamelCase			(	):

			'''simple docstring'''




			__lowerCAmelCase       					=    total_frequency_distribution(
			    sides_number=4					,				dice_number=9   )
			__lowerCAmelCase       					=    total_frequency_distribution(
			    sides_number=6					,				dice_number=6   )

			__lowerCAmelCase       					=    0
			__lowerCAmelCase       					=    9
			__lowerCAmelCase       					=    4 * 9
			__lowerCAmelCase       					=    6
			for peter_total in range(_UpperCamelCase					,				max_peter_total + 1   ):
						peter_wins_count += peter_totals_frequencies[peter_total] * sum(
						    colin_totals_frequencies[min_colin_total:peter_total]   )

			__lowerCAmelCase       					=    (4**9) * (6**6)
			__lowerCAmelCase       					=    peter_wins_count / total_games_number

			__lowerCAmelCase       					=    round(_UpperCamelCase					,				ndigits=7   )

			return rounded_peter_win_probability


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




