


'''simple docstring'''

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
class 						__lowerCAmelCase		(lowercase_  ):





      '''simple docstring'''






      lowerCAmelCase__      :  torch.FloatTensor
      lowerCAmelCase__      :  torch.FloatTensor






def _SCREAMING_SNAKE_CASE   (A						,				A=0.999						,				A="cosine"						,				) -> Dict:






       """simple docstring"""







       if alpha_transform_type == "cosine":

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

       elif alpha_transform_type == "exp":

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

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

       lowercase__       =				[]
       for i in range(A ):
              lowercase__       =				i / num_diffusion_timesteps
              lowercase__       =				(i + 1) / num_diffusion_timesteps
              betas.append(min(1 - alpha_bar_fn(A ) / alpha_bar_fn(A )						,				A ) )
       return torch.tensor(A						,				dtype=torch.floataa )

class 						__lowerCAmelCase		(lowercase_						,  lowercase_  ):





      '''simple docstring'''






      lowerCAmelCase__      :  List[str]						      =							1



      @register_to_config
      def __init__(self					:					Tuple     ,		UpperCamelCase					:					int = 1000     ,		UpperCamelCase					:					float = 0.00_01     ,		UpperCamelCase					:					float = 0.02     ,		UpperCamelCase					:					str = "linear"     ,		UpperCamelCase					:					float = 0.0     ,		UpperCamelCase					:					Optional[np.ndarray] = None     ,		UpperCamelCase					:					bool = True     ,		):

             '''simple docstring'''







             if trained_betas is not None:
                    lowercase__       =				torch.from_numpy(UpperCamelCase				)
             elif beta_schedule == "linear":
                    lowercase__       =				torch.linspace(UpperCamelCase     ,		UpperCamelCase     ,		UpperCamelCase     ,		dtype=torch.floataa				)
             elif beta_schedule == "scaled_linear":
                    # this schedule is very specific to the latent diffusion model.
                    lowercase__       =				(
                        torch.linspace(beta_start**0.5     ,		beta_end**0.5     ,		UpperCamelCase     ,		dtype=torch.floataa				) ** 2
                    )
             elif beta_schedule == "squaredcos_cap_v2":
                    # Glide cosine schedule
                    lowercase__       =				betas_for_alpha_bar(UpperCamelCase				)
             elif beta_schedule == "sigmoid":
                    # GeoDiff sigmoid schedule
                    lowercase__       =				torch.linspace(-6     ,		6     ,		UpperCamelCase				)
                    lowercase__       =				torch.sigmoid(UpperCamelCase				) * (beta_end - beta_start) + beta_start
             else:
                    raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}"				)

             lowercase__       =				1.0 - self.betas
             lowercase__       =				torch.cumprod(self.alphas     ,		dim=0				)
             lowercase__       =				torch.tensor(1.0				)

             lowercase__       =				torch.tensor(1.0				)

             # standard deviation of the initial noise distribution
             lowercase__       =				1.0

             # setable values
             lowercase__       =				None
             lowercase__       =				torch.from_numpy(np.arange(0     ,		UpperCamelCase				)[::-1].copy()				)

             lowercase__       =				eta



      def    UpperCamelCase__	(self					:					int     ,		UpperCamelCase					:					torch.FloatTensor     ,		UpperCamelCase					:					Optional[int] = None				):

             '''simple docstring'''







             return sample



      def    UpperCamelCase__	(self					:					str     ,		UpperCamelCase					:					int     ,		UpperCamelCase					:					int = 10     ,		UpperCamelCase					:					int = 10     ,		UpperCamelCase					:					Union[str, torch.device] = None     ,		):

