

import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class        A_		(       SCREAMING_SNAKE_CASE				):
							_UpperCAmelCase    :  torch.FloatTensor
							_UpperCAmelCase    :  Optional[torch.FloatTensor]						      =      None






def    SCREAMING_SNAKE_CASE__       (  lowerCamelCase__	, lowerCamelCase__=0.999	, lowerCamelCase__="cosine"	, )  ->     Dict:
	if alpha_transform_type == "cosine":

		def alpha_bar_fn(lowerCamelCase__			):
			return math.cos((t + 0.008) / 1.008 * math.pi / 2			) ** 2

	elif alpha_transform_type == "exp":

		def alpha_bar_fn(lowerCamelCase__			):
			return math.exp(t * -12.0			)

	else:
		raise ValueError(F"Unsupported alpha_tranform_type: {alpha_transform_type}"			)

	__lowerCamelCase				:				List[Any]					       = []
	for i in range(lowerCamelCase__			):
		__lowerCamelCase				:				str					       = i / num_diffusion_timesteps
		__lowerCamelCase				:				Optional[int]					       = (i + 1) / num_diffusion_timesteps
		betas.append(min(1 - alpha_bar_fn(lowerCamelCase__			) / alpha_bar_fn(lowerCamelCase__			)	, lowerCamelCase__			)			)
	return torch.tensor(lowerCamelCase__	, dtype=torch.floataa			)






class        A_		(       SCREAMING_SNAKE_CASE			,							SCREAMING_SNAKE_CASE				):
							@register_to_config
							def __init__(		self		:			Tuple   ,SCREAMING_SNAKE_CASE__		:			int = 1_0_0_0   ,SCREAMING_SNAKE_CASE__		:			str = "fixed_small_log"   ,SCREAMING_SNAKE_CASE__		:			bool = True   ,SCREAMING_SNAKE_CASE__		:			Optional[float] = 1.0   ,SCREAMING_SNAKE_CASE__		:			str = "epsilon"   ,SCREAMING_SNAKE_CASE__		:			str = "squaredcos_cap_v2"   ,):
								if beta_schedule != "squaredcos_cap_v2":
									raise ValueError('UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\'')

								__lowerCamelCase				:				Tuple					       = betas_for_alpha_bar(SCREAMING_SNAKE_CASE__)

								__lowerCamelCase				:				int					       = 1.0 - self.betas
								__lowerCamelCase				:				List[str]					       = torch.cumprod(self.alphas   ,dim=0)
								__lowerCamelCase				:				str					       = torch.tensor(1.0)

								# standard deviation of the initial noise distribution
								__lowerCamelCase				:				Tuple					       = 1.0

								# setable values
								__lowerCamelCase				:				Optional[int]					       = None
								__lowerCamelCase				:				List[Any]					       = torch.from_numpy(np.arange(0   ,SCREAMING_SNAKE_CASE__)[::-1].copy())

								__lowerCamelCase				:				Optional[int]					       = variance_type
							def     lowerCAmelCase     (		self		:			List[Any]   ,SCREAMING_SNAKE_CASE__		:			torch.FloatTensor   ,SCREAMING_SNAKE_CASE__		:			Optional[int] = None):
								return sample
							def     lowerCAmelCase     (		self		:			List[Any]   ,SCREAMING_SNAKE_CASE__		:			int   ,SCREAMING_SNAKE_CASE__		:			Union[str, torch.device] = None):
								__lowerCamelCase				:				List[str]					       = num_inference_steps
								__lowerCamelCase				:				List[str]					       = (self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
								__lowerCamelCase				:				int					       = (np.arange(0   ,SCREAMING_SNAKE_CASE__) * step_ratio).round()[::-1].copy().astype(np.intaa)
								__lowerCamelCase				:				List[str]					       = torch.from_numpy(SCREAMING_SNAKE_CASE__).to(SCREAMING_SNAKE_CASE__)
							def     lowerCAmelCase     (		self		:			List[Any]   ,SCREAMING_SNAKE_CASE__		:			str   ,SCREAMING_SNAKE_CASE__		:			Optional[int]=None   ,SCREAMING_SNAKE_CASE__		:			List[Any]=None   ,SCREAMING_SNAKE_CASE__		:			Any=None):
								if prev_timestep is None:
									__lowerCamelCase				:				Any					       = t - 1

