




def 		a_       (   __lowerCAmelCase = 10_00							):
  lowerCAmelCase__								=			0
  lowerCAmelCase__								=			0
  while 1:
    num += 3
    if num >= n:
      break
    total += num
    num += 2
    if num >= n:
      break
    total += num
    num += 1
    if num >= n:
      break
    total += num
    num += 3
    if num >= n:
      break
    total += num
    num += 1
    if num >= n:
      break
    total += num
    num += 2
    if num >= n:
      break
    total += num
    num += 3
    if num >= n:
      break
    total += num
  return total


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







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

import flax
import jax.numpy as jnp
from scipy import integrate

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





@flax.struct.dataclass
class 						SCREAMING_SNAKE_CASE__		:
     lowercase_   :			CommonSchedulerState

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

     # running values
     lowercase_   :			Optional[jnp.ndarray]   =   None
     @classmethod
     def 					A__			(	cls  :		List[str]					,	__lowerCamelCase  :		CommonSchedulerState					,	__lowerCamelCase  :		jnp.ndarray					,	__lowerCamelCase  :		jnp.ndarray					,	__lowerCamelCase  :		jnp.ndarray	):



       """simple docstring"""
       return cls(common=__lowerCamelCase					,	init_noise_sigma=__lowerCamelCase					,	timesteps=__lowerCamelCase					,	sigmas=__lowerCamelCase	)





@dataclass
class 						SCREAMING_SNAKE_CASE__		(_a ):
     lowercase_   :			LMSDiscreteSchedulerState





class 						SCREAMING_SNAKE_CASE__		(_a						,				_a ):
     lowercase_   :			int   =   [e.name for e in FlaxKarrasDiffusionSchedulers]

     lowercase_   :			jnp.dtype
     @property
     def 					A__			(	self  :		Optional[Any]	):



       """simple docstring"""
       return True
     @register_to_config
     def __init__(	self  :		int					,	__lowerCamelCase  :		int = 10_00					,	__lowerCamelCase  :		float = 0.0001					,	__lowerCamelCase  :		float = 0.02					,	__lowerCamelCase  :		str = "linear"					,	__lowerCamelCase  :		Optional[jnp.ndarray] = None					,	__lowerCamelCase  :		str = "epsilon"					,	__lowerCamelCase  :		jnp.dtype = jnp.floataa					,	):



       """simple docstring"""
       lowerCAmelCase__								=			dtype
     def 					A__			(	self  :		List[str]					,	__lowerCamelCase  :		Optional[CommonSchedulerState] = None	):



       """simple docstring"""
       if common is None:
         lowerCAmelCase__								=			CommonSchedulerState.create(self	)

       lowerCAmelCase__								=			jnp.arange(0					,	self.config.num_train_timesteps	).round()[::-1]
       lowerCAmelCase__								=			((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5

       # standard deviation of the initial noise distribution
       lowerCAmelCase__								=			sigmas.max()

       return LMSDiscreteSchedulerState.create(
           common=__lowerCamelCase					,	init_noise_sigma=__lowerCamelCase					,	timesteps=__lowerCamelCase					,	sigmas=__lowerCamelCase					,	)
     def 					A__			(	self  :		str					,	__lowerCamelCase  :		LMSDiscreteSchedulerState					,	__lowerCamelCase  :		jnp.ndarray					,	__lowerCamelCase  :		int	):



       """simple docstring"""
       ((lowerCAmelCase__)							,			)								=			jnp.where(state.timesteps == timestep					,	size=1	)
       lowerCAmelCase__								=			step_index[0]

       lowerCAmelCase__								=			state.sigmas[step_index]
       lowerCAmelCase__								=			sample / ((sigma**2 + 1) ** 0.5)
       return sample
     def 					A__			(	self  :		List[Any]					,	__lowerCamelCase  :		LMSDiscreteSchedulerState					,	__lowerCamelCase  :		Optional[int]					,	__lowerCamelCase  :		str					,	__lowerCamelCase  :		Any	):



