




# DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim

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

import flax
import jax
import jax.numpy as jnp

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
    CommonSchedulerState,
    FlaxKarrasDiffusionSchedulers,
    FlaxSchedulerMixin,
    FlaxSchedulerOutput,
    add_noise_common,
    get_velocity_common,
)







@flax.struct.dataclass
class 				lowerCAmelCase_       :
				__a     :       CommonSchedulerState

				# setable values
				__a     :       jnp.ndarray
				__a     :       jnp.ndarray
				__a     :       Optional[int]						=     None






				@classmethod
				def 		snake_case	(			cls      ,snake_case__      ,snake_case__      ,snake_case__ ):
							return cls(common=snake_case__      ,init_noise_sigma=snake_case__      ,timesteps=snake_case__ )







@dataclass
class 				lowerCAmelCase_       (					lowerCamelCase_							):
				__a     :       DDPMSchedulerState







class 				lowerCAmelCase_       (					lowerCamelCase_						,     lowerCamelCase_							):
				__a     :       Tuple						=     [e.name for e in FlaxKarrasDiffusionSchedulers]

				__a     :       jnp.dtype






				@property
				def 		snake_case	(			self ):
							return True






				@register_to_config
				def __init__(			self      ,snake_case__ = 1000      ,snake_case__ = 0.0001      ,snake_case__ = 0.02      ,snake_case__ = "linear"      ,snake_case__ = None      ,snake_case__ = "fixed_small"      ,snake_case__ = True      ,snake_case__ = "epsilon"      ,snake_case__ = jnp.floataa      ,):
							SCREAMING_SNAKE_CASE_   : Any					  =      dtype






				def 		snake_case	(			self      ,snake_case__ = None ):
							if common is None:
										SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      CommonSchedulerState.create(self )

							# standard deviation of the initial noise distribution
							SCREAMING_SNAKE_CASE_   : Tuple					  =      jnp.array(1.0      ,dtype=self.dtype )

							SCREAMING_SNAKE_CASE_   : List[Any]					  =      jnp.arange(0      ,self.config.num_train_timesteps ).round()[::-1]

							return DDPMSchedulerState.create(
							    common=snake_case__      ,init_noise_sigma=snake_case__      ,timesteps=snake_case__      ,)






				def 		snake_case	(			self      ,snake_case__      ,snake_case__      ,snake_case__ = None ):
							return sample






				def 		snake_case	(			self      ,snake_case__      ,snake_case__      ,snake_case__ = () ):
							SCREAMING_SNAKE_CASE_   : Optional[int]					  =      self.config.num_train_timesteps // num_inference_steps
							# creates integer timesteps by multiplying by ratio
							# rounding to avoid issues when num_inference_step is power of 3
							SCREAMING_SNAKE_CASE_   : Optional[int]					  =      (jnp.arange(0      ,snake_case__ ) * step_ratio).round()[::-1]

							return state.replace(
							    num_inference_steps=snake_case__      ,timesteps=snake_case__      ,)






				def 		snake_case	(			self      ,snake_case__      ,snake_case__      ,snake_case__=None      ,snake_case__=None ):
							SCREAMING_SNAKE_CASE_   : List[str]					  =      state.common.alphas_cumprod[t]
							SCREAMING_SNAKE_CASE_   : int					  =      jnp.where(t > 0      ,state.common.alphas_cumprod[t - 1]      ,jnp.array(1.0      ,dtype=self.dtype ) )

							# 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
							SCREAMING_SNAKE_CASE_   : Dict					  =      (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

							if variance_type is None:
										SCREAMING_SNAKE_CASE_   : int					  =      self.config.variance_type

							# hacks - were probably added for training stability
							if variance_type == "fixed_small":
										SCREAMING_SNAKE_CASE_   : List[Any]					  =      jnp.clip(snake_case__      ,a_min=1E-20 )
							# for rl-diffuser https://arxiv.org/abs/2205.09991
							elif variance_type == "fixed_small_log":
										SCREAMING_SNAKE_CASE_   : str					  =      jnp.log(jnp.clip(snake_case__      ,a_min=1E-20 ) )
							elif variance_type == "fixed_large":
										SCREAMING_SNAKE_CASE_   : Any					  =      state.common.betas[t]
							elif variance_type == "fixed_large_log":
										# Glide max_log
										SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      jnp.log(state.common.betas[t] )
							elif variance_type == "learned":
										return predicted_variance
							elif variance_type == "learned_range":
										SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      variance
										SCREAMING_SNAKE_CASE_   : Tuple					  =      state.common.betas[t]
										SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      (predicted_variance + 1) / 2
										SCREAMING_SNAKE_CASE_   : List[Any]					  =      frac * max_log + (1 - frac) * min_log

							return variance






				def 		snake_case	(			self      ,snake_case__      ,snake_case__      ,snake_case__      ,snake_case__      ,snake_case__ = None      ,snake_case__ = True      ,):
							SCREAMING_SNAKE_CASE_   : int					  =      timestep

							if key is None:
										SCREAMING_SNAKE_CASE_   : int					  =      jax.random.PRNGKey(0 )

							if model_output.shape[1] == sample.shape[1] * 2 and self.config.variance_type in ["learned", "learned_range"]:
										SCREAMING_SNAKE_CASE_  ,    SCREAMING_SNAKE_CASE_   : Any					  =      jnp.split(snake_case__      ,sample.shape[1]      ,axis=1 )
							else:
										SCREAMING_SNAKE_CASE_   : List[str]					  =      None