								__lowerCamelCase				:				List[str]					       = self.alphas_cumprod[t]
								__lowerCamelCase				:				Union[str, Any]					       = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
								__lowerCamelCase				:				Optional[int]					       = 1 - alpha_prod_t
								__lowerCamelCase				:				Dict					       = 1 - alpha_prod_t_prev

								if prev_timestep == t - 1:
									__lowerCamelCase				:				Any					       = self.betas[t]
								else:
									__lowerCamelCase				:				Dict					       = 1 - alpha_prod_t / alpha_prod_t_prev

								# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
								# and sample from it to get previous sample
								# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
								__lowerCamelCase				:				Union[str, Any]					       = beta_prod_t_prev / beta_prod_t * beta

								if variance_type is None:
									__lowerCamelCase				:				Tuple					       = self.config.variance_type

								# hacks - were probably added for training stability
								if variance_type == "fixed_small_log":
									__lowerCamelCase				:				Optional[int]					       = torch.log(torch.clamp(SCREAMING_SNAKE_CASE__   ,min=1E-20))
									__lowerCamelCase				:				Dict					       = torch.exp(0.5 * variance)
								elif variance_type == "learned_range":
									# NOTE difference with DDPM scheduler
									__lowerCamelCase				:				List[Any]					       = variance.log()
									__lowerCamelCase				:				List[str]					       = beta.log()

									__lowerCamelCase				:				str					       = (predicted_variance + 1) / 2
									__lowerCamelCase				:				Tuple					       = frac * max_log + (1 - frac) * min_log

								return variance
							def     lowerCAmelCase     (		self		:			Union[str, Any]   ,SCREAMING_SNAKE_CASE__		:			torch.FloatTensor   ,SCREAMING_SNAKE_CASE__		:			int   ,SCREAMING_SNAKE_CASE__		:			torch.FloatTensor   ,SCREAMING_SNAKE_CASE__		:			Optional[int] = None   ,SCREAMING_SNAKE_CASE__		:			Tuple=None   ,SCREAMING_SNAKE_CASE__		:			bool = True   ,):
								__lowerCamelCase				:				Union[str, Any]					       = timestep

								if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
									__lowerCamelCase       , __lowerCamelCase				:				Optional[Any]					       = torch.split(SCREAMING_SNAKE_CASE__   ,sample.shape[1]   ,dim=1)
								else:
									__lowerCamelCase				:				str					       = None

								# 1. compute alphas, betas
								if prev_timestep is None:
									__lowerCamelCase				:				int					       = t - 1

								__lowerCamelCase				:				str					       = self.alphas_cumprod[t]
								__lowerCamelCase				:				List[str]					       = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
								__lowerCamelCase				:				List[str]					       = 1 - alpha_prod_t
								__lowerCamelCase				:				Tuple					       = 1 - alpha_prod_t_prev

								if prev_timestep == t - 1:
									__lowerCamelCase				:				str					       = self.betas[t]
									__lowerCamelCase				:				Union[str, Any]					       = self.alphas[t]
								else:
									__lowerCamelCase				:				Dict					       = 1 - alpha_prod_t / alpha_prod_t_prev
									__lowerCamelCase				:				Optional[Any]					       = 1 - beta

								# 2. compute predicted original sample from predicted noise also called
								# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
								if self.config.prediction_type == "epsilon":
									__lowerCamelCase				:				List[str]					       = (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
								elif self.config.prediction_type == "sample":
									__lowerCamelCase				:				Tuple					       = model_output
								else:
									raise ValueError(
									    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"
									    ' for the UnCLIPScheduler.')