       """simple docstring"""

       def lms_derivative(__lowerCamelCase  :		int	):
         lowerCAmelCase__								=			1.0
         for k in range(__lowerCamelCase	):
           if current_order == k:
             continue
           prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
         return prod

       lowerCAmelCase__								=			integrate.quad(__lowerCamelCase					,	state.sigmas[t]					,	state.sigmas[t + 1]					,	epsrel=1e-4	)[0]

       return integrated_coeff
     def 					A__			(	self  :		str					,	__lowerCamelCase  :		LMSDiscreteSchedulerState					,	__lowerCamelCase  :		int					,	__lowerCamelCase  :		Tuple = ()	):



       """simple docstring"""
       lowerCAmelCase__								=			jnp.linspace(self.config.num_train_timesteps - 1					,	0					,	__lowerCamelCase					,	dtype=self.dtype	)

       lowerCAmelCase__								=			jnp.floor(__lowerCamelCase	).astype(jnp.intaa	)
       lowerCAmelCase__								=			jnp.ceil(__lowerCamelCase	).astype(jnp.intaa	)

       lowerCAmelCase__								=			jnp.mod(__lowerCamelCase					,	1.0	)

       lowerCAmelCase__								=			((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
       lowerCAmelCase__								=			(1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
       lowerCAmelCase__								=			jnp.concatenate([sigmas, jnp.array([0.0]					,	dtype=self.dtype	)]	)

       lowerCAmelCase__								=			timesteps.astype(jnp.intaa	)

       # initial running values
       lowerCAmelCase__								=			jnp.zeros((0,) + shape					,	dtype=self.dtype	)

       return state.replace(
           timesteps=__lowerCamelCase					,	sigmas=__lowerCamelCase					,	num_inference_steps=__lowerCamelCase					,	derivatives=__lowerCamelCase					,	)
     def 					A__			(	self  :		Union[str, Any]					,	__lowerCamelCase  :		LMSDiscreteSchedulerState					,	__lowerCamelCase  :		jnp.ndarray					,	__lowerCamelCase  :		int					,	__lowerCamelCase  :		jnp.ndarray					,	__lowerCamelCase  :		int = 4					,	__lowerCamelCase  :		bool = True					,	):



       """simple docstring"""
       if state.num_inference_steps is None:
         raise ValueError(
             '''Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler'''	)

       lowerCAmelCase__								=			state.sigmas[timestep]

       # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
       if self.config.prediction_type == "epsilon":
         lowerCAmelCase__								=			sample - sigma * model_output
       elif self.config.prediction_type == "v_prediction":
         # * c_out + input * c_skip
         lowerCAmelCase__								=			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
       else:
         raise ValueError(
             F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"""	)

       # 2. Convert to an ODE derivative
       lowerCAmelCase__								=			(sample - pred_original_sample) / sigma
       lowerCAmelCase__								=			state.replace(derivatives=jnp.append(state.derivatives					,	__lowerCamelCase	)	)
       if len(state.derivatives	) > order:
         lowerCAmelCase__								=			state.replace(derivatives=jnp.delete(state.derivatives					,	0	)	)

       # 3. Compute linear multistep coefficients
       lowerCAmelCase__								=			min(timestep + 1					,	__lowerCamelCase	)
       lowerCAmelCase__								=			[self.get_lms_coefficient(__lowerCamelCase					,	__lowerCamelCase					,	__lowerCamelCase					,	__lowerCamelCase	) for curr_order in range(__lowerCamelCase	)]

       # 4. Compute previous sample based on the derivatives path
       lowerCAmelCase__								=			sample + sum(
           coeff * derivative for coeff, derivative in zip(__lowerCamelCase					,	reversed(state.derivatives	)	)	)

       if not return_dict:
         return (prev_sample, state)

       return FlaxLMSSchedulerOutput(prev_sample=__lowerCamelCase					,	state=__lowerCamelCase	)
     def 					A__			(	self  :		Dict					,	__lowerCamelCase  :		LMSDiscreteSchedulerState					,	__lowerCamelCase  :		jnp.ndarray					,	__lowerCamelCase  :		jnp.ndarray					,	__lowerCamelCase  :		jnp.ndarray					,	):



       """simple docstring"""
       lowerCAmelCase__								=			state.sigmas[timesteps].flatten()
       lowerCAmelCase__								=			broadcast_to_shape_from_left(__lowerCamelCase					,	noise.shape	)

       lowerCAmelCase__								=			original_samples + noise * sigma

       return noisy_samples



     def __len__(	self  :		str	):



       """simple docstring"""
       return self.config.num_train_timesteps

