


'''simple docstring'''


def 		_lowercase   ():




     '''simple docstring'''





     for a in range(300       ):
          for b in range(a + 1					,				400       ):
               for c in range(b + 1					,				500       ):
                    if (a + b + c) == 1000 and (a**2) + (b**2) == (c**2):
                         return a * b * c

     return -1


def 		_lowercase   ():




     '''simple docstring'''





     for a in range(300       ):
          for b in range(400       ):
               __A  :					Optional[Any]						     =       1000 - a - b
               if a < b < c and (a**2) + (b**2) == (c**2):
                    return a * b * c

     return -1


def 		_lowercase   ():




     '''simple docstring'''





     import timeit

     print(
         timeit.timeit("solution()"					,				setup="from __main__ import solution"					,				number=1000       )       )
     print(
         timeit.timeit(
             "solution_fast()"					,				setup="from __main__ import solution_fast"					,				number=1000       )       )


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





'''simple docstring'''


# DISCLAIMER: This file is strongly influenced by https://github.com/yang-song/score_sde_pytorch

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

import flax
import jax.numpy as jnp
from jax import random

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import FlaxSchedulerMixin, FlaxSchedulerOutput, broadcast_to_shape_from_left







@flax.struct.dataclass
class        __magic_name__  :

     """simple docstring"""






     lowerCamelCase__						=							None
     lowerCamelCase__						=							None
     lowerCamelCase__						=							None


     @classmethod
     def lowerCAmelCase__     (      cls		):


          '''simple docstring'''





          return cls()







@dataclass
class        __magic_name__  (					lowerCAmelCase   ):

     """simple docstring"""






     lowerCamelCase__						=							42
     lowerCamelCase__						=							42
     lowerCamelCase__						=							None







class        __magic_name__  (					lowerCAmelCase						,		lowerCAmelCase   ):

     """simple docstring"""






     @property
     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          return True


     @register_to_config
     def __init__(      self ,    lowerCamelCase = 2000 ,    lowerCamelCase = 0.15 ,    lowerCamelCase = 0.01 ,    lowerCamelCase = 1348.0 ,    lowerCamelCase = 1E-5 ,    lowerCamelCase = 1 ,    ):


          '''simple docstring'''





          pass


     def lowerCAmelCase__     (      self		):


          '''simple docstring'''





          __A  :					List[Any]						     =       ScoreSdeVeSchedulerState.create()
          return self.set_sigmas(
              lowerCamelCase ,    self.config.num_train_timesteps ,    self.config.sigma_min ,    self.config.sigma_max ,    self.config.sampling_eps ,    )


     def lowerCAmelCase__     (      self ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase = () ,    lowerCamelCase = None		):


          '''simple docstring'''





          __A  :					Tuple						     =       sampling_eps if sampling_eps is not None else self.config.sampling_eps

          __A  :					Optional[int]						     =       jnp.linspace(1 ,    lowerCamelCase ,    lowerCamelCase		)
          return state.replace(timesteps=lowerCamelCase		)


     def lowerCAmelCase__     (      self ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase = None ,    lowerCamelCase = None ,    lowerCamelCase = None ,    ):


          '''simple docstring'''





          __A  :					str						     =       sigma_min if sigma_min is not None else self.config.sigma_min
          __A  :					Union[str, Any]						     =       sigma_max if sigma_max is not None else self.config.sigma_max
          __A  :					Dict						     =       sampling_eps if sampling_eps is not None else self.config.sampling_eps
          if state.timesteps is None:
               __A  :					Union[str, Any]						     =       self.set_timesteps(lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase		)

          __A  :					Dict						     =       jnp.exp(jnp.linspace(jnp.log(lowerCamelCase		) ,    jnp.log(lowerCamelCase		) ,    lowerCamelCase		)		)
          __A  :					int						     =       jnp.array([sigma_min * (sigma_max / sigma_min) ** t for t in state.timesteps]		)

          return state.replace(discrete_sigmas=lowerCamelCase ,    sigmas=lowerCamelCase		)


     def lowerCAmelCase__     (      self ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase		):


          '''simple docstring'''





          return jnp.where(timesteps == 0 ,    jnp.zeros_like(lowerCamelCase		) ,    state.discrete_sigmas[timesteps - 1]		)


     def lowerCAmelCase__     (      self ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase = True ,    ):


          '''simple docstring'''





          if state.timesteps is None:
               raise ValueError(
                   "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"		)

          __A  :					Any						     =       timestep * jnp.ones(
              sample.shape[0] ,    )
          __A  :					Any						     =       (timestep * (len(state.timesteps		) - 1)).long()

          __A  :					Any						     =       state.discrete_sigmas[timesteps]
          __A  :					Union[str, Any]						     =       self.get_adjacent_sigma(lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase		)
          __A  :					List[str]						     =       jnp.zeros_like(lowerCamelCase		)
          __A  :					Union[str, Any]						     =       (sigma**2 - adjacent_sigma**2) ** 0.5

          # equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x)
          # also equation 47 shows the analog from SDE models to ancestral sampling methods
          __A  :					List[Any]						     =       diffusion.flatten()
          __A  :					List[Any]						     =       broadcast_to_shape_from_left(lowerCamelCase ,    sample.shape		)
          __A  :					str						     =       drift - diffusion**2 * model_output

          #  equation 6: sample noise for the diffusion term of
          __A  :					Any						     =       random.split(lowerCamelCase ,    num=1		)
          __A  :					Union[str, Any]						     =       random.normal(key=lowerCamelCase ,    shape=sample.shape		)
          __A  :					Dict						     =       sample - drift  # subtract because `dt` is a small negative timestep
          # TODO is the variable diffusion the correct scaling term for the noise?
          __A  :					int						     =       prev_sample_mean + diffusion * noise  # add impact of diffusion field g

          if not return_dict:
               return (prev_sample, prev_sample_mean, state)

          return FlaxSdeVeOutput(prev_sample=lowerCamelCase ,    prev_sample_mean=lowerCamelCase ,    state=lowerCamelCase		)


     def lowerCAmelCase__     (      self ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase ,    lowerCamelCase = True ,    ):


          '''simple docstring'''





          if state.timesteps is None:
               raise ValueError(
                   "`state.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler"		)

          # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z"
          # sample noise for correction
          __A  :					int						     =       random.split(lowerCamelCase ,    num=1		)
          __A  :					int						     =       random.normal(key=lowerCamelCase ,    shape=sample.shape		)

          # compute step size from the model_output, the noise, and the snr
          __A  :					Optional[Any]						     =       jnp.linalg.norm(lowerCamelCase		)
          __A  :					Dict						     =       jnp.linalg.norm(lowerCamelCase		)
          __A  :					Any						     =       (self.config.snr * noise_norm / grad_norm) ** 2 * 2
          __A  :					List[str]						     =       step_size * jnp.ones(sample.shape[0]		)

          # compute corrected sample: model_output term and noise term
          __A  :					Optional[Any]						     =       step_size.flatten()
          __A  :					Optional[int]						     =       broadcast_to_shape_from_left(lowerCamelCase ,    sample.shape		)
          __A  :					Dict						     =       sample + step_size * model_output
          __A  :					List[Any]						     =       prev_sample_mean + ((step_size * 2) ** 0.5) * noise

          if not return_dict:
               return (prev_sample, state)

          return FlaxSdeVeOutput(prev_sample=lowerCamelCase ,    state=lowerCamelCase		)


     def __len__(      self		):


          '''simple docstring'''





          return self.config.num_train_timesteps