             '''simple docstring'''







             lowercase__       =				min(self.config.num_train_timesteps     ,		UpperCamelCase				)
             lowercase__       =				num_inference_steps

             lowercase__       =				[]

             lowercase__       =				{}
             for j in range(0     ,		num_inference_steps - jump_length     ,		UpperCamelCase				):
                    lowercase__       =				jump_n_sample - 1

             lowercase__       =				num_inference_steps
             while t >= 1:
                    lowercase__       =				t - 1
                    timesteps.append(UpperCamelCase				)

                    if jumps.get(UpperCamelCase     ,		0				) > 0:
                           lowercase__       =				jumps[t] - 1
                           for _ in range(UpperCamelCase				):
                                  lowercase__       =				t + 1
                                  timesteps.append(UpperCamelCase				)

             lowercase__       =				np.array(UpperCamelCase				) * (self.config.num_train_timesteps // self.num_inference_steps)
             lowercase__       =				torch.from_numpy(UpperCamelCase				).to(UpperCamelCase				)



      def    UpperCamelCase__	(self					:					str     ,		UpperCamelCase					:					Optional[int]				):

             '''simple docstring'''







             lowercase__       =				t - self.config.num_train_timesteps // self.num_inference_steps

             lowercase__       =				self.alphas_cumprod[t]
             lowercase__       =				self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
             lowercase__       =				1 - alpha_prod_t
             lowercase__       =				1 - 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
             # Is equivalent to formula (16) in https://arxiv.org/pdf/2010.02502.pdf
             # without eta.
             # variance = (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * self.betas[t]
             lowercase__       =				(beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

             return variance



      def    UpperCamelCase__	(self					:					int     ,		UpperCamelCase					:					torch.FloatTensor     ,		UpperCamelCase					:					int     ,		UpperCamelCase					:					torch.FloatTensor     ,		UpperCamelCase					:					torch.FloatTensor     ,		UpperCamelCase					:					torch.FloatTensor     ,		UpperCamelCase					:					Optional[torch.Generator] = None     ,		UpperCamelCase					:					bool = True     ,		):

             '''simple docstring'''







             lowercase__       =				timestep
             lowercase__       =				timestep - self.config.num_train_timesteps // self.num_inference_steps

             # 1. compute alphas, betas
             lowercase__       =				self.alphas_cumprod[t]
             lowercase__       =				self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
             lowercase__       =				1 - alpha_prod_t

             # 2. compute predicted original sample from predicted noise also called
             # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
             lowercase__       =				(sample - beta_prod_t**0.5 * model_output) / alpha_prod_t**0.5

             # 3. Clip "predicted x_0"
             if self.config.clip_sample:
                    lowercase__       =				torch.clamp(UpperCamelCase     ,		-1     ,		1				)

             # We choose to follow RePaint Algorithm 1 to get x_{t-1}, however we
             # substitute formula (7) in the algorithm coming from DDPM paper
             # (formula (4) Algorithm 2 - Sampling) with formula (12) from DDIM paper.
             # DDIM schedule gives the same results as DDPM with eta = 1.0
             # Noise is being reused in 7. and 8., but no impact on quality has
             # been observed.

             # 5. Add noise
             lowercase__       =				model_output.device
             lowercase__       =				randn_tensor(model_output.shape     ,		generator=UpperCamelCase     ,		device=UpperCamelCase     ,		dtype=model_output.dtype				)
             lowercase__       =				self.eta * self._get_variance(UpperCamelCase				) ** 0.5

             lowercase__       =				0
             if t > 0 and self.eta > 0:
                    lowercase__       =				std_dev_t * noise

             # 6. compute "direction pointing to x_t" of formula (12)
             # from https://arxiv.org/pdf/2010.02502.pdf
             lowercase__       =				(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

             # 7. compute x_{t-1} of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
             lowercase__       =				alpha_prod_t_prev**0.5 * pred_original_sample + pred_sample_direction + variance

             # 8. Algorithm 1 Line 5 https://arxiv.org/pdf/2201.09865.pdf
             lowercase__       =				(alpha_prod_t_prev**0.5) * original_image + ((1 - alpha_prod_t_prev) ** 0.5) * noise

