
'''simple docstring'''


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

import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin, SchedulerOutput

@dataclass
class 		__lowercase (     _lowerCAmelCase			):
			lowerCamelCase	:						torch.FloatTensor
			lowerCamelCase	:						torch.FloatTensor

class 		__lowercase (     _lowerCAmelCase					,   _lowerCAmelCase			):
			lowerCamelCase	:						List[str]							=	1

			@register_to_config
			def __init__(self	,      A = 2_0_0_0	,      A = 0.15	,      A = 0.01	,      A = 1_3_4_8.0	,      A = 1E-5	,      A = 1	,      ):
								lowerCamelCase_    :					Any   =						sigma_max

								# setable values
								lowerCamelCase_    :					Optional[int]   =						None

								self.set_sigmas(_lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase	,      _lowerCamelCase					)

			def 				UpperCAmelCase__       (self	,      A	,      A = None					):
								return sample

			def 				UpperCAmelCase__       (self	,      A	,      A = None	,      A = None					):
								lowerCamelCase_    :					int   =						sampling_eps if sampling_eps is not None else self.config.sampling_eps

								lowerCamelCase_    :					Dict   =						torch.linspace(1	,      _lowerCamelCase	,      _lowerCamelCase	,      device=_lowerCamelCase					)

			def 				UpperCAmelCase__       (self	,      A	,      A = None	,      A = None	,      A = None					):
								lowerCamelCase_    :					Any   =						sigma_min if sigma_min is not None else self.config.sigma_min
								lowerCamelCase_    :					Dict   =						sigma_max if sigma_max is not None else self.config.sigma_max
								lowerCamelCase_    :					Optional[int]   =						sampling_eps if sampling_eps is not None else self.config.sampling_eps
								if self.timesteps is None:
													self.set_timesteps(_lowerCamelCase	,      _lowerCamelCase					)

								lowerCamelCase_    :					Dict   =						sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps)
								lowerCamelCase_    :					Tuple   =						torch.exp(torch.linspace(math.log(_lowerCamelCase					)	,      math.log(_lowerCamelCase					)	,      _lowerCamelCase					)					)
								lowerCamelCase_    :					Optional[Any]   =						torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]					)

			def 				UpperCAmelCase__       (self	,      A	,      A					):
								return torch.where(
								    timesteps == 0	,      torch.zeros_like(t.to(timesteps.device					)					)	,      self.discrete_sigmas[timesteps - 1].to(timesteps.device					)	,      )

			def 				UpperCAmelCase__       (self	,      A	,      A	,      A	,      A = None	,      A = True	,      ):
								if self.timesteps is None:
													raise ValueError(
													    '''`self.timesteps` is not set, you need to run \'set_timesteps\' after creating the scheduler'''					)

								lowerCamelCase_    :					Union[str, Any]   =						timestep * torch.ones(
								    sample.shape[0]	,      device=sample.device					)  # torch.repeat_interleave(timestep, sample.shape[0])
								lowerCamelCase_    :					Any   =						(timestep * (len(self.timesteps					) - 1)).long()

								# mps requires indices to be in the same device, so we use cpu as is the default with cuda
								lowerCamelCase_    :					List[str]   =						timesteps.to(self.discrete_sigmas.device					)

								lowerCamelCase_    :					str   =						self.discrete_sigmas[timesteps].to(sample.device					)
								lowerCamelCase_    :					Optional[int]   =						self.get_adjacent_sigma(_lowerCamelCase	,      _lowerCamelCase					).to(sample.device					)
								lowerCamelCase_    :					int   =						torch.zeros_like(_lowerCamelCase					)
								lowerCamelCase_    :					str   =						(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
								lowerCamelCase_    :					int   =						diffusion.flatten()
								while len(diffusion.shape					) < len(sample.shape					):
													lowerCamelCase_    :					List[str]   =						diffusion.unsqueeze(-1					)
								lowerCamelCase_    :					Tuple   =						drift - diffusion**2 * model_output