								# 3. Clip "predicted x_0"
								if self.config.clip_sample:
									__lowerCamelCase				:				Tuple					       = torch.clamp(
									    SCREAMING_SNAKE_CASE__   ,-self.config.clip_sample_range   ,self.config.clip_sample_range)

								# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
								# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
								__lowerCamelCase				:				Optional[int]					       = (alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
								__lowerCamelCase				:				List[Any]					       = alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

								# 5. Compute predicted previous sample µ_t
								# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
								__lowerCamelCase				:				List[str]					       = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

								# 6. Add noise
								__lowerCamelCase				:				Tuple					       = 0
								if t > 0:
									__lowerCamelCase				:				List[str]					       = randn_tensor(
									    model_output.shape   ,dtype=model_output.dtype   ,generator=SCREAMING_SNAKE_CASE__   ,device=model_output.device)

									__lowerCamelCase				:				Dict					       = self._get_variance(
									    SCREAMING_SNAKE_CASE__   ,predicted_variance=SCREAMING_SNAKE_CASE__   ,prev_timestep=SCREAMING_SNAKE_CASE__   ,)

									if self.variance_type == "fixed_small_log":
										__lowerCamelCase				:				List[Any]					       = variance
									elif self.variance_type == "learned_range":
										__lowerCamelCase				:				Optional[int]					       = (0.5 * variance).exp()
									else:
										raise ValueError(
										    F"variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"
										    ' for the UnCLIPScheduler.')

									__lowerCamelCase				:				Union[str, Any]					       = variance * variance_noise

								__lowerCamelCase				:				Dict					       = pred_prev_sample + variance

								if not return_dict:
									return (pred_prev_sample,)

								return UnCLIPSchedulerOutput(prev_sample=SCREAMING_SNAKE_CASE__   ,pred_original_sample=SCREAMING_SNAKE_CASE__)


							def     lowerCAmelCase     (		self		:			Tuple   ,SCREAMING_SNAKE_CASE__		:			torch.FloatTensor   ,SCREAMING_SNAKE_CASE__		:			torch.FloatTensor   ,SCREAMING_SNAKE_CASE__		:			torch.IntTensor   ,):
								# Make sure alphas_cumprod and timestep have same device and dtype as original_samples
								__lowerCamelCase				:				List[Any]					       = self.alphas_cumprod.to(device=original_samples.device   ,dtype=original_samples.dtype)
								__lowerCamelCase				:				Optional[int]					       = timesteps.to(original_samples.device)

								__lowerCamelCase				:				Tuple					       = alphas_cumprod[timesteps] ** 0.5
								__lowerCamelCase				:				Dict					       = sqrt_alpha_prod.flatten()
								while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
									__lowerCamelCase				:				int					       = sqrt_alpha_prod.unsqueeze(-1)

								__lowerCamelCase				:				Any					       = (1 - alphas_cumprod[timesteps]) ** 0.5
								__lowerCamelCase				:				Dict					       = sqrt_one_minus_alpha_prod.flatten()
								while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
									__lowerCamelCase				:				Optional[int]					       = sqrt_one_minus_alpha_prod.unsqueeze(-1)

								__lowerCamelCase				:				Optional[int]					       = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
								return noisy_samples











"""simple docstring"""
def      __lowerCamelCase   (							a_     :		Union[str, Any]							)			->      Optional[int]:
      __SCREAMING_SNAKE_CASE   :List[str]						=  1
      __SCREAMING_SNAKE_CASE   :Dict						=  2
      while i * i <= n:
            __SCREAMING_SNAKE_CASE   :Tuple						=  0
            while n % i == 0:
                  n //= i
                  multiplicity += 1
            n_divisors *= multiplicity + 1
            i += 1
      if n > 1:
            n_divisors *= 2
      return n_divisors



def      __lowerCamelCase   (							)			->      int:
      __SCREAMING_SNAKE_CASE   :Dict						=  1
      __SCREAMING_SNAKE_CASE   :Dict						=  1

      while True:
            i += 1
            t_num += i

            if count_divisors(a_							) > 5_00:
                  break

      return t_num


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