             # 9. Algorithm 1 Line 8 https://arxiv.org/pdf/2201.09865.pdf
             lowercase__       =				mask * prev_known_part + (1.0 - mask) * prev_unknown_part

             if not return_dict:
                    return (
                        pred_prev_sample,
                        pred_original_sample,
                    )

             return RePaintSchedulerOutput(prev_sample=UpperCamelCase     ,		pred_original_sample=UpperCamelCase				)



      def    UpperCamelCase__	(self					:					Tuple     ,		UpperCamelCase					:					int     ,		UpperCamelCase					:					Any     ,		UpperCamelCase					:					List[str]=None				):

             '''simple docstring'''







             lowercase__       =				self.config.num_train_timesteps // self.num_inference_steps

             for i in range(UpperCamelCase				):
                    lowercase__       =				self.betas[timestep + i]
                    if sample.device.type == "mps":
                           # randn does not work reproducibly on mps
                           lowercase__       =				randn_tensor(sample.shape     ,		dtype=sample.dtype     ,		generator=UpperCamelCase				)
                           lowercase__       =				noise.to(sample.device				)
                    else:
                           lowercase__       =				randn_tensor(sample.shape     ,		generator=UpperCamelCase     ,		device=sample.device     ,		dtype=sample.dtype				)

                    # 10. Algorithm 1 Line 10 https://arxiv.org/pdf/2201.09865.pdf
                    lowercase__       =				(1 - beta) ** 0.5 * sample + beta**0.5 * noise

             return sample



      def    UpperCamelCase__	(self					:					str     ,		UpperCamelCase					:					torch.FloatTensor     ,		UpperCamelCase					:					torch.FloatTensor     ,		UpperCamelCase					:					torch.IntTensor     ,		):

             '''simple docstring'''







             raise NotImplementedError('''Use `DDPMScheduler.add_noise()` to train for sampling with RePaint.'''				)






      def __len__(self					:					Dict				):

             '''simple docstring'''







             return self.config.num_train_timesteps








'''simple docstring'''

from __future__ import annotations

from collections import Counter

def _SCREAMING_SNAKE_CASE   (A ) -> list[int]:






       """simple docstring"""







       lowercase__       =				[True] * n
       lowercase__       =				False
       lowercase__       =				False
       lowercase__       =				True

       for i in range(3						,				int(n**0.5 + 1 )						,				2 ):
              lowercase__       =				i * 2
              while index < n:
                     lowercase__       =				False
                     lowercase__       =				index + i

       lowercase__       =				[2]

       for i in range(3						,				A						,				2 ):
              if is_prime[i]:
                     primes.append(A )

       return primes

def _SCREAMING_SNAKE_CASE   (A ) -> list[list[int]]:






       """simple docstring"""







       lowercase__       =				str(A )
       lowercase__       =				[]
       lowercase__       =				['''0''', '''1''', '''2''', '''3''', '''4''', '''5''', '''6''', '''7''', '''8''', '''9''']

       for duplicate in Counter(A ) - Counter(set(A ) ):
              lowercase__       =				[int(number_str.replace(A						,				A ) ) for digit in digits]
              replacements.append(A )

       return replacements

def _SCREAMING_SNAKE_CASE   (A = 8 ) -> int:






       """simple docstring"""







       lowercase__       =				set()

       # Filter primes with less than 3 replaceable digits
       lowercase__       =				{
           x for x in set(prime_sieve(1_000_000 ) ) if len(str(A ) ) - len(set(str(A ) ) ) >= 3
       }

       for prime in primes:
              if prime in numbers_checked:
                     continue

              lowercase__       =				digit_replacements(A )

              for family in replacements:
                     numbers_checked.update(A )
                     lowercase__       =				primes.intersection(A )

                     if len(A ) != family_length:
                            continue

                     return min(A )

       return -1


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