								#  equation 6: sample noise for the diffusion term of
								lowerCamelCase_    :					Optional[int]   =						randn_tensor(
								    sample.shape	,      layout=sample.layout	,      generator=_lowerCamelCase	,      device=sample.device	,      dtype=sample.dtype					)
								lowerCamelCase_    :					Optional[int]   =						sample - drift  # subtract because `dt` is a small negative timestep
								# TODO is the variable diffusion the correct scaling term for the noise?
								lowerCamelCase_    :					Union[str, Any]   =						prev_sample_mean + diffusion * noise  # add impact of diffusion field g

								if not return_dict:
													return (prev_sample, prev_sample_mean)

								return SdeVeOutput(prev_sample=_lowerCamelCase	,      prev_sample_mean=_lowerCamelCase					)

			def 				UpperCAmelCase__       (self	,      A	,      A	,      A = None	,      A = True	,      ):
								if self.timesteps is None:
													raise ValueError(
													    '''`self.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
								lowerCamelCase_    :					Optional[Any]   =						randn_tensor(sample.shape	,      layout=sample.layout	,      generator=_lowerCamelCase					).to(sample.device					)

								# compute step size from the model_output, the noise, and the snr
								lowerCamelCase_    :					Any   =						torch.norm(model_output.reshape(model_output.shape[0]	,      -1					)	,      dim=-1					).mean()
								lowerCamelCase_    :					Optional[Any]   =						torch.norm(noise.reshape(noise.shape[0]	,      -1					)	,      dim=-1					).mean()
								lowerCamelCase_    :					Union[str, Any]   =						(self.config.snr * noise_norm / grad_norm) ** 2 * 2
								lowerCamelCase_    :					Optional[int]   =						step_size * torch.ones(sample.shape[0]					).to(sample.device					)
								# self.repeat_scalar(step_size, sample.shape[0])

								# compute corrected sample: model_output term and noise term
								lowerCamelCase_    :					int   =						step_size.flatten()
								while len(step_size.shape					) < len(sample.shape					):
													lowerCamelCase_    :					Dict   =						step_size.unsqueeze(-1					)
								lowerCamelCase_    :					Tuple   =						sample + step_size * model_output
								lowerCamelCase_    :					Any   =						prev_sample_mean + ((step_size * 2) ** 0.5) * noise

								if not return_dict:
													return (prev_sample,)

								return SchedulerOutput(prev_sample=_lowerCamelCase					)

			def 				UpperCAmelCase__       (self	,      A	,      A	,      A	,      ):
								lowerCamelCase_    :					Union[str, Any]   =						timesteps.to(original_samples.device					)
								lowerCamelCase_    :					List[Any]   =						self.discrete_sigmas.to(original_samples.device					)[timesteps]
								lowerCamelCase_    :					Union[str, Any]   =						(
								    noise * sigmas[:, None, None, None]
								    if noise is not None
								    else torch.randn_like(_lowerCamelCase					) * sigmas[:, None, None, None]
								)
								lowerCamelCase_    :					Optional[Any]   =						noise + original_samples
								return noisy_samples






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










"""simple docstring"""


from collections import defaultdict
from math import ceil, sqrt



def 					lowerCAmelCase				(    __UpperCamelCase = 1_0_0_0_0_0_0		,       __UpperCamelCase = 1_0 ):




  """simple docstring"""







  __A									= defaultdict(__UpperCamelCase )

  for outer_width in range(3		,       (t_limit // 4) + 2 ):
    if outer_width * outer_width > t_limit:
      __A									= max(
          ceil(sqrt(outer_width * outer_width - t_limit ) )		,       1 )
    else:
      __A									= 1

    hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

    for hole_width in range(__UpperCamelCase		,       outer_width - 1		,       2 ):
      count[outer_width * outer_width - hole_width * hole_width] += 1

  return sum(1 for n in count.values() if 1 <= n <= 1_0 )


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