							# 1. compute alphas, betas
							SCREAMING_SNAKE_CASE_   : List[Any]					  =      state.common.alphas_cumprod[t]
							SCREAMING_SNAKE_CASE_   : int					  =      jnp.where(t > 0      ,state.common.alphas_cumprod[t - 1]      ,jnp.array(1.0      ,dtype=self.dtype ) )
							SCREAMING_SNAKE_CASE_   : List[str]					  =      1 - alpha_prod_t
							SCREAMING_SNAKE_CASE_   : int					  =      1 - alpha_prod_t_prev

							# 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":
										SCREAMING_SNAKE_CASE_   : List[Any]					  =      (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
							elif self.config.prediction_type == "sample":
										SCREAMING_SNAKE_CASE_   : int					  =      model_output
							elif self.config.prediction_type == "v_prediction":
										SCREAMING_SNAKE_CASE_   : Optional[int]					  =      (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output
							else:
										raise ValueError(
										    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` '
										    ' for the FlaxDDPMScheduler.' )

							# 3. Clip "predicted x_0"
							if self.config.clip_sample:
										SCREAMING_SNAKE_CASE_   : Tuple					  =      jnp.clip(snake_case__      ,-1      ,1 )

							# 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
							SCREAMING_SNAKE_CASE_   : int					  =      (alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
							SCREAMING_SNAKE_CASE_   : Tuple					  =      state.common.alphas[t] ** 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
							SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

							# 6. Add noise
							def random_variance():
										SCREAMING_SNAKE_CASE_   : int					  =      jax.random.split(snake_case__      ,num=1 )
										SCREAMING_SNAKE_CASE_   : List[str]					  =      jax.random.normal(snake_case__      ,shape=model_output.shape      ,dtype=self.dtype )
										return (self._get_variance(snake_case__      ,snake_case__      ,predicted_variance=snake_case__ ) ** 0.5) * noise

							SCREAMING_SNAKE_CASE_   : Optional[int]					  =      jnp.where(t > 0      ,random_variance()      ,jnp.zeros(model_output.shape      ,dtype=self.dtype ) )

							SCREAMING_SNAKE_CASE_   : str					  =      pred_prev_sample + variance

							if not return_dict:
										return (pred_prev_sample, state)

							return FlaxDDPMSchedulerOutput(prev_sample=snake_case__      ,state=snake_case__ )






				def 		snake_case	(			self      ,snake_case__      ,snake_case__      ,snake_case__      ,snake_case__      ,):
							return add_noise_common(state.common      ,snake_case__      ,snake_case__      ,snake_case__ )






				def 		snake_case	(			self      ,snake_case__      ,snake_case__      ,snake_case__      ,snake_case__      ,):
							return get_velocity_common(state.common      ,snake_case__      ,snake_case__      ,snake_case__ )






				def __len__(			self ):
							return self.config.num_train_timesteps







from math import isqrt




def       a_ (       SCREAMING_SNAKE_CASE__   : int	):
       '''simple docstring'''





       _lowerCamelCase			:						Optional[int]            =[True] * max_number
       for i in range(2						,     isqrt(max_number - 1	) + 1	):
              if is_prime[i]:
                     for j in range(i**2						,     SCREAMING_SNAKE_CASE__						,     SCREAMING_SNAKE_CASE__	):
                            _lowerCamelCase			:						str            =False

       return [i for i in range(2						,     SCREAMING_SNAKE_CASE__	) if is_prime[i]]




def       a_ (       SCREAMING_SNAKE_CASE__   : int = 10**8	):
       '''simple docstring'''





       _lowerCamelCase			:						Union[str, Any]            =calculate_prime_numbers(max_number // 2	)

       _lowerCamelCase			:						Dict            =0
       _lowerCamelCase			:						int            =0
       _lowerCamelCase			:						Optional[Any]            =len(SCREAMING_SNAKE_CASE__	) - 1
       while left <= right:
              while prime_numbers[left] * prime_numbers[right] >= max_number:
                     right -= 1
              semiprimes_count += right - left + 1
              left += 1

       return semiprimes_count


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


