"""simple docstring"""





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 			_snake_case  :
						snake_case__      	=      42

						# setable values
						snake_case__      	=      42
						snake_case__      	=      42
						snake_case__      	=      None






						@classmethod
						def    lowerCamelCase__  (							cls   :      Union[str, Any]				,       UpperCAmelCase   :      CommonSchedulerState				,       UpperCAmelCase   :      jnp.ndarray				,       UpperCAmelCase   :      jnp.ndarray     ):
													return cls(common=A_				,       init_noise_sigma=A_				,       timesteps=A_     )

@dataclass
class 			_snake_case  (       a__		):
						snake_case__      	=      42

class 			_snake_case  (       a__					,			a__		):
						snake_case__      	=      [e.name for e in FlaxKarrasDiffusionSchedulers]

						snake_case__      	=      42






						@property
						def    lowerCamelCase__  (							self   :      str     ):
													return True






						@register_to_config
						def __init__(							self   :      str				,       UpperCAmelCase   :      int = 1000				,       UpperCAmelCase   :      float = 0.0_0_0_1				,       UpperCAmelCase   :      float = 0.0_2				,       UpperCAmelCase   :      str = "linear"				,       UpperCAmelCase   :      Optional[jnp.ndarray] = None				,       UpperCAmelCase   :      str = "fixed_small"				,       UpperCAmelCase   :      bool = True				,       UpperCAmelCase   :      str = "epsilon"				,       UpperCAmelCase   :      jnp.dtype = jnp.floataa				,       ):
													__lowerCamelCase       :		Dict		 =  dtype






						def    lowerCamelCase__  (							self   :      int				,       UpperCAmelCase   :      Optional[CommonSchedulerState] = None     ):
													if common is None:
																				__lowerCamelCase       :		int		 =  CommonSchedulerState.create(self     )

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

													__lowerCamelCase       :		Union[str, Any]		 =  jnp.arange(0				,       self.config.num_train_timesteps     ).round()[::-1]

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






						def    lowerCamelCase__  (							self   :      List[Any]				,       UpperCAmelCase   :      DDPMSchedulerState				,       UpperCAmelCase   :      jnp.ndarray				,       UpperCAmelCase   :      Optional[int] = None     ):
													return sample






						def    lowerCamelCase__  (							self   :      str				,       UpperCAmelCase   :      DDPMSchedulerState				,       UpperCAmelCase   :      int				,       UpperCAmelCase   :      Tuple = ()     ):
													__lowerCamelCase       :		Dict		 =  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
													__lowerCamelCase       :		Tuple		 =  (jnp.arange(0				,       A_     ) * step_ratio).round()[::-1]

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






						def    lowerCamelCase__  (							self   :      int				,       UpperCAmelCase   :      DDPMSchedulerState				,       UpperCAmelCase   :      List[str]				,       UpperCAmelCase   :      List[Any]=None				,       UpperCAmelCase   :      Optional[int]=None     ):
													__lowerCamelCase       :		Union[str, Any]		 =  state.common.alphas_cumprod[t]
													__lowerCamelCase       :		Optional[Any]		 =  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
													__lowerCamelCase       :		Optional[Any]		 =  (1 - alpha_prod_t_prev) / (1 - alpha_prod_t) * state.common.betas[t]

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

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

													return variance






						def    lowerCamelCase__  (							self   :      List[Any]				,       UpperCAmelCase   :      DDPMSchedulerState				,       UpperCAmelCase   :      jnp.ndarray				,       UpperCAmelCase   :      int				,       UpperCAmelCase   :      jnp.ndarray				,       UpperCAmelCase   :      Optional[jax.random.KeyArray] = None				,       UpperCAmelCase   :      bool = True				,       ):
													__lowerCamelCase       :		Dict		 =  timestep

													if key is None:
																				__lowerCamelCase       :		List[str]		 =  jax.random.PRNGKey(0     )

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

													# 1. compute alphas, betas
													__lowerCamelCase       :		int		 =  state.common.alphas_cumprod[t]
													__lowerCamelCase       :		Any		 =  jnp.where(t > 0				,       state.common.alphas_cumprod[t - 1]				,       jnp.array(1.0				,       dtype=self.dtype     )     )
													__lowerCamelCase       :		Dict		 =  1 - alpha_prod_t
													__lowerCamelCase       :		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":
																				__lowerCamelCase       :		Tuple		 =  (sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
													elif self.config.prediction_type == "sample":
																				__lowerCamelCase       :		List[str]		 =  model_output
													elif self.config.prediction_type == "v_prediction":
																				__lowerCamelCase       :		Any		 =  (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:
																				__lowerCamelCase       :		List[str]		 =  jnp.clip(A_				,       -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
													__lowerCamelCase       :		List[Any]		 =  (alpha_prod_t_prev ** 0.5 * state.common.betas[t]) / beta_prod_t
													__lowerCamelCase       :		Optional[int]		 =  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
													__lowerCamelCase       :		Any		 =  pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

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

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

													__lowerCamelCase       :		List[Any]		 =  pred_prev_sample + variance

													if not return_dict:
																				return (pred_prev_sample, state)

													return FlaxDDPMSchedulerOutput(prev_sample=A_				,       state=A_     )






						def    lowerCamelCase__  (							self   :      Union[str, Any]				,       UpperCAmelCase   :      DDPMSchedulerState				,       UpperCAmelCase   :      jnp.ndarray				,       UpperCAmelCase   :      jnp.ndarray				,       UpperCAmelCase   :      jnp.ndarray				,       ):
													return add_noise_common(state.common				,       A_				,       A_				,       A_     )






						def    lowerCamelCase__  (							self   :      Dict				,       UpperCAmelCase   :      DDPMSchedulerState				,       UpperCAmelCase   :      jnp.ndarray				,       UpperCAmelCase   :      jnp.ndarray				,       UpperCAmelCase   :      jnp.ndarray				,       ):
													return get_velocity_common(state.common				,       A_				,       A_				,       A_     )







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



"""simple docstring"""




def       a_ (	lowercase__ :int = 10**9     ):
			__lowerCamelCase          =      1
			__lowerCamelCase          =      2

			__lowerCamelCase          =      0
			__lowerCamelCase          =      0
			__lowerCamelCase          =      0
			while perimeter <= max_perimeter:
						perimeters_sum += perimeter

						prev_value += 2 * value
						value += prev_value

						__lowerCamelCase          =      2 * value + 2 if i % 2 == 0 else 2 * value - 2
						i += 1

			return perimeters_sum


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